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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 08 Dec 2023 21:09:12 +0000Multirate time-stepping least squares shadowing method
https://resolver.caltech.edu/CaltechAUTHORS:20210322-151621646
Authors: Bae, H. J.; Moin, P.
Year: 2014
The recently developed least squares shadowing (LSS) method reformulates unsteady
turbulent flow simulations to be well-conditioned time-domain boundary-value problems.
We see from Wang et al. (2013) that the reformulation from LSS can enable scalable
parallel in-time simulation of turbulent flows. It utilizes the large number of processors in
high-performance machines in order to find a trajectory that satisfies the given governing
equation effectively by relaxing the initial condition. This method can speed up the wall
clock time of finding the solution by effectively parallelizing in the temporal domain as
well as the spatial domain. However, the traditional LSS method was limited by the
smallest time-step of the entire domain, and thus required solving of extremely large
block tri-diagonal systems.https://authors.library.caltech.edu/records/9kg9y-xxy62Numerical scale separation in large-eddy simulation
https://resolver.caltech.edu/CaltechAUTHORS:20210326-095748691
Authors: Verstappen, R. W. C. P.; Rozema, W.; Bae, H. J.
Year: 2014
Large-eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The essence of a scale-separation LES model is that it stops the nonlinear
production of smaller scales of motion at the scale set by the filter: there the modeled
eddy dissipation has to balance the production. Numerical discretization changes both
the nonlinear production and dissipation of sub-filter scales. Therefore, the discrete balance between production and dissipation can deviate from the continuous balance, in
particular if a balance is imposed near the scale set by the numerical grid. This paper
demonstrates that a scale-separation LES model should attain a production-dissipation
balance in the numerical setting. Eddy-viscosity models based on this requirement are
derived and successfully applied in simulations of decaying isotropic turbulence and channel flow.https://authors.library.caltech.edu/records/dds0a-cgz43A low-cost time-advancing strategy for energy-preserving turbulent simulations
https://resolver.caltech.edu/CaltechAUTHORS:20210325-145350953
Authors: Capuano, F.; Coppola, G.; Balarac, G.; Bae, H. J.; de Luca, L.
Year: 2014
Energy-conserving discretizations are widely regarded as a fundamental requirement
for high-fidelity simulations of turbulent flows. The skew-symmetric splitting of the non-
linear term is a well-known approach to obtain semi-discrete conservation of energy in
the inviscid limit. However, its computation is roughly twice as expensive as that of the
divergence or advective forms alone. A novel time-advancement strategy that retains the
conservation properties of skew-symmetric-based schemes at a reduced computational
cost has been developed. This method is based on properly constructed Runge-Kutta
schemes in which a different form (advective or divergence) for the convective term is
adopted at each stage. A general framework is presented to derive schemes with prescribed accuracy on both solution and energy conservation. Simulations of homogeneous
isotropic turbulence show that, on equal results, the new procedure can be considerably
faster than skew-symmetric-based techniques.https://authors.library.caltech.edu/records/fbeny-5mv56Minimum-dissipation models for large-eddy simulation
https://resolver.caltech.edu/CaltechAUTHORS:20210315-152246966
Authors: Rozema, Wybe; Bae, Hyun J.; Moin, Parviz; Verstappen, Roel
Year: 2015
DOI: 10.1063/1.4928700
Minimum-dissipation eddy-viscosity models are a class of sub-filter models for large-eddy simulation that give the minimum eddy dissipation required to dissipate the energy of sub-filter scales. A previously derived minimum-dissipation model is the QR model. This model is based on the invariants of the resolved rate-of-strain tensor and has many desirable properties. It appropriately switches off for laminar and transitional flows, has low computational complexity, and is consistent with the exact sub-filter tensor on isotropic grids. However, the QR model proposed in the literature gives insufficient eddy dissipation. It is demonstrated that this can be corrected by increasing the model constant. The corrected QR model gives good results in simulations of decaying grid turbulence on an isotropic grid. On anisotropic grids the QR model is not consistent with the exact sub-filter tensor and requires an approximation of the filter width. It is demonstrated that the results of the QR model on anisotropic grids are primarily determined by the used filter width approximation, and that no approximation gives satisfactory results in simulations of both a temporal mixing layer and turbulent channel flow. A new minimum-dissipation model for anisotropic grids is proposed. This anisotropic minimum-dissipation (AMD) model generalizes the desirable practical and theoretical properties of the QR model to anisotropic grids and does not require an approximation of the filter width. The AMD model is successfully applied in simulations of decaying grid turbulence on an isotropic grid and in simulations of a temporal mixing layer and turbulent channel flow on anisotropic grids.https://authors.library.caltech.edu/records/kefzd-2py54Turbulent channel with slip boundaries as a benchmark for subgrid-scale models in LES
https://resolver.caltech.edu/CaltechAUTHORS:20210317-083626390
Authors: Lozano-Durán, A.; Bae, H. J.
Year: 2016
PMCID: PMC6800701
Most turbulent flows cannot be calculated by direct numerical simulation (DNS) of the Navier-Stokes equations because the range of scales of motion is so large that the computational cost becomes prohibitive. In large-eddy simulations (LES), only the large eddies are resolved and the effect of the small scales on the larger ones is supplied through a subgrid-scale (SGS) model in order to overcome most of the computational cost. In this sense, the role of SGS models is to provide the missing large-scale Reynolds stresses that can not be resolved in coarser LES computational grids.https://authors.library.caltech.edu/records/wvb5f-apv75Investigation of the slip boundary condition in wall-modeled LES
https://resolver.caltech.edu/CaltechAUTHORS:20210315-143345631
Authors: Bae, H. J.; Lozano-Durán, A.; Moin, P.
Year: 2016
PMCID: PMC6800698
The near-wall resolution requirement to accurately resolve the boundary layer in wall-bounded flows remains one of the largest obstacles in large-eddy simulation (LES) of high-Reynolds-number engineering applications. Chapman (1979) estimated that the number of grid points necessary for a wall-resolved (WR) LES scales as N_(WR) ~ Re^(9/5), where Re is the characteristic Reynolds number of the problem. A more recent study by Choi & Moin (2012), using more accurate correlations for the skin friction coefficients, concluded that N_(WR) ~ Re^(13/7), which is far too expensive for many practical engineering applications and not very different from the N_(DNS) ~ Re^(37/14) scaling required for direct numerical simulation (DNS) where all the relevant scales of motion are resolved.https://authors.library.caltech.edu/records/e2td0-4w440Minimum-dissipation scalar transport model for large-eddy simulation of turbulent flows
https://resolver.caltech.edu/CaltechAUTHORS:20210315-142512722
Authors: Abkar, Mahdi; Bae, Hyun J.; Moin, Parviz
Year: 2016
DOI: 10.1103/physrevfluids.1.041701
Minimum-dissipation models are a simple alternative to the Smagorinsky-type approaches to parametrize the subfilter turbulent fluxes in large-eddy simulation. A recently derived model of this type for subfilter stress tensor is the anisotropic minimum-dissipation (AMD) model [Rozema et al., Phys. Fluids 27, 085107 (2015)], which has many desirable properties. It is more cost effective than the dynamic Smagorinsky model, it appropriately switches off in laminar and transitional flows, and it is consistent with the exact subfilter stress tensor on both isotropic and anisotropic grids. In this study, an extension of this approach to modeling the subfilter scalar flux is proposed. The performance of the AMD model is tested in the simulation of a high-Reynolds-number rough-wall boundary-layer flow with a constant and uniform surface scalar flux. The simulation results obtained from the AMD model show good agreement with well-established empirical correlations and theoretical predictions of the resolved flow statistics. In particular, the AMD model is capable of accurately predicting the expected surface-layer similarity profiles and power spectra for both velocity and scalar concentration.https://authors.library.caltech.edu/records/gazgn-mg645Exploring nonlinear subgrid-scale models and new characteristic length scales for large-eddy simulation
https://resolver.caltech.edu/CaltechAUTHORS:20210315-110422387
Authors: Silvis, M. H.; Trias, F. X.; Abkar, M.; Bae, H. J.; Lozano-Durán, A.; Verstappen, R. W. C. P.
Year: 2016
We study subgrid-scale modeling for large-eddy simulation of anisotropic turbulent flows on anisotropic grids.
In particular, we show how the addition of a velocity-gradient-based nonlinear model term to an eddy viscosity model provides a better representation of energy transfer.
This is shown to lead to improved predictions of rotating and nonrotating homogeneous isotropic turbulence.
%We furthermore show that spanwise-rotating turbulent plane-channel flows form a challenging test case for large-eddy simulation.
Our research further focuses on calculation of the subgrid characteristic length, a key element for any eddy viscosity model.
In the current work, we propose a new formulation of this quantity based on a Taylor series expansion of the subgrid stress tensor in the computational space.
Numerical tests of decaying homogeneous isotropic turbulence and a plane-channel flow illustrate the robustness of this flow-dependent characteristic length scale with respect to mesh anisotropy.https://authors.library.caltech.edu/records/6km8j-c4p73Dynamic wall models for the slip boundary condition
https://resolver.caltech.edu/CaltechAUTHORS:20210316-070322625
Authors: Lozano-Durán, A.; Bae, H. J.; Bose, S. T.; Moin, P.
Year: 2017
PMCID: PMC6800703
The near-wall resolution requirements to accurately resolve the boundary layer in wall-bounded flows remains a pacing item in large-eddy simulation (LES) for high-Reynolds-number engineering applications. Chapman (1979) and Choi & Moin (2012) estimated that the number of grid points necessary for a wall-resolved LES scales as Re^(1.9), where Re is the characteristic Reynolds number of the problem. The computational cost is still too high for many practical problems, especially for external aerodynamics, despite the favorable comparison to the Re^(2.6) scaling required for direct numerical simulation (DNS) where all the relevant scales of motion are resolved.https://authors.library.caltech.edu/records/72ap3-hbw40Convergence of large-eddy simulation in the outer region of wall-bounded turbulence
https://resolver.caltech.edu/CaltechAUTHORS:20210322-154129661
Authors: Lozano-Durán, A.; Bae, H. J.
Year: 2017
PMCID: PMC6800699
Most turbulent flows cannot be calculated by direct numerical simulation (DNS) of the Navier-Stokes equations because the range of scales of motions is so large that the computational cost becomes prohibitive. In large-eddy simulation (LES), only the large eddies are resolved and the effect of the small scales on the larger ones is modeled through a subgrid scale (SGS) model. This process enables a reduction of the computational cost by several orders of magnitude.https://authors.library.caltech.edu/records/ve0a5-feg42Turbulence intensities in large-eddy simulation of wall-bounded flows
https://resolver.caltech.edu/CaltechAUTHORS:20210315-113239124
Authors: Bae, H. J.; Lozano-Durán, A.; Bose, S. T.; Moin, P.
Year: 2018
DOI: 10.1103/physrevfluids.3.014610
A persistent problem in wall-bounded large-eddy simulations (LES) with Dirichlet no-slip boundary conditions is that the near-wall streamwise velocity fluctuations are overpredicted, while those in the wall-normal and spanwise directions are underpredicted. The problem may become particularly pronounced when the near-wall region is underresolved. The prediction of the fluctuations is known to improve for wall-modeled LES, where the no-slip boundary condition at the wall is typically replaced by Neumann and no-transpiration conditions for the wall-parallel and wall-normal velocities, respectively. However, the turbulence intensity peaks are sensitive to the grid resolution and the prediction may degrade when the grid is refined. In the present study, a physical explanation of this phenomena is offered in terms of the behavior of the near-wall streaks. We also show that further improvements are achieved by introducing a Robin (slip) boundary condition with transpiration instead of the Neumann condition. By using a slip condition, the inner energy production peak is damped, and the blocking effect of the wall is relaxed such that the splatting of eddies at the wall is mitigated. As a consequence, the slip boundary condition provides an accurate and consistent prediction of the turbulence intensities regardless of the near-wall resolution.https://authors.library.caltech.edu/records/6869c-vnn72DNS-aided explicitly filtered LES of channel flow
https://resolver.caltech.edu/CaltechAUTHORS:20210315-113839281
Authors: Bae, H. J.; Lozano-Durán, A.
Year: 2018
DOI: 10.48550/arXiv.1902.02508
PMCID: PMC6800716
The equations for large-eddy simulation (LES) are formally derived by applying a low-pass filter to the Navier–Stokes (NS) equations (Leonard 1975). However, in most numerical simulations, no explicit filter form is specified, and the computational grid and the low-pass characteristics of the discrete differentiation operators act as an effective implicit filter. The resulting velocity field is then assumed to be representative of the filtered velocity. Although the discrete operators have a low-pass filtering effect, the associated filter acts only in the single spatial direction in which the derivative is applied (Lund 2003); thus each term in the NS equations takes on a different filter form. In addition, numerical errors and the frequency content are uncontrolled for the implicit filter approach, and the solutions are grid dependent (Kravchenko & Moin 2000; Meyers & Sagaut 2007).https://authors.library.caltech.edu/records/4wneh-9nd72Causal analysis of self-sustaining processes in the logarithmic layer of wall-bounded turbulence
https://resolver.caltech.edu/CaltechAUTHORS:20210315-145613612
Authors: Bae, H. J.; Encinar, M. P.; Lozano-Durán, A.
Year: 2018
DOI: 10.1088/1742-6596/1001/1/012013
PMCID: PMC6800676
Despite the large amount of information provided by direct numerical simulations of turbulent flows, their underlying dynamics remain elusive even in the most simple and canonical configurations. Most common approaches to investigate the turbulence phenomena do not provide a clear causal inference between events, which is essential to determine the dynamics of self-sustaining processes. In the present work, we examine the causal interactions between streaks, rolls and mean shear in the logarithmic layer of a minimal turbulent channel flow. Causality between structures is assessed in a non-intrusive manner by transfer entropy, i.e., how much the uncertainty of one structure is reduced by knowing the past states of the others. We choose to represent streaks by the first Fourier modes of the streamwise velocity, while rolls are defined by the wall-normal and spanwise velocity modes. The results show that the process is mainly unidirectional rather than cyclic, and that the log-layer motions are sustained by extracting energy from the mean shear which controls the dynamics and time-scales. The well-known lift-up effect is also identified, but shown to be of secondary importance in the causal network between shear, streaks and rolls.https://authors.library.caltech.edu/records/w8qj8-qag10Mandala-inspired representation of the turbulent energy cascade
https://resolver.caltech.edu/CaltechAUTHORS:20210315-111745889
Authors: Bassenne, Maxime; Bae, Hyunji Jane; Lozano-Durán, Adrián
Year: 2018
DOI: 10.1103/physrevfluids.3.100505
PMCID: PMC6800704
This paper is associated with a poster winner of a 2017 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2017.GFM.P0026https://authors.library.caltech.edu/records/08k49-8th65Regularity diagnostics applied to a turbulent boundary layer
https://resolver.caltech.edu/CaltechAUTHORS:20210322-152610635
Authors: Bae, H. J.; Gibbon, J. D.; Kerr, R. M.; Lozano-Durán, A.
Year: 2018
Regularity diagnostics for the Navier-Stokes equations based on rescaled high-order
vorticity moments are applied to direct numerical simulation (DNS) of plane turbulent
channel flow and calculations of high-Reynolds-number vortex reconnection. At the
wall-normal height typical of the tips of hairpin vortices, the temporal evolution of the
vorticity moments is qualitatively similar to that of controlled high-Reynolds-number
vortex reconnection in the absence of walls. Both the channel flow and vortex reconnection
data exhibit higher measure of vorticity than previous results from decaying and
forced isotropic turbulence. This allows for future analysis of vortex dynamics based on
new results detailing the vorticity and helicity dynamics of reconnection events.https://authors.library.caltech.edu/records/kqytt-tjs48A minimal flow unit of the logarithmic layer in the absence of near-wall eddies and large scales
https://resolver.caltech.edu/CaltechAUTHORS:20210326-121043266
Authors: Bae, H. J.; Lozano-Durán, A.
Year: 2019
In the vicinity of walls, turbulent flows are found to be highly organized, consisting
of streamwise rolls and low- and high-speed streaks (Klebanoff et al. 1962; Kline et al.
1967; Smith & Metzler 1983; Blackwelder & Eckelmann 1979; Johansson et al. 1987) that
are involved in a quasi-periodic regeneration cycle (Robinson 1991; Panton 2001; Adrian
2007; Smits et al. 2011; Jiménez 2018). Important progress regarding the study of this
regeneration cycle was made using the "minimal flow unit" approach, which indicated
that buffer layer streaks can self-sustain even when motions at larger scales are inhibited
and that their existence, therefore, relies on an autonomous process (Jiménez & Moin
1991). The observation that the buffer and viscous layers of wall-bounded flows can be
simulated in periodic boxes of minimal dimensions has been useful in understanding wall
turbulence since it enables the study of individual flow features in isolation from their
mutual interactions.https://authors.library.caltech.edu/records/n0vdj-0yz76Dynamic slip wall model for large-eddy simulation
https://resolver.caltech.edu/CaltechAUTHORS:20210315-154630091
Authors: Bae, Hyunji Jane; Lozano-Durán, Adrián; Bose, Sanjeeb T.; Moin, Parviz
Year: 2019
DOI: 10.1017/jfm.2018.838
Wall modelling in large-eddy simulation (LES) is necessary to overcome the prohibitive near-wall resolution requirements in high-Reynolds-number turbulent flows. Most existing wall models rely on assumptions about the state of the boundary layer and require a priori prescription of tunable coefficients. They also impose the predicted wall stress by replacing the no-slip boundary condition at the wall with a Neumann boundary condition in the wall-parallel directions while maintaining the no-transpiration condition in the wall-normal direction. In the present study, we first motivate and analyse the Robin (slip) boundary condition with transpiration (non-zero wall-normal velocity) in the context of wall-modelled LES. The effect of the slip boundary condition on the one-point statistics of the flow is investigated in LES of turbulent channel flow and a flat-plate turbulent boundary layer. It is shown that the slip condition provides a framework to compensate for the deficit or excess of mean momentum at the wall. Moreover, the resulting non-zero stress at the wall alleviates the well-known problem of the wall-stress under-estimation by current subgrid-scale (SGS) models (Jiménez & Moser, AIAA J., vol. 38 (4), 2000, pp. 605–612). Second, we discuss the requirements for the slip condition to be used in conjunction with wall models and derive the equation that connects the slip boundary condition with the stress at the wall. Finally, a dynamic procedure for the slip coefficients is formulated, providing a dynamic slip wall model free of a priori specified coefficients. The performance of the proposed dynamic wall model is tested in a series of LES of turbulent channel flow at varying Reynolds numbers, non-equilibrium three-dimensional transient channel flow and a zero-pressure-gradient flat-plate turbulent boundary layer. The results show that the dynamic wall model is able to accurately predict one-point turbulence statistics for various flow configurations, Reynolds numbers and grid resolutions.https://authors.library.caltech.edu/records/h9vg3-vea70Characteristic scales of Townsend's wall-attached eddies
https://resolver.caltech.edu/CaltechAUTHORS:20190508-161433596
Authors: Lozano-Durán, Adrián; Bae, Hyunji Jane
Year: 2019
DOI: 10.1017/jfm.2019.209
PMCID: PMC6800708
Townsend (The Structure of Turbulent Shear Flow, 1976, Cambridge University Press) proposed a structural model for the logarithmic layer (log layer) of wall turbulence at high Reynolds numbers, where the dominant momentum-carrying motions are organised into a multiscale population of eddies attached to the wall. In the attached-eddy framework, the relevant length and velocity scales of the wall-attached eddies are the friction velocity and the distance to the wall. In the present work, we hypothesise that the momentum-carrying eddies are controlled by the mean momentum flux and mean shear with no explicit reference to the distance to the wall and propose new characteristic velocity, length and time scales consistent with this argument. Our hypothesis is supported by direct numerical simulation of turbulent channel flows driven by non-uniform body forces and modified mean velocity profiles, where the resulting outer-layer flow structures are substantially altered to accommodate the new mean momentum transfer. The proposed scaling is further corroborated by simulations where the no-slip wall is replaced by a Robin boundary condition for the three velocity components, allowing for substantial wall-normal transpiration at all length scales. We show that the outer-layer one-point statistics and spectra of this channel with transpiration agree quantitatively with those of its wall-bounded counterpart. The results reveal that the wall-parallel no-slip condition is not required to recover classic wall-bounded turbulence far from the wall and, more importantly, neither is the impermeability condition at the wall.https://authors.library.caltech.edu/records/g9wfe-grx62Error scaling of large-eddy simulation in the outer region of wall-bounded turbulence
https://resolver.caltech.edu/CaltechAUTHORS:20190507-111646634
Authors: Lozano-Durán, Adrián; Bae, Hyunji Jane
Year: 2019
DOI: 10.1016/j.jcp.2019.04.063
PMCID: PMC6800710
We study the error scaling properties of large-eddy simulation (LES) in the outer region of wall-bounded turbulence at moderately high Reynolds numbers. In order to avoid the additional complexity of wall-modeling, we perform LES of turbulent channel flows in which the no-slip condition at the wall is replaced by a Neumann condition supplying the exact mean wall-stress. The statistics investigated are the mean velocity profile, turbulence intensities, and kinetic energy spectra. The errors follow (Δ/L)^αRe_τ^γ, where Δ is the characteristic grid resolution, Reτ is the friction Reynolds number, and L is the meaningful length-scale to normalize Δ in order to collapse the errors across the wall-normal distance. We show that Δ can be expressed as the L_2-norm of the grid vector and that L is well represented by the ratio of the friction velocity and mean shear. The exponent α is estimated from theoretical arguments for each statistical quantity of interest and shown to roughly match the values computed by numerical simulations. For the mean profile and kinetic energy spectra, α ≈ 1, whereas the turbulence intensities converge at a slower rate α < 1. The exponent γ is approximately 0, i.e. the LES solution is independent of the Reynolds number. The expected behavior of the turbulence intensities at high Reynolds numbers is also derived and shown to agree with the classic log-layer profiles for grid resolutions lying within the inertial range. Further examination of the LES turbulence intensities and spectra reveals that both quantities resemble their filtered counterparts from direct numerical simulation (DNS) data, but that the mechanism responsible for this similarity is related to the balance between the input power and dissipation rather than to filtering.https://authors.library.caltech.edu/records/jqtwb-snc28Studying the effect of wall cooling in supersonic boundary layer flow using resolvent analysis
https://resolver.caltech.edu/CaltechAUTHORS:20200113-074130443
Authors: Bae, Hyunji Jane; Dawson, Scott T.; McKeon, Beverley J.
Year: 2020
DOI: 10.2514/6.2020-0575
Analysis of the resolvent operator is used to study the properties of high-speed turbulent boundary layers for cooled walls. Previous study [1] shows that the resolvent response modes in the relatively subsonic region of high-speed turbulent boundary layers with adiabatic wall boundary conditions follow the same scaling law as those of the incompressible boundary layer case, validating Morkovin's hypothesis on a mode-by-mode basis. Here, we study the effect of the cooled-wall boundary condition on the individual resolvent response modes to understand the underlying mechanisms that cause the failure of Morkovin's hypothesis and velocity transformations for increasingly non-adiabatic walls. In particular, we show that the density and temperature resolvent mode shapes for the cooled-wall case exhibit a secondary peak in the inner and logarithmic layer, which is a result of the non-monotonic mean temperature profile that is absent in adiabatic cases. We also show that the secondary peak becomes more prominent with decreasing surface temperature ratio. The deviation of the mean velocity profiles is attributed to the change in the response modes in the near-wall region, the effect of which is propagated further away from the wall through nonlinear interactions.https://authors.library.caltech.edu/records/xcxb2-wba52Causality of energy-containing eddies in wall turbulence
https://resolver.caltech.edu/CaltechAUTHORS:20191120-001542074
Authors: Lozano-Durán, Adrián; Bae, H. Jane; Encinar, Miguel P.
Year: 2020
DOI: 10.1017/jfm.2019.801
Turbulent flows in the presence of walls may be apprehended as a collection of momentum- and energy-containing eddies (energy-eddies), whose sizes differ by many orders of magnitude. These eddies follow a self-sustaining cycle, i.e. existing eddies are seeds for the inception of new ones, and so forth. Understanding this process is critical for the modelling and control of geophysical and industrial flows, in which a non-negligible fraction of the energy is dissipated by turbulence in the immediate vicinity of walls. In this study, we examine the causal interactions of energy-eddies in wall-bounded turbulence by quantifying how the knowledge of the past states of eddies reduces the uncertainty of their future states. The analysis is performed via direct numerical simulation of turbulent channel flows in which time-resolved energy-eddies are isolated at a prescribed scale. Our approach unveils, in a simple manner, that causality of energy-eddies in the buffer and logarithmic layers is similar and independent of the eddy size. We further show an example of how novel flow control and modelling strategies can take advantage of such self-similar causality.https://authors.library.caltech.edu/records/r7txx-naf94Resolvent-based study of compressibility effects on supersonic turbulent boundary layers
https://resolver.caltech.edu/CaltechAUTHORS:20200128-124558577
Authors: Bae, H. Jane; Dawson, Scott T. M.; McKeon, Beverley J.
Year: 2020
DOI: 10.1017/jfm.2019.881
The resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) is applied to supersonic turbulent boundary layers to study the validity of Morkovin's hypothesis, which postulates that high-speed turbulence structures in zero-pressure-gradient turbulent boundary layers remain largely the same as their incompressible counterparts. Supersonic zero-pressure-gradient turbulent boundary layers with adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are considered. Resolvent analysis highlights two distinct regions of the supersonic turbulent boundary layer in the wave parameter space: the relatively supersonic region and the relatively subsonic region. In the relatively supersonic region, where the flow is supersonic relative to the free-stream, resolvent modes display structures consistent with Mach wave radiation that are absent in the incompressible regime. In the relatively subsonic region, we show that the low-rank approximation of the resolvent operator is an effective approximation of the full system and that the response modes predicted by the model exhibit universal and geometrically self-similar behaviour via a transformation given by the semi-local scaling. Moreover, with the semi-local scaling, we show that the resolvent modes follow the same scaling law as their incompressible counterparts in this region, which has implications for modelling and the prediction of turbulent high-speed wall-bounded flows. We also show that the thermodynamic variables exhibit similar mode shapes to the streamwise velocity modes, supporting the strong Reynolds analogy. Finally, we demonstrate that the principal resolvent modes can be used to capture the energy distribution between momentum and thermodynamic fluctuations.https://authors.library.caltech.edu/records/3wz5g-ryp87Characterization of vortex regeneration mechanism in the self-sustaining process of wall-bounded flows using resolvent analysis
https://resolver.caltech.edu/CaltechAUTHORS:20200701-133438084
Authors: Bae, H. Jane; McKeon, Beverley J.
Year: 2020
DOI: 10.1088/1742-6596/1522/1/012001
The regeneration mechanism of streamwise vortical structures in the self-sustaining process of wall-bounded turbulence is investigated. Resolvent analysis [1] is used to identify the principal forcing mode which produces the maximum amplification of the response modes in the minimal channel for the buffer [2] and logarithmic layer [3]. The identified mode is then projected out from the nonlinear term of the Navier-Stokes equations at each time step from the direct numerical simulations (DNS) of the corresponding minimal channel. The results show that the removal of the principal forcing mode is able to significantly inhibit turbulence for the buffer and logarithmic layer while removing the subsequent modes instead of the principal one only marginally affects the flow. Analysis of the dyadic interactions in the nonlinear term shows that the contributions toward the principal forcing mode come from a limited number of wavenumber interactions. Using conditional averaging, the flow structures that are responsible for generating the principal forcing mode, and thus the nonlinear interaction to self-sustain turbulence, are identified to be spanwise rolls interacting with meandering streaks.https://authors.library.caltech.edu/records/eq3d2-n2j56Effect of Wall Boundary Conditions on a Wall-Modeled Large-Eddy Simulation in a Finite-Difference Framework
https://resolver.caltech.edu/CaltechAUTHORS:20210311-101157248
Authors: Bae, H. Jane; Lozano-Durán, Adrián
Year: 2021
DOI: 10.3390/fluids6030112
We studied the effect of wall boundary conditions on the statistics in a wall-modeled large-eddy simulation (WMLES) of turbulent channel flows. Three different forms of the boundary condition based on the mean stress-balance equations were used to supply the correct mean wall shear stress for a wide range of Reynolds numbers and grid resolutions applicable to WMLES. In addition to the widely used Neumann boundary condition at the wall, we considered a case with a no-slip condition at the wall in which the wall stress was imposed by adjusting the value of the eddy viscosity at the wall. The results showed that the type of boundary condition utilized had an impact on the statistics (e.g., mean velocity profile and turbulence intensities) in the vicinity of the wall, especially at the first off-wall grid point. Augmenting the eddy viscosity at the wall resulted in improved predictions of statistics in the near-wall region, which should allow the use of information from the first off-wall grid point for wall models without additional spatial or temporal filtering. This boundary condition is easy to implement and provides a simple solution to the well-known log-layer mismatch in WMLES.https://authors.library.caltech.edu/records/4t2cm-zhg75Self-critical machine-learning wall-modeled LES for external aerodynamics
https://resolver.caltech.edu/CaltechAUTHORS:20210315-144531131
Authors: Lozano-Durán, A.; Bae, H. J.
Year: 2021
DOI: 10.48550/arXiv.2012.10005
The prediction of aircraft aerodynamic quantities of interest remains among the most pressing challenges for computational fluid dynamics. The aircraft aerodynamics are inherently turbulent with mean-flow three-dimensionality, often accompanied by laminar-to-turbulent transition, flow separation, secondary flow motions at corners, and shock wave formation, to name a few. However, the most widespread wall models are built upon the assumption of statistically-in-equilibrium wall-bounded turbulence and do not faithfully account for the wide variety of flow conditions described above. This raises the question of how to devise models capable of accounting for such a vast and rich collection of flow physics in a feasible manner. In this work, we propose tackling the wall-modeling challenge by devising the flow as a collection of building blocks, whose information enables the prediction of the stress as the wall. The model relies on the assumption that simple canonical flows contain the essential flow physics to devise accurate models. Three types of building block units were used to train the model: turbulent channel flows, turbulent ducts and turbulent boundary layers with separation. This limited training set will be extended in future versions of the model. The approach is implemented using two interconnected artificial neural networks: a classifier, which identifies the contribution of each building block in the flow; and a predictor, which estimates the wall stress via non-linear combinations of building-block units. The output of the model is accompanied by the confidence in the prediction. The latter value aids the detection of areas where the model underperforms, such as flow regions that are not representative of the building blocks used to train the model. The model is validated in a unseen case representative of external aerodynamic applications: the NASA Juncture Flow Experiment.https://authors.library.caltech.edu/records/397p3-jea62A nonlinear subgrid-scale model for large-eddy simulations of rotating turbulent flows
https://resolver.caltech.edu/CaltechAUTHORS:20210504-092729293
Authors: Silvis, Maurits H.; Bae, H. Jane; Trias, F. Xavier; Abkar, Mahdi; Verstappen, Roel
Year: 2021
DOI: 10.48550/arXiv.1904.12748
Rotating turbulent flows form a challenging test case for large-eddy simulation (LES). We, therefore, propose and validate a new subgrid-scale (SGS) model for such flows. The proposed SGS model consists of a dissipative eddy viscosity term as well as a nondissipative term that is nonlinear in the rate-of-strain and rate-of-rotation tensors. The two corresponding model coefficients are a function of the vortex stretching magnitude. Therefore, the model is consistent with many physical and mathematical properties of the Navier-Stokes equations and turbulent stresses, and is easy to implement. We determine the two model constants using a nondynamic procedure that takes into account the interaction between the model terms. Using detailed direct numerical simulations (DNSs) and LESs of rotating decaying turbulence and spanwise-rotating plane-channel flow, we reveal that the two model terms respectively account for dissipation and backscatter of energy, and that the nonlinear term improves predictions of the Reynolds stress anisotropy near solid walls. We also show that the new SGS model provides good predictions of rotating decaying turbulence and leads to outstanding predictions of spanwise-rotating plane-channel flow over a large range of rotation rates for both fine and coarse grid resolutions. Moreover, the new nonlinear model performs as well as the dynamic Smagorinsky and scaled anisotropic minimum-dissipation models in LESs of rotating decaying turbulence and outperforms these models in LESs of spanwise-rotating plane-channel flow, without requiring (dynamic) adaptation or near-wall damping of the model constants.https://authors.library.caltech.edu/records/qpyhg-k8t52Nonlinear mechanism of the self-sustaining process in the buffer and logarithmic layer of wall-bounded flows
https://resolver.caltech.edu/CaltechAUTHORS:20191223-155902555
Authors: Bae, H. Jane; McKeon, Beverley J.
Year: 2021
DOI: 10.1017/jfm.2020.857
The nonlinear mechanism in the self-sustaining process (SSP) of wall-bounded turbulence is investigated. Resolvent analysis is used to identify the principal forcing mode that produces the maximum amplification of the velocities in numerical simulations of the minimal channel for the buffer layer and a modified logarithmic (log) layer. The wavenumbers targeted in this study are those of the fundamental mode, which is infinitely long in the streamwise direction and once-periodic in the spanwise direction. The identified mode is then projected out from the nonlinear term of the Navier–Stokes equations at each time step from the simulation of the corresponding minimal channel. The results show that the removal of the principal forcing mode of the fundamental wavenumber can inhibit turbulence in both the buffer and log layer, with the effect being greater in the buffer layer. Removing other modes instead of the principal mode of the fundamental wavenumber only marginally affects the flow. Closer inspection of the dyadic interactions in the nonlinear term shows that contributions to the principal forcing mode come from a limited set of wavenumber interactions. Using conditional averaging, the flow structures that are responsible for generating the nonlinear interaction to self-sustain turbulence are identified as spanwise rolls interacting with oblique streaks. This method, based on the equations of motion, validates the similarities in the SSP of the buffer and log layer, and characterises the underlying quadratic interactions in the SSP of the minimal channel.https://authors.library.caltech.edu/records/hz1q5-ttm93Life cycle of streaks in the buffer layer of wall-bounded turbulence
https://resolver.caltech.edu/CaltechAUTHORS:20210315-141739187
Authors: Bae, H. Jane; Lee, Myoungkyu
Year: 2021
DOI: 10.1103/PhysRevFluids.6.064603
Streaks in the buffer layer of wall-bounded turbulence are tracked in time to study their life cycle. Spatially and temporally resolved direct numerical simulation data are used to analyze the strong wall-parallel movements conditioned to low-speed streamwise flow. The analysis of the streaks shows that there is a clear distinction between wall-attached and detached streaks, and that the wall-attached streaks can be further categorized into streaks that are contained in the buffer layer and the ones that reach the outer region. The results reveal that streaks are born in the buffer layer, coalescing with each other to create larger streaks that are still attached to the wall. Once the streak becomes large enough, it starts to meander due to the large streamwise-to-wall-normal aspect ratio, and consequently the elongation in the streamwise direction, which makes it more difficult for the streak to be oriented strictly in the streamwise direction. While the continuous interaction of the streaks allows the superstructure to span extremely long temporal and length scales, individual streak components are relatively small and short-lived. Tall-attached streaks eventually split into wall-attached and wall-detached components. These wall-detached streaks have a strong wall-normal velocity away from the wall, similar to ejections or bursts observed in the literature. Conditionally averaging the flow fields to these split events show that the detached streak has not only a larger wall-normal velocity compared to the wall-attached counterpart, it also has a larger (less negative) streamwise velocity, similar to the velocity field at the tip of a vortex cluster.https://authors.library.caltech.edu/records/cqw8h-57d63Resolvent analysis of stratification effects on wall-bounded shear flows
https://resolver.caltech.edu/CaltechAUTHORS:20210223-153658783
Authors: Ahmed, M. A.; Bae, H. J.; Thompson, A. F.; McKeon, B. J.
Year: 2021
DOI: 10.1103/PhysRevFluids.6.084804
The interaction between shear-driven turbulence and stratification is a key process in a wide array of geophysical flows with spatiotemporal scales that span many orders of magnitude. A quick numerical model prediction based on external parameters of stratified boundary layers could greatly benefit the understanding of the interaction between velocity and scalar flux at varying scales. For these reasons, here we use the resolvent framework [McKeon and Sharma, J. Fluid Mech., 658 (2010)] to investigate the effects of an active scalar on incompressible wall-bounded turbulence. We obtain the state of the flow system by applying the linear resolvent operator to the nonlinear terms in the governing Navier-Stokes equations with the Boussinesq approximation. This extends the formulation to include the scalar advection equation with the scalar component acting in the wall-normal direction in the momentum equations [Dawson, Saxton-Fox and McKeon, AIAA Fluid Dyn. Conf. 4042 (2018)]. We use the mean velocity profiles from a direct numerical simulation (DNS) of a stably stratified turbulent channel flow at varying friction Richardson number Ri_τ. The results obtained from the resolvent analysis are compared to the premultiplied energy spectra, autocorrelation coefficient, and the energy budget terms obtained from the DNS. It is shown that despite using only a very limited range of representative scales, the resolvent model is able to reproduce the balance of energy budget terms as well as provide meaningful insight into coherent structures occurring in the flow. Computation of the leading resolvent models, despite considering a limited range of scales, reproduces the balance of energy budget terms, provides meaningful predictions of coherent structures in the flow, and is more cost-effective than performing full-scale simulations. This quick model can provide a further understanding of stratified flows with only information about the mean profile and prior knowledge of energetic scales of motion in the neutrally buoyant boundary layers.https://authors.library.caltech.edu/records/xjg67-b4e50Scientific multi-agent reinforcement learning for wall-models of turbulent flows
https://resolver.caltech.edu/CaltechAUTHORS:20220317-189733300
Authors: Bae, H. Jane; Koumoutsakos, Petros
Year: 2022
DOI: 10.1038/s41467-022-28957-7
PMCID: PMC8931082
The predictive capabilities of turbulent flow simulations, critical for aerodynamic design and weather prediction, hinge on the choice of turbulence models. The abundance of data from experiments and simulations and the advent of machine learning have provided a boost to turbulence modeling efforts. However, simulations of turbulent flows remain hindered by the inability of heuristics and supervised learning to model the near-wall dynamics. We address this challenge by introducing scientific multi-agent reinforcement learning (SciMARL) for the discovery of wall models for large-eddy simulations (LES). In SciMARL, discretization points act also as cooperating agents that learn to supply the LES closure model. The agents self-learn using limited data and generalize to extreme Reynolds numbers and previously unseen geometries. The present simulations reduce by several orders of magnitude the computational cost over fully-resolved simulations while reproducing key flow quantities. We believe that SciMARL creates unprecedented capabilities for the simulation of turbulent flows.https://authors.library.caltech.edu/records/y0zn0-xky07Local dynamic gradient Smagorinsky model for large-eddy simulation
https://resolver.caltech.edu/CaltechAUTHORS:20220722-768544000
Authors: Rozema, Wybe; Bae, H. Jane; Verstappen, Roel W. C. P.
Year: 2022
DOI: 10.1103/physrevfluids.7.074604
This paper introduces a local dynamic model for large-eddy simulation (LES) without averaging in the homogeneous directions. It is demonstrated that the widely used dynamic Smagorinsky model (DSM) has a singular dynamic model constant if it is used without averaging. The singularity can cause exceedingly large local values of the dynamic model constant. If these large values are not mitigated by the application of averaging, they can amplify discretization errors and impair the stability of simulations. To improve the local applicability of the DSM, the singularity is removed by replacing the resolved rate-of-strain tensors in the Smagorinsky model with the resolved velocity gradient tensor. This replacement results in the dynamic gradient Smagorinsky model (DGSM). Results of simulations of three canonical turbulent flows (decaying homogeneous isotropic turbulence, a temporal mixing layer, and turbulent channel flow) are presented to demonstrate the potential of this model. The DGSM provides improved stability compared to the local DSM and does not require averaging for stability at time step sizes that are typically used for a locally consistent static LES model. Results obtained with the DGSM are generally as accurate as results obtained with the DSM, while the DGSM has lower computational complexity. Moreover, the DGSM is easy to implement and does not require any homogeneous direction in space or time. It is therefore concluded that the DGSM is a promising local dynamic model for LES.https://authors.library.caltech.edu/records/wjsq8-7bv47Wavelet-based resolvent analysis for statistically-stationary and temporally-evolving flows
https://resolver.caltech.edu/CaltechAUTHORS:20230327-902843000.16
Authors: Ballouz, Eric; Lopez-Doriga, Barbara; Dawson, Scott T. M.; Bae, Hyunji Jane
Year: 2023
DOI: 10.2514/6.2023-0676
This work introduces a formulation of resolvent analysis that uses wavelet transforms rather than Fourier transforms in time. This allows resolvent analysis to be extended to turbulent flows with non-stationary means in addition to statistically-stationary flows. The optimal resolvent modes for this formulation correspond to the potentially time-transient structures that are most amplified by the linearized Navier-Stokes operator. We validate this methodology for turbulent channel flow and show that the wavelet-based and Fourier-based resolvent analyses are equivalent for statistically-stationary flows. We then apply the wavelet-based resolvent analysis to study the transient growth mechanism in the buffer layer of a turbulent channel flow by windowing the resolvent operator in time and frequency. The method is also applied to temporally-evolving parallel shear flows such as an oscillating boundary layer and three-dimensional channel flow, in which a lateral pressure gradient perturbs a fully-developed turbulent flow in a channel.https://authors.library.caltech.edu/records/ee50k-ns830A sparsity-promoting resolvent analysis for the identification of spatiotemporally-localized amplification mechanisms
https://resolver.caltech.edu/CaltechAUTHORS:20230327-902835000.15
Authors: Lopez-Doriga, Barbara; Ballouz, Eric; Bae, Hyunji Jane; Dawson, Scott T. M.
Year: 2023
DOI: 10.2514/6.2023-0677
This work introduces a variant of resolvent analysis that identifies forcing and response modes that are sparse in both space and time. This is achieved through the use of a sparse principal component analysis (PCA) algorithm, which formulates the associated optimization problem as a nonlinear eigenproblem that can be solved with an inverse power method. We apply this method to parallel shear flows, both in the case where we assume Fourier modes in time (as in standard resolvent analysis) and obtain spatial localization, and where we allow for temporally-sparse modes through the use of a linearized Navier--Stokes operator discretized in both space and time. Appropriate choice of desired mode sparsity allows for the identification of structures corresponding to high amplification that are localized in both space and time. We report on the similarities and differences between these structures and those from standard methods of analysis. After validating this space-time resolvent analysis on statistically-stationary channel flow, we next implement the methodology on a time-periodic Stokes boundary layer, demonstrating the applicability of the approach to non-statistically-stationary systems.https://authors.library.caltech.edu/records/1s2nv-jcw28Wavelet-based resolvent analysis for statistically-stationary and temporally-evolving flows
https://resolver.caltech.edu/CaltechAUTHORS:20230327-235358200
Authors: Ballouz, Eric; Lopez-Doriga, Barbara; Dawson, Scott T. M.; Bae, H. Jane
Year: 2023
This work introduces a formulation of resolvent analysis that uses wavelet transforms rather than Fourier transforms in time. This allows resolvent analysis to be extended to turbulent flows with non-stationary means in addition to statistically-stationary flows. The optimal resolvent modes for this formulation correspond to the potentially time-transient structures that are most amplified by the linearized Navier-Stokes operator. We validate this methodology for turbulent channel flow and show that the wavelet-based and Fourier-based resolvent analyses are equivalent for statistically-stationary flows. We then apply the wavelet-based resolvent analysis to study the transient growth mechanism in the buffer layer of a turbulent channel flow by windowing the resolvent operator in time and frequency. The method is also applied to temporally-evolving parallel shear flows such as an oscillating boundary layer and three-dimensional channel flow, in which a lateral pressure gradient perturbs a fully-developed turbulent flow in a channel.https://authors.library.caltech.edu/records/m4n8m-7cz15A sparsity-promoting resolvent analysis for the identification of spatiotemporally-localized amplification mechanisms
https://resolver.caltech.edu/CaltechAUTHORS:20230328-000129999
Authors: Lopez-Doriga, Barbara; Ballouz, Eric; Bae, H. Jane; Dawson, Scott T. M.
Year: 2023
This work introduces a variant of resolvent analysis that identifies forcing and response modes that are sparse in both space and time. This is achieved through the use of a sparse principal component analysis (PCA) algorithm, which formulates the associated optimization problem as a nonlinear eigenproblem that can be solved with an inverse power method. We apply this method to parallel shear flows, both in the case where we assume Fourier modes in time (as in standard resolvent analysis) and obtain spatial localization, and where we allow for temporally-sparse modes through the use of a linearized Navier-Stokes operator discretized in both space and time. Appropriate choice of desired mode sparsity allows for the identification of structures corresponding to high amplification that are localized in both space and time. We report on the similarities and differences between these structures and those from standard methods of analysis. After validating this space-time resolvent analysis on statistically-stationary channel flow, we next implement the methodology on a time-periodic Stokes boundary layer, demonstrating the applicability of the approach to non-statistically-stationary systems.https://authors.library.caltech.edu/records/xx50t-27h26Log-law recovery through reinforcement-learning wall model for large eddy simulation
https://resolver.caltech.edu/CaltechAUTHORS:20230602-251566000.18
Authors: Vadrot, Aurélien; Yang, Xiang I. A.; Bae, H. Jane; Abkar, Mahdi
Year: 2023
DOI: 10.1063/5.0147570
This paper focuses on the use of reinforcement learning (RL) as a machine-learning (ML) modeling tool for near-wall turbulence. RL has demonstrated its effectiveness in solving high-dimensional problems, especially in domains such as games. Despite its potential, RL is still not widely used for turbulence modeling and is primarily used for flow control and optimization purposes. A new RL wall model (WM) called VYBA23 is developed in this work, which uses agents dispersed in the flow near the wall. The model is trained on a single Reynolds number (Reτ=10⁴) and does not rely on high-fidelity data, as the backpropagation process is based on a reward rather than an output error. The states of the RLWM, which are the representation of the environment by the agents, are normalized to remove dependence on the Reynolds number. The model is tested and compared to another RLWM (BK22) and to an equilibrium wall model, in a half-channel flow at eleven different Reynolds numbers {Reτ∈[180;10¹⁰]}. The effects of varying agents' parameters, such as actions range, time step, and spacing, are also studied. The results are promising, showing little effect on the average flow field but some effect on wall-shear stress fluctuations and velocity fluctuations. This work offers positive prospects for developing RLWMs that can recover physical laws and for extending this type of ML models to more complex flows in the future.https://authors.library.caltech.edu/records/rk2qv-8sy62Machine learning building-block-flow wall model for large-eddy simulation
https://resolver.caltech.edu/CaltechAUTHORS:20230605-334871000.18
Authors: Lozano-Durán, Adrián; Bae, H. Jane
Year: 2023
DOI: 10.1017/jfm.2023.331
A wall model for large-eddy simulation (LES) is proposed by devising the flow as a combination of building blocks. The core assumption of the model is that a finite set of simple canonical flows contains the essential physics to predict the wall shear stress in more complex scenarios. The model is constructed to predict zero/favourable/adverse mean pressure gradient wall turbulence, separation, statistically unsteady turbulence with mean flow three-dimensionality, and laminar flow. The approach is implemented using two types of artificial neural networks: a classifier, which identifies the contribution of each building block in the flow, and a predictor, which estimates the wall shear stress via a combination of the building-block flows. The training data are obtained directly from wall-modelled LES (WMLES) optimised to reproduce the correct mean quantities. This approach guarantees the consistency of the training data with the numerical discretisation and the gridding strategy of the flow solver. The output of the model is accompanied by a confidence score in the prediction that aids the detection of regions where the model underperforms. The model is validated in canonical flows (e.g. laminar/turbulent boundary layers, turbulent channels, turbulent Poiseuille–Couette flow, turbulent pipe) and two realistic aircraft configurations: the NASA Common Research Model High-lift and NASA Juncture Flow experiment. It is shown that the building-block-flow wall model outperforms (or matches) the predictions by an equilibrium wall model. It is also concluded that further improvements in WMLES should incorporate advances in subgrid-scale modelling to minimise error propagation to the wall model.https://authors.library.caltech.edu/records/7xb67-waf13