In this work, we develop a wavelet-based formulation of resolvent analysis in order to extend the method to transient phenomena and non-stationary flows. We apply this method in two ways: first, to analyze systems that were not previously amenable to traditional resolvent analysis, and second, to probe the limits of the resolvent forcing modes' \"optimality\" in a nonlinear simulation as well as investigate the mechanisms that suppress their effectiveness. In wavelet-based resolvent analysis, the Navier-Stokes equations are linearized about a mean profile, Fourier-transformed in the homogeneous directions, and wavelet-transformed in time. The nonlinear terms are represented as forcing terms acting on the system, and a maximally perturbing forcing mode and the response it produces are then computed for this linear system. The wavelet formulation enables the forcing and response modes to represent transient trajectories. By windowing the wavelet-based resolvent operator, we can also compute optimal forcing modes restricted to a time-localized pulse along with their transient response.
\r\n\r\nFor the first application of the method, we use the windowing approach to study bursting in channel flow. The optimal response mode grows and decays in time scales that match turbulent data, and we show that this optimal burst exploits the Orr mechanism.\r\nWe also study channel flow subjected to a spanwise pressure gradient. The corresponding resolvent modes mirror the mean flow and gradually realign themselves according to the new flow conditions. More interestingly, they exhibit a collapse of the lift-up mechanism during this realignment, which offers an explanation to the depletion of tangential Reynolds stresses in the turbulent system.
\r\n\r\nFor the second application of the method, we inject time-localized resolvent forcing modes for the minimal flow unit into a simulation of the system, at different intensities. The principal resolvent forcing mode is much more effective than a randomly generated forcing structure at amplifying the near-wall streak. For initial times and close to the wall, the turbulent minimal flow unit matches the principal response mode well, but due to nonlinear effects, the response decays prematurely. By computing the nonlinear energy transfer to secondary scales, we find that the breakdown of the actuated mode proceeds similarly across all forcing intensities: in the near-wall region, the induced streak forks into two branches, while in the outer region, the streak breaks up in the streamwise direction. In both regions, spanwise gradients account for the dominant share of nonlinear energy transfer.
", "doi": "10.7907/t9sw-b215", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:17211", "collection": "thesis", "collection_id": "17211", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05082025-223940273", "primary_object_url": { "basename": "Mohebbi_Nina_2025.pdf", "content": "final", "filesize": 9737531, "license": "other", "mime_type": "application/pdf", "url": "/17211/1/Mohebbi_Nina_2025.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Flow Induced by Collective Vertical Migration: Impact of Swimmer Distribution, Buoyancy, and Wake Interactions", "author": [ { "family_name": "Mohebbi", "given_name": "Nina", "orcid": "0000-0003-4014-6111", "clpid": "Mohebbi-Nina" } ], "thesis_advisor": [ { "family_name": "Dabiri", "given_name": "John O.", "orcid": "0000-0002-6722-9008", "clpid": "Dabiri-J-O" } ], "thesis_committee": [ { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" }, { "family_name": "Dickinson", "given_name": "Michael H.", "orcid": "0000-0002-8587-9936", "clpid": "Dickinson-M-H" }, { "family_name": "Lozano-Duran", "given_name": "Adrian", "orcid": "0000-0001-9306-0261", "clpid": "Lozano-Duran-A" }, { "family_name": "Dabiri", "given_name": "John O.", "orcid": "0000-0002-6722-9008", "clpid": "Dabiri-J-O" } ], "local_group": [ { "literal": "GALCIT" }, { "literal": "div_eng" } ], "abstract": "Various animal species exhibit collective motion, characterized by coordinated movement within groups of organisms. A prominent oceanic example is diel vertical migration (DVM), wherein zooplankton migrate vertically from deeper waters during the day to shallower regions at night, often covering distances of approximately 1 kilometer. Despite numerous field measurements, laboratory observations, and theoretical studies of biogenic mixing resulting from collective swimming, the scale of fluid mixing induced by DVM remains unresolved. A key challenge is linking the behavior and flows created by large numbers of individual organisms to collective-scale fluid dynamics. Since most swimmers involved in DVM operate at intermediate Reynolds numbers, the dynamics of these systems are nonlinear and span a wide range of spatial and temporal scales.
\r\n\r\nThis thesis investigates flow scaling generated by vertical migration of brine shrimp (Artemia salina) aggregates, using laboratory measurements complemented by semi-analytical modeling. A volumetric laser scanning system first measured swimmer behaviors and flow interactions during laboratory-induced vertical migrations. Swimmers consistently maintained vertical swimming velocities under varying environmental conditions, showed a Gaussian horizontal distribution within the tank cross-section, and exhibited a pronounced tendency toward the tank center, where illumination was brightest. A scaling relationship between swimmer buoyancy, ascent speeds, and resulting flow velocities was developed to contextualize these results.
\r\n\r\nA semi-analytical model was then developed to estimate the flow generated by wakes of multiple swimmers in proximity. Individual swimmer behaviors were informed by empirical observations and combined through an iterative approach that conserves mass and momentum, providing an aggregation-scale flow solution. Numerical results indicated that induced upstream flows within the aggregation were relatively insensitive to downstream swimmer presence, that average flow speeds approached a plateau beyond a critical aggregation length, and that closer swimmer spacing significantly enhanced induced flow velocities.
", "doi": "10.7907/hz5j-g795", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:17321", "collection": "thesis", "collection_id": "17321", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05302025-232647443", "type": "thesis", "title": "Beyond Symmetry: Normality-Based Analysis of Velocity Gradients in Turbulent Flows", "author": [ { "family_name": "Arun", "given_name": "Rahul", "orcid": "0000-0002-5942-169X", "clpid": "Arun-Rahul" } ], "thesis_advisor": [ { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" } ], "thesis_committee": [ { "family_name": "Lozano-Dur\u00e1n", "given_name": "Adri\u00e1n", "orcid": "0000-0001-9306-0261", "clpid": "Lozano-Duran-A" }, { "family_name": "Colonius", "given_name": "Tim", "orcid": "0000-0003-0326-3909", "clpid": "Colonius-T" }, { "family_name": "Pullin", "given_name": "Dale Ian", "orcid": "0009-0007-5991-2863", "clpid": "Pullin-D-I" }, { "family_name": "Leonard", "given_name": "Anthony", "clpid": "Leonard-A" } ], "local_group": [ { "literal": "GALCIT" }, { "literal": "div_eng" } ], "abstract": "Small-scale turbulence is a hallmark of countless natural and engineered flows. Its features are often described and modeled using the velocity gradient tensor (VGT), which is conventionally decomposed into the (symmetric) strain-rate tensor and the (antisymmetric) vorticity tensor. Although this symmetry-based decomposition has found use in areas such as vortex identification and closure modeling, it provides limited insight into local flow structure. A more refined description can be obtained by further distinguishing the normal and non-normal parts of the VGT. The resulting normality-based decomposition identifies contributions associated with normal straining (symmetric/normal), rigid rotation (antisymmetric/normal), and pure shearing (non-normal). We use this decomposition to identify flow features that are obscured by symmetry-based analyses yet have significant implications for efforts to understand and model turbulent flows.
\r\n\r\nWe first demonstrate that partitioning the strength of velocity gradients using our normality-based approach can distinguish between different regimes in various turbulent flows. In wall-bounded flows, the near-wall partitioning is dominated by shearing whereas the partitioning far from the wall collapses onto the partitioning associated with isotropic turbulence. In an unbounded vortex ring collision, our analysis distinguishes the initial vortex rings, which have a strong imprint from rigid rotation, from the decaying turbulent cloud produced by their collision, for which the partitioning is similar to that of isotropic turbulence. It also identifies enhanced shear\u2013rotation correlations as a distinctive fingerprint of the elliptic instability during transition, which can be interpreted using relevant geometric features of local streamlines. By deriving algebraic expressions for the partitioning constituents in terms of the invariants of the VGT and an additional parameter, which represents the alignment of shear vorticity with the local rotation axis, we identify a key facet of our analysis that goes beyond previous analyses of the VGT.
\r\n\r\nWe then apply our normality-based framework to filtered velocity gradients in direct and large-eddy simulations of isotropic turbulence. Our analysis enables shear layers, which are associated with shear vorticity, to be distinguished from vortex cores, which are associated with rigid rotation, in a multiscale setting. It reveals that filtering mitigates the relative contribution of shear layers in the subinertial range of the energy cascade. Moreover, it identifies crucial (yet perhaps overlooked) contributions from shear layers to fundamental energy transfer mechanisms, including strain self-amplification, vortex stretching, and backscatter associated with strain\u2013vorticity covariance. The dominant role of shear layers in the backscatter mechanism suggests that they contribute significantly to the bottleneck effect in the subinertial range of the cascade. Our analysis of large-eddy simulation data shows that they also amplify the artificial bottleneck effect produced by an eddy viscosity model in the inertial range. This reflects that the eddy viscosity model mimics an unfiltered direct numerical simulation at a lower Reynolds number. A mixed model can be used to mitigate the artificial bottleneck effect since it more accurately mimics a filtered direct numerical simulation.
", "doi": "10.7907/3py1-wj85", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" } ]