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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:04:16 +0000On the spectrum of a stretched spiral vortex
https://resolver.caltech.edu/CaltechAUTHORS:PULpof94b
Authors: {'items': [{'id': 'Pullin-D-I', 'name': {'family': 'Pullin', 'given': 'D. I.'}}, {'id': 'Buntine-J-D', 'name': {'family': 'Buntine', 'given': 'James D.'}}, {'id': 'Saffman-P-G', 'name': {'family': 'Saffman', 'given': 'P. G.'}}]}
Year: 1994
DOI: 10.1063/1.868127
Corrections are found to the k^–5/3 spectrum of Lundgren [Phys. Fluids 25, 2193 (1982)] for a stretched spiral vortex model (a is the stretching strain rate and k the scalar wave number) of turbulent fine scales. These take the form of additional terms arising from the early time evolution, when the stretching of vortex lines is small. For the special case when the spiral takes the form of a rolled-up shear layer, it is shown that the composite spectrum is divergent, thus requiring the introduction of a finite early cutoff time tau1 in the time integral for the nonaxisymmetric contribution. The identity nuomega2 = 2nu[integral]<sub>0</sub><sup>[infinity]</sup>k^2E(k)dk which gives the dissipation is then satisfied self-consistently. Direct numerical calculation of the energy spectrum from the approximate vorticity field for a special choice of spiral structure nevertheless indicates that the one-term k^–5/3-spectrum result is asymptotically valid in the inertial range provided atau1 is O(1) but that the numerically calculated dissipation spectrum appears to lie somewhere between an exp(–B1k2) and an exp(–B2k) form. It is also shown that the stretched, rolled-up shear-layer model predicts asymptotic shell-summed spectra of the energy dissipation and of the square of the vorticity, each asymptotically constant, with no power-law dependence, for k smaller than the Kolmogorov wave number.The corresponding one-dimensional spectra each show –log(k1) behavior for small k1. The extension of the model given by Pullin and Saffman [Phys. Fluids A 5, 126 (1993)] is reformulated by the introduction of a long-time cutoff in the vortex lifetime and an additional requirement that the vortex structures be approximately space filling. This gives a reduction in the number of model free-parameters but introduces a dependence of the calculated Kolmogorov constant and skewness on the ratio of the initial vortex radius to the equivalent Burgers-vortex radius. A scaling for this ratio in terms of the Taylor microscale Reynolds number is proposed in which the stretching strain is assumed to be provided by the large scales with spatial coherence limited to the maximum stretched length of the structures. Postdictions of the fourth-order flatness factor and of higher moments of the longitudinal velocity gradient statistics are compared with numerical simulation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wpg3x-9cj19Inviscid Swirling Flows and Vortex Breakdown
https://resolver.caltech.edu/CaltechAUTHORS:20141217-153936617
Authors: {'items': [{'id': 'Buntine-J-D', 'name': {'family': 'Buntine', 'given': 'J. D.'}}, {'id': 'Saffman-P-G', 'name': {'family': 'Saffman', 'given': 'P. G.'}}]}
Year: 1995
The steady axisymmetric Euler flow of an inviscid incompressible swirling fluid
is described exactly by the Squire-Long equation. This equation is studied numerically
for the case of diverging flow to investigate the dependence of solutions
on upstream, or inlet, and downstream, or outlet, boundary conditions and flow
geometry. The work is performed with a view to understanding how the phenomenon
of vortex breakdown occurs. It is shown that solutions fail to exist or,
alternatively, that the axial flow ceases to be unidirectional, so that breakdown
can be inferred, when a parameter measuring the relative magnitude of rotation
and axial flow (the Squire number) exceeds critical values depending upon the geometry
and inlet profiles. A 'quasi-cylindrical' simplification of the Squire-Long
equation is compared with the more complete Euler model and shown to be able
to account for most of the latter's behaviour. The relationship is examined between
'failure' of the quasi-cylindrical model and the occurrence of a 'critical'
flow state in which disturbances can stand in the flow.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b4sjp-adb21