On the interaction between turbulence and a planar rarefaction

Journal Article · Tue Apr 01 04:00:00 EDT 2014 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/784/2/117· OSTI ID:22357273

Johnson, Bryan M. ^[1]

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1. Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550 (United States)

The modeling of turbulence, whether it be numerical or analytical, is a difficult challenge. Turbulence is amenable to analysis with linear theory if it is subject to rapid distortions, i.e., motions occurring on a timescale that is short compared to the timescale for nonlinear interactions. Such an approach (referred to as rapid distortion theory) could prove useful for understanding aspects of astrophysical turbulence, which is often subject to rapid distortions, such as supernova explosions or the free-fall associated with gravitational instability. As a proof of principle, a particularly simple problem is considered here: the evolution of vorticity due to a planar rarefaction in an ideal gas. Analytical solutions are obtained for incompressive modes having a wave vector perpendicular to the distortion; as in the case of gradient-driven instabilities, these are the modes that couple most strongly to the mean flow. Vorticity can either grow or decay in the wake of a rarefaction front, and there are two competing effects that determine which outcome occurs: entropy fluctuations couple to the mean pressure gradient to produce vorticity via baroclinic effects, whereas vorticity is damped due to the conservation of angular momentum as the fluid expands. Whether vorticity grows or decays depends upon the ratio of entropic to vortical fluctuations at the location of the front; growth occurs if this ratio is of order unity or larger. In the limit of purely entropic fluctuations in the ambient fluid, a strong rarefaction generates vorticity with a turbulent Mach number on the order of the rms of the ambient entropy fluctuations. The analytical results are shown to compare well with results from two- and three-dimensional numerical simulations. Analytical solutions are also derived in the linear regime of Reynolds-averaged turbulence models. This highlights an inconsistency in standard turbulence models that prevents them from accurately capturing the physics of rarefaction-turbulence interaction. In addition to providing physical insight, the solutions derived here can be used to verify algorithms of both the Reynolds-averaged and direct numerical simulation variety. Finally, dimensional analysis of the equations indicates that rapid distortion of turbulence can give rise to two distinct regimes in the turbulent spectrum: a distortion range at large scales where linear distortion effects dominate, and an inertial range at small scales where nonlinear effects dominate.

• OSTI ID: 22357273
• Journal Information: Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 2 Vol. 784; ISSN ASJOAB; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
ALGORITHMS
ANALYTICAL SOLUTION
ANGULAR MOMENTUM
ASTROPHYSICS
CAPTURE
COMPUTERIZED SIMULATION
ENTROPY
EQUATIONS
EVOLUTION
FLUCTUATIONS
FLUIDS
GALAXY CLUSTERS
GRAVITATIONAL INSTABILITY
MACH NUMBER
PRESSURE GRADIENTS
REYNOLDS NUMBER
SPECTRA
THREE-DIMENSIONAL CALCULATIONS
TURBULENCE