69 research outputs found
The conservative cascade of kinetic energy in compressible turbulence
The physical nature of compressible turbulence is of fundamental importance
in a variety of astrophysical settings. We present the first direct evidence
that mean kinetic energy cascades conservatively beyond a transitional
"conversion" scale-range despite not being an invariant of the compressible
flow dynamics. We use high-resolution three-dimensional simulations of
compressible hydrodynamic turbulence on and grids. We probe
regimes of forced steady-state isothermal flows and of unforced decaying ideal
gas flows. The key quantity we measure is pressure dilatation cospectrum,
, where we provide the first numerical evidence that it decays at a
rate faster than as a function of wavenumber. This is sufficient to
imply that mean pressure dilatation acts primarily at large-scales and that
kinetic and internal energy budgets statistically decouple beyond a
transitional scale-range. Our results suggest that an extension of Kolmogorov's
inertial-range theory to compressible turbulence is possible.Comment: 14 pages, 4 figure
Compressible Turbulence: The Cascade and its Locality
We prove that inter-scale transfer of kinetic energy in compressible
turbulence is dominated by local interactions. In particular, our results
preclude direct transfer of kinetic energy from large-scales directly to
dissipation scales, such as into shocks, in high Reynolds number turbulence as
is commonly believed. Our assumptions on the scaling of structure functions are
weak and enjoy compelling empirical support. Under a stronger assumption on
pressure dilatation co-spectrum, we show that mean kinetic and internal energy
budgets statistically decouple beyond a transitional "conversion" range. Our
analysis establishes the existence of an ensuing inertial range over which mean
SGS kinetic energy flux becomes constant, independent of scale. Over this
inertial range, mean kinetic energy cascades locally and in a conservative
fashion, despite not being an invariant.Comment: 4 pages, submitted to Phys. Rev. Let
Scale decomposition in compressible turbulence
This work presents a rigorous framework based on coarse-graining to analyze
highly compressible turbulence. We show how the requirement that viscous
effects on the dynamics of large-scale momentum and kinetic energy be
negligible ---an inviscid criterion--- naturally supports a density weighted
coarse-graining of the velocity field. Such a coarse-graining method is already
known in the literature as Favre filtering; however its use has been primarily
motivated by appealing modeling properties rather than underlying physical
considerations. We also prove that kinetic energy injection can be localized to
the largest scales by proper stirring, and argue that stirring with an external
acceleration field rather than a body force would yield a longer inertial range
in simulations. We then discuss the special case of buoyancy-driven flows
subject to a spatially-uniform gravitational field. We conclude that a range of
scales can exist over which the mean kinetic energy budget is dominated by
inertial processes and is immune from contributions due to molecular viscosity
and external stirring.Comment: 31 pages, 1 figure, to appear in Physica
Measuring Scale-dependent Shape Anisotropy by Coarse-Graining: Application to Inhomogeneous Rayleigh-Taylor Turbulence
We generalize the `filtering spectrum' [1] to probe scales along different
directions by spatial coarse-graining. This multi-dimensional filtering
spectrum quantifies the spectral content of flows that are not necessarily
homogeneous. From multi-dimensional spectral information, we propose a simple
metric for shape anisotropy at various scales. The method is applied to
simulations of 2D and 3D Rayleigh-Taylor (RT) turbulence, which is
inhomogeneous and anisotropic. We show that 3D RT has clear shape anisotropy at
large scales with approximately vertical to horizontal aspect ratio, but
tends toward isotropy at small scales as expected [2,3,4]. In sharp contrast,
we find that RT in 2D simulations, which are still the main modeling framework
for many applications, is isotropic at large scales and its shape anisotropy
increases at smaller scales where structures tend to be horizontally elongated.
While this may be surprising, it is consistent with recent results in [5];
large-scale isotropy in 2D RT is due to the generation of a large-scale
overturning circulation via an upscale cascade, while small scale anisotropy is
due to the stable stratification resultant from such overturning and the
inefficient mixing in 2D
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