(Color) Decaying turbulence in a NI fluid coupled to an IN fluid through nonlinear interactions. (a) Initial condition specified on the component of NI velocity field shows random fluctuations in a two-dimensional box. (b), (c), and (d) show fields at , respectively. Box size is . , . Other constants are , , , .
(Color) Coherent structure formation corresponding to the component of the NI fluid velocity.
The ratio of kinetic energies of incompressible and weakly compressible fluid, i.e., . The ratio shows a finite value at long times.
Evolution of mean Fourier mode associated with selective decay rates. Dashed and solid curves are and rates for IN and NI turbulence, respectively. Decay rates are stronger in NI turbulence than in IN hydrodynamics.
(Color online) Comparison of analytic and numerical results of the vortex amplitude distribution in space. Shown is a 1D cut along the vorticity distribution. Clearly, the analytic and numerical solutions show excellent agreement.
Density power spectrum is plotted as a function of (along the horizontal axis) from a decaying NI hydrodynamics simulation. The incompressible velocity fluctuations follow a Kolmogorov spectrum close to (with an error ) in a forward (or enstrophy) cascade regime of decaying turbulence. The density fluctuations are passively convected by the incompressible velocity fluctuations and exhibit nearly the same spectrum. The intermediate curve represents the temperature spectrum.
A driven turbulence NI hydrodynamic simulation yields a Kolmogorov-type spectrum close to (with an error ) in the inverse (or energy) cascade regime for incompressible velocity fluctuations (left). Turbulence is driven by a random forcing in space and time. The compressible density fluctuations (right) follow the incompressible velocity spectrum closely in the inertial regime of turbulence. In the right panel, the temperature spectrum is shown below the density spectrum. The horizontal axis represents the modes .
Energy associated with temperature and density fluctuations in NI turbulence are shown, respectively, in (a) and (b). Shown here are solid , dashed , and dashed-dot curves. The decay rates depends critically upon the Prandtl number Pr. The density and the temperature fluctuations are clearly anticorrelated in agreement with the prediction of Ref. 8.
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