Incorporating linear dynamics and strong anisotropy in KS. Application to diffusion in rotating, stratified, MHD turbulence, and to aeroacoustics

Abstract

We discuss the merits of the Kinematic Simulation model for representing turbulence statistics, and especially the two-time velocity correlations in relation with Lagrangian dispersion or the acoustic emission of turbulence.We generalize the model to account for anisotropy, along two main axes. First, the discretization technique itself is modified to adapt automatically to anisotropic kinetic energy spectra, prescribed in the model. We discuss how the introduction of unsteadiness can be done from the classical assumption by relating the space and time spectra, but also by associating each wave vector with a pseudo dispersion frequency. In so doing, we show the importance of both the inclusion of a deterministic and a stochastic parts. In addition, the unsteadiness is related to the specific choice of a timescale associated with the sweeping or the straining hypothesis. A KSnew model is developed, in order to improve the original version (referred as KSorig in the following) along two lines: first, the randomization of the wave vector is more general, and it is possible to prescribe the fully anisotropic two-point second order statistics (energy-polarization-helicity) and not only the spherically averaged energy spectrum. Second, we present how to include in the KSnew model the explicit linear dynamics associated with the distortion of turbulence by external forces. Analytical solutions provided by the Rapid Distortion Theory are used, and we show that the thus-modeled velocity fields incorporate several anisotropic features that are consistent with the physics of e.g. rotating stratified turbulence or magneto-hydrodynamics turbulence. The corresponding detailed characterization of general axisymmetric anisotropy in spectral space is of general relevance in turbulent fields produced by Direct Numerical Simulations.