Influence of zero-modes on the inertial-range anisotropy of Rayleigh-Taylor and unstably stratified homogeneous turbulence

The purpose of this work is to study the anisotropic properties of the inertial range of Rayleigh-Taylor and unstably stratified homogeneous (USH) turbulence. More precisely, we aim to understand the role played by the so-called zero-modes, i.e., modes that nullify the anisotropic part of transfer terms. To this end, we determine several characteristic properties of zero-modes using an eddy-damped quasinormal Markovianized (EDQNM) model. Then we perform a high-Reynolds-number EDQNM simulation of a USH flow and check whether the predicted zero-mode properties are indeed observed in this idealized setting. Finally, we carry out a large-eddy simulation of a Rayleigh-Taylor flow and verify if zero-modes can also be identified in this configuration. Among the main findings of this work, we show that the small-scale anisotropy of the velocity and concentration spectra is dominated by the nonlocal contribution of zero-modes rather than by the local action of buoyancy forces. As a result, we predict inertial scaling exponents close to -7/3 (rather than -3) for the second-order harmonics of the velocity and concentration spectra. By contrast, the concentration flux spectrum remains controlled by buoyancy forces. Still, we show that the zero-mode contribution vanishes slowly as the Reynolds number increases. This translates into a slow convergence of the scaling exponent of the second-order harmonic of the concentration flux to -7/3.