Large-scale energy and pressure dynamics in decaying 2D incompressible isotropic turbulence.
Résumé
Numerical simulations using either molecular or hyper-viscosity are carried out to study the temporal evolution of large-scale energy and pressure statistics in decaying two-dimensional incompressible isotropic turbulence. Initial Gaussian velocity fields peaking at small scales are considered. For each set of initial parameters, multiple realizations are performed to achieve reasonable statistical convergence. A wide range of Reynolds numbers (based on an equivalent Taylor microscale) is explored. For an initial energy spectrum E(k,0) ∝ k s 0 as k → 0 with s 0 ≥ 3, and at high enough Reynolds number, the numerical simulations display an important energy backscatter at subsequent times: E(k,t) ∝ t γ e k s , where s ≈ 3 and γ e converges at high times towards 2.5. The pressure spectrum E pp (k,0) is initially proportional to k 1 at small wavenumbers, in agreement with the predictions of quasi-normal theory. After a short transient decay, the infrared pressure spectrum increases significantly with time, while becoming steeper than k 1. However, a Gaussian randomization of the velocity allows the k 1 pressure spectrum to be recovered. In the high-Reynolds-number regime, the infrared pressure spectrum increases enough to induce a temporal growth of the pressure variance. We examine self-similar behaviours based on Taylor, integral and dissipative scales. Finally, we determine pressure pdf's, which compare favourably with earlier analytic predictions based on shell models made by Holzer and Siggia.
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