Large-scale energy and pressure dynamics in decaying 2D incompressible isotropic turbulence

Numerical simulations using either molecular or hyper-viscosity are carried out to study the temporal evolution of large-scale energy and pressure sta tistics in decaying two-dimensional incompressible isotropic turbulence. In itial Gaussian velocity fields peaking at small scales are considered. For each set of initial parameters, multiple realizations are performed to achi eve reasonable statistical convergence. A wide range of Reynolds numbers (b ased on an equivalent Taylor microscale) is explored. For an initial energy spectrum E(k, 0) proportional to K(s0)as k --> 0 with s(0) greater than or equal to 3, and at high enough Reynolds number, the numerical simulations display an important energy backscatter at subsequent times: E(k, t) propor tional to t(gammae)k(s), where s approximate to 3 and gamma (e) converges a t high times towards 2.5. The pressure spectrum E-pp(k, 0) is initially pro portional to k(1) at small wavenumbers, in agreement with the predictions o f 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) press ure spectrum to be recovered. In the high-Reynolds-number regime, the infra red pressure spectrum increases enough to induce a temporal growth of the p ressure variance. We examine self-similar behaviours based on Taylor, integ ral and dissipative scales. Finally, we determine pressure pdf's, which com pare favourably with earlier analytic predictions based on shell models mad e by Holzer and Siggia.