The response of isotropic turbulence to isotropic and anisotropic forcing at the large scales

Abstract

The nonlinear interscale couplings in a turbulent flow are studied through direct numerical simulations of the response of isotropic turbulence to isotropic and anisotropic forcing applied at the large scales. Specifically, forcing is applied to the energy‐containing wave‐number range for about two eddy turnover times to fully developed isotropic turbulence at Taylor‐scale Reynolds number 32 on an 1283 grid. When forced isotropically, the initially isotropic turbulence remains isotropic at all wave numbers. However, anisotropic forcing applied through an array of counter‐rotating rectilinear vortices induces high levels of anisotropy at the small scales. At low wave numbers the force term feeds energy directly into two velocity components in the plane of the forced vortices. In contrast, at high wave numbers the third (spanwise) component receives the most energy, producing small‐scale anisotropy very different from that at the large scales. Detailed analysis shows that the development of small‐scale anisotropy is caused primarily by nonlocal wave‐vector triads with one leg in the forced low‐wave‐number range. This latter result is particularly significant because asymptotic analysis of the Fourier‐transformed Navier–Stokes equations shows that distant triadic interactions coupling the energy‐containing and dissipative scales persist at asymptotically high Reynolds numbers, suggesting that the structural couplings between large and small scales in these moderate Reynolds number simulations would also exist in high Reynolds number forced turbulence. The results therefore imply a departure from the classical hypothesis of statistical independence between large‐ and small‐scale structure and local isotropy.