A generic model for transport in turbulent shear flows

Turbulence regulation by large-scale shear flows is crucial for a predictive modeling of transport in plasma. In this paper the suppression of turbulent transport by large-scale flows is studied numerically by measuring the turbulent diffusion D-t and scalar amplitude < n('2)> of decaying passive scalar fields n' advected by various turbulent flows. Both uniform flows and shear flows are shown to suppress turbulence causing the quenching in transport and turbulence amplitude. The uniform flows U-0 = Lambda y with the advection rate K in the case of a finite correlated forcing with tau(F) 1 gives rise to the advection/sweeping effect which suppresses D-t, < u'(2)> and < n'(2)> as proportional to Lambda(-2) for Lambda >> tau(-1)(F) F. In contrast, no influence of the uniform flow is found in the case of a short correlated forcing tau(F) > 0 due to Galilean invariance. For the shear flow U-0 Omega sin x (y) over cap (Omega = constant shearing rate) with the appropriate choice of the forcing (tau(F) > 0) the nature of transport suppression is shown to crucially depend on the properties of the turbulence. Specifically, for prescribed turbulence with a short correlation time tau(F) = tau(F) << Omega(-1), the turbulence statistics scale as D-t proportional to Omega(-0.02), < n'(2)> proportional to Omega(-0.62) and cross-phase cos theta proportional to Omega(0.29). For consistently evolved turbulence with a finite correlation time tau(c) >= Omega(-1), turbulence statistics are suppressed more strongly as D-t proportional to Omega(1.75), < n'(2)> proportional to Omega(2.41), < u'(x)2 > proportional to Omega(0.65) and <omega'(2)> proportional to Omega(0.50). A novel renormalization scheme is then introduced to rescale our results into the regime within which the kinetic energy and enstrophy are unchanged by shear flow. This allows our numerical results to closely match previous analytical predictions [E. Kim, Mod. Phys. Lett. B 18, 1 (2004)] and to understand different experimental scalings observed in laboratory plasmas. Furthermore, Dt is found to be related to < n'(2)> by < n'(2)> proportional to D-t/D-Omega, where D-Omega proportional to Omega(2/3) is the shear accelerated diffusion of n' with an interesting scaling cos theta proportional to root DtD Omega. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3582097]