Reynolds stress and eddy diffusivity of beta-plane shear flows

Srinivasan, K, Young WR.  2014.  Reynolds stress and eddy diffusivity of beta-plane shear flows. Journal of the Atmospheric Sciences. 71:2169-2185.

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circulation, convection, couette-flow, disturbances, mean flows, moist, numerical simulations, shallow-water turbulence, suppression, Vorticity, zonal jets


The Reynolds stress induced by anisotropically forcing an unbounded Couette flow, with uniform shear gamma, on a beta plane, is calculated in conjunction with the eddy diffusivity of a coevolving passive tracer. The flow is damped by linear drag on a time scale mu(-1). The stochastic forcing is white noise in time and its spatial anisotropy is controlled by a parameter alpha that characterizes whether eddies are elongated along the zonal direction (alpha < 0), are elongated along the meridional direction (alpha > 0), or are isotropic (alpha = 0). The Reynolds stress varies linearly with alpha and nonlinearly and nonmonotonically with gamma, but the Reynolds stress is independent of beta. For positive values of alpha, the Reynolds stress displays an "antifrictional" effect (energy is transferred from the eddies to the mean flow); for negative values of alpha, it displays a frictional effect. When gamma/mu << 1, these transfers can be identified as negative and positive eddy viscosities, respectively. With gamma = beta = 0, the meridional tracer eddy diffusivity is (upsilon'(2)) over bar (2 mu), where upsilon' is the meridional eddy velocity. In general, nonzero beta and gamma suppress the eddy diffusivity below (upsilon'(2)) over bar (2 mu). When the shear is strong, the suppression due to gamma varies as gamma(-1) while the suppression due to beta varies between beta(-1) and beta(-2) depending on whether the shear is strong or weak, respectively.