= Reynolds-stress energy production in a shearing sheet
For shear $\mathbf u_0=-2Ax\mathbf e_y$, the spatially averaged perturbation <kinetic energy> obeys $dE/dt=2A\rho\langle u_x'u_y'\rangle-\rho\nu\langle|\nabla\mathbf u'|^2\rangle$. <Pressure> and the <Coriolis force> do no net work. Thus positive radial-azimuthal velocity correlation extracts mean-flow <energy>. A leading two-dimensional <shearing wave> has $\operatorname{Re}(v_xv_y^*)=-k_xk_y|Z|^2/k^4>0$.
// Target: astrophysics.bigb
Back to article page
