= Landau angular-momentum argument for turbulent decay
{c}
For a confined <incompressible flow> with no velocity flux across the boundary, an integrated divergence identity gives $\langle|\int\boldsymbol x\times\boldsymbol u\,dV|^2\rangle=-\iint r^2\langle\boldsymbol u\cdot\boldsymbol u'\rangle dVdV'$. In a large approximately homogeneous region with short correlations, the latter is approximately $VI$. <Conservation of angular momentum> in an isolated torque-free cloud then motivates conservation of the <Loitsyansky integral>. A fixed subvolume of infinite turbulence is not an isolated cloud: advective transport, pressure torques, wall stresses and long-range correlations can invalidate the argument.
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