= Infinite-Prandtl-number convection
{title2=$\operatorname{Pr}\to\infty$}
In thermal-time units, taking the <Prandtl number> large removes momentum inertia at leading order. The <Stokes flow> momentum equation then determines <velocity> instantaneously from the <temperature> perturbation, while the nonlinear <heat equation> retains its time derivative. Small <Prandtl number> does not generally give this model. An exact contrasting shear in a free-slip layer is $u=U_0e^{-\operatorname{Pr}\pi^2t}\cos\pi z$, $w=\theta=0$: it decays slowly as the <Prandtl number> tends to zero but is excluded by the instantaneous Stokes equation.
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