= Stellar thermal-wind balance
{title2=$\varpi\partial_z\Omega^2=\frac{g}{rc_p}\partial_\theta S$}
Taking the <curl> of axisymmetric <hydrostatic equilibrium> with centrifugal acceleration gives $\varpi\partial_z\Omega^2=(\nabla p\times\nabla\rho)_\phi/\rho^2$. For an approximately spherical <ideal gas> with constant composition, use $\nabla\rho=\nabla p/c_s^2-\rho\nabla S/c_p$ to obtain the displayed relation. Latitudinal <entropy> differences can support noncylindrical <differential rotation>. A <barotropic fluid> gives cylindrical rotation in this leading balance; the relation does not determine the transport stresses or circulation rate.
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