= Euler equation in a uniformly rotating frame
{c}
{title2=$\partial_t\mathbf u+(\mathbf u\cdot\nabla)\mathbf u+2\boldsymbol\Omega\times\mathbf u=-\nabla\Pi$}
For constant <mass density> $\rho_0$, a frame with constant <angular velocity> $\boldsymbol\Omega$ absorbs <centrifugal acceleration> into reduced <pressure> $\Pi=p/\rho_0-|\boldsymbol\Omega\times\mathbf r|^2/2$. Indeed $\boldsymbol\Omega\times(\boldsymbol\Omega\times\mathbf r)=-\nabla|\boldsymbol\Omega\times\mathbf r|^2/2$. Transforming the <material acceleration> in the <Euler equations> gives the displayed equation. The <Coriolis acceleration> remains velocity dependent and cannot be absorbed into a scalar potential. A conservative physical <body force> can be included by adding its potential to $\Pi$.
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