Reduced models for fluid flows with strong constraints

The presence of a dominant balance in the equations for fluid flow can be exploited to derive an asymptotically exact but simpler set of governing equations. These permit semianalytical and/or numerical explorations of parameter regimes that would otherwise be inaccessible to direct numerical simulation. The derivation of the resulting reduced models is illustrated here for (i) rapidly rotating convection in a plane layer, (ii) convection in a strong magnetic field, and (iii) the magnetorotational instability in accretion disks and the results used to extend our understanding of these systems in the strongly nonlinear regime.