Tuesday 08 Feb 2022: "Sound-proofing" fluid dynamics via Hamilton's principle
Dr Toby Wood - Newcastle University
In many geo- and astro-physical flows the dynamics of interest is much slower than the propagation of sound waves, which motivates using a "sound-proof" model in which acoustic waves are neglected (e.g. the incompressible, anelastic, or hydrostatic approximations). Such approximations are usually derived via formal asymptotics, by assuming a particular scaling for each physical quantity. An alternative approach is to obtain the equations of motion via Hamilton's Principle, having first obtained a suitable action for the physical system. This second approach guarantees that the model respects similar conservation laws to the exact system. We will demonstrate how this approach can be used to generalise existing sound-proof models, an in particular the pseudo-incompressible approximation. Time-permitting, we will also discuss an MHD generalisation of this model, and its application to magnetic buoyancy instability.