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Abstract
We consider the dynamics of a set of reduced equations describing the evolution of a magnetised, rotating stably stratified fluid layer, atop a stagnant dense, perfectly conducting layer. We consider two closely related models. In the first, the layer has, above it, relatively light fluid where the magnetic pressure is much larger than the gas pressure, and the magnetic field is largely forcefree. In the second model, the magnetic field is constrained to lie within the dynamical layer by the implementation of a model diffusion operator for the magnetic field. The model derivation proceeds by assuming that the horizontal velocity and the horizontal magnetic field are independent of the vertical coordinate, whilst the vertical components in the layer have a linear dependence on height. The full system comprises evolution equations for the magnetic field, horizontal velocity and height field together with a linear elliptic equation for the vertically integrated nonhydrostatic pressure. In the magnetohydrostatic limit, these equations simplify to equations of shallowwater type. Numerical solutions for both models are provided for the fiducial case of a Gaussian vortex interacting with a magnetic field. The solutions are shown to differ negligibly. We investigate how the interaction of the vortex changes in response to the magnetic Reynolds number Rm, the Rossby deformation radius L_{D}, and a Coriolis buoyancy frequency ratio f/N measuring the significance of nonhydrostatic effects. The magnetohydrostatic limit corresponds to f/N→0.
Original language  English 

Article number  A17 
Number of pages  27 
Journal  Journal of Fluid Mechanics 
Volume  973 
Early online date  17 Oct 2023 
DOIs  
Publication status  Published  25 Oct 2023 
Keywords
 Shallow water flows
 Magnetic fluids
 Contour dynamics
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 1 Finished

A Fudemental reassessment of shallow: A Fundamental reassessment of shallowwater fluid dynamics
Dritschel, D. G. (PI)
1/01/21 → 31/12/21
Project: Fellowship