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We present results from the first fully relativistic simulations of the critical collapse of rotating radiation fluids. We observe critical scaling both in subcritical evolutions-in which case the fluid disperses to infinity and leaves behind flat space-and in supercritical evolutions, which lead to the formation of black holes. We measure the mass and angular momentum of these black holes, and...

In this paper we develop and test a structure-preserving discretization scheme for rotating and/or stratified fluid dynamics. The numerical scheme is based on a finite dimensional approximation of the group of volume preserving diffeomorphisms recently proposed in [25, 9] and is derived via a discrete version of the Euler-Poincaré variational formulation of rotating stratified fluids. The resul...

We consider a singular limit problem for the NavierStokes system of a rotating compressible fluid, where the Rossby and Mach numbers tend simultaneously to zero. The limit problem is identified as the 2-D Navier-Stokes system in the “horizontal” variables containing an extra term that accounts for compressibility in the original system.

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PART I. GENERAL CONSIDERATIONS