In this paper, we prove the existence of analytic relative equilibria with holes for quasi-geostrophic shallow-water equations. More precisely, using bifurcation techniques, establish any m large enough two branches m-fold doubly-connected V-states bifurcating from annulus arbitrary size.

Simulated free surface transients in periodic urban layouts have been reported to be self-similar the space-time domain when averaged on scale of building period. Such self-similarity is incompatible with head loss model formulae used most porosity-based shallow water models. Verifying it experimentally thus salient importance. New dam-break flow laboratory experiments are reported, where two d...

The classical dam break problem has become the de facto standard in validating the nonlinear shallow water equations solvers. Moreover, the Nonlinear Shallow Water Equations (NSWE) are widely used for flooding simulations. While applied mathematics community is essentially focused on developing new numerical schemes, we tried to examine the validity of the mathematical model under consideration...

In this paper, we study basic properties of the diffusive wave approximation of the shallow water equations (DSW). This equation is a doubly non-linear diffusion equation arising in shallow water flow models. It has been used as a model to simulate water flow driven mainly by gravitational forces and dominated by shear stress, that is, under uniform and fully developed turbulent flow conditions...