The rigid-lid approximation is a commonly used simplification in the study of densitystratified fluids in oceanography. Roughly speaking, one assumes that the displacements of the surface are negligible compared with interface displacements. In this paper, we offer a rigorous justification of this approximation in the case of two shallow layers of immiscible fluids with constant and quasi-equal...

This paper reviews the problem of a thin rigid rod sliding on a horizontal surface in the plane, which is commonly cited as an example of the inconsistency of planar rigid-body Newtonian mechanics. We demonstrate the existence of a consistent solution, using Routh's analysis of rigid-body impact. Copyright © 1987 Carnegie-Mel lon University This work was supported under grants from the System D...

This paper discusses the well posedness of an initial value problem describing motion a Bingham fluid in basin with degenerate bottom topography. A physical interpretation such is discussed. The system governing obtained from Shallow Water-Bingham models regime where Froude number degenerates, i.e taking limit equations as tends to zero. Since we are considering coefficients, then shall work we...

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.