Atmospheric flows feature length scales from 10− 5 to 105 m and timescales from
microseconds to weeks or more. For scales above several kilometers and minutes, there is a …

These notes are devoted to the study of some problems related to shallow-water equations.
In particular, we will review results from derivations of shallow-water systems which depend …

We consider the system of partial differential equations governing the one-dimensional flow
of two superposed immiscible layers of shallow water. The difficulty in this system comes …

The present book is entirely devoted to the development of mathematical models and
numerical algorithms to simulate the generation and propagation of long surface water …

Turbulence and the associated turbulent transport of scalar and vector fields is a classical
physics problem that has dazzled scientists for over a century, yet many fundamental …

The thermal shallow water equations provide a depth-averaged description of motions in a
fluid layer that permits horizontal variations in material properties. They typically arise …

The present work is devoted to the derivation of a fully well-balanced and positivepreserving
numerical scheme for the shallow water equations with Coriolis force. The first main issue …

We consider a singular limit problem for the Navier–Stokes system of a rotating
compressible fluid, where the Rossby and Mach numbers tend simultaneously to zero. The …

Lie symmetry analysis is applied to study the non-linear rotating shallow-water equations.
The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is …

We review here the derivation of many of the most important models that appear in the
literature (mainly in coastal oceanography) for the description of waves in shallow water. We …