We extend the formalism of statistical mechanics developed for the two-dimensional (2D) Euler equation to the case of shallow water system. Relaxation equations towards the maximum entropy state are proposed, which provide a parametrization of subgrid-scale eddies in 2D compressible turbulence.

The complex interplay between depositional facies and diagenesis in dolostones presents numerous challenges for calculating petrophysical properties from wireline logs. Complex pore geometries and mineralogies control rock petrophysical properties, and equations for calculating porosities and saturations must therefore be tailored to specific pore geometry-mineralogy combinations. The complex m...

In this report we will discuss some numerical techniques for approximating the Shallow Water equations. In particular we will discuss finite difference schemes, adaptations of Roe’s approximate Riemann solver and the Q-Schemes of Bermudez & Vazquez with the objective of accurately approximating the solution of the Shallow Water equations. We consider four different test problems for the Shallow...

On the basis of the integrable Kaup–Boussinesq version of the shallow-water equations, an analytical theory of undular bores is constructed. A complete classification for the problem of the decay of an initial discontinuity is made.

The method of weak asymptotics is used to find singular solutions of the shallow-water system which can contain Dirac-δ distributions (Espinosa & Omel’yanov, 2005). Complex-valued approximations which become real-valued in the distributional limit are shown to extend the range of possible singular solutions. It is shown, in this paper, how this approach can be used to construct solutions contai...

The traditional shallow water model for waves propagating over varying bathymetry depends for its derivation on the asymptotic analysis of a Dirichlet-Neumann operator. This analysis however is restricted to smoothly varying topographies. We propose an adaptation to one dimensional polygonal bottoms using the conformal mapping idea of Hamilton and Nachbin. The asymptotic analysis of the Dirichl...

Early ontogenetic adaptations reflect the evolutionary history of a species. To understand the evolution of the deep-sea fauna and its adaptation to high pressure, it is important to know the effects of pressure on their shallow-water relatives. In this study we analyse the temperature and pressure tolerances of early life-history stages of the shallow-water species Mytilus edulis. This species...