The Mathematics of Marine Modelling : Water Solute and Particle Dynamics in Estuaries and Shallow Seas Over the past few decades numerical simulation has become instrumental in understanding the dynamics of seas coastal regions and estuaries. The decision makers rely more and more frequently on model results for the management of these regions. Some modellers are insufficiently aware of the theoretical underpinning of the simulation tools they are using. On the other hand a number of applied mathematicians tend to view marine sciences as a domain in which they would like to use the tools they have a good command of. Bridging the gap between model users and applied mathematicians is the main objective of the present book. In this respect a vast number of issues in which mathematics plays a crucial role will be addressed. Basic equations of marine flows Water waves in isotropic and anisotropic media: a comparison A Review of Nonlinear Boussinesq Type Models for Coastal Ocean Modeling Tides in coastal seas. Influence of topography and bottom friction Variational water wave modeling: from deep water to beaches Quasi 2D turbulence in shallow fluid layers Turbulent dispersion Spreading and mixing in near field river plumes Lagrangian modelling of transport phenomena using stochastic differential equations Morphodynamic modelling in marine environments: model formulation and solution techniques Wetting and Drying Procedures for Shallow Water Simulations Index.