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The Mathematics of Marine Modelling

Part of the Mathematics of Planet Earth Book Series (volume 9)

Editors: Schuttelaars, Henk; Heemink, Arnold; Deleersnijder, Eric

DOI: 10.1007/978-3-031-09559-7

ISBN: 978-3-031-09558-0

Publisher: Springer International Publishing - Springer Journals

Dec 1, 2022

1 - 10 of 11 Chapters

LitStream

Chapter 1Basic Equations of Marine Flows

Klingbeil, Knut; Deleersnijder, Eric; Fringer, Oliver; Umlauf, Lars

Pages: 1 –9

[The modeling of ocean basins, coastal seas, estuaries, and lagoons requires an adequate mathematical description of the state of the fluid in these systems. The state can be characterised by a set of macroscopic variables including density, velocity, temperature, concentrations of salt and other...
LitStream

Chapter 2Water Waves in Isotropic and Anisotropic Media: A comparison

Maas, Leo R. M.

Pages: 11 –44

[Restoring forces as gravity, Coriolis force or their combination, endow geo and astrophysical fluids with an anisotropy direction. Breaking the underlying hydrostatic or cyclostrophic force balances in fluids that are stratified in density or angular momentum results in obliquely-propagating...
LitStream

Chapter 3A Review of Nonlinear Boussinesq-Type Models for Coastal Ocean Modeling

Dawson, Clint; Samii, Ali

Pages: 45 –71

[We review some of the key developments in wave models used in the coastal oceanography. To this end, we first recall the well-known shallowness, nonlinearity, and topography parameters, which are used to describe the dominant features in our problem. Next, we compare different wave models based...
LitStream

Chapter 4Tides in Coastal Seas. Influence of Topography and Bottom Friction

Roos, Pieter C.; de Swart, Huib E.

Pages: 73 –102

[Tides are important in various ways, e.g., by affecting navigation and coastal safety and by acting as a driver for sediment transport and seabed dynamics. To explain spatial patterns of tidal phase and range, observed in coastal seas around the world, we present an idealised process-based...
LitStream

Chapter 5Variational Water-Wave Modeling: From Deep Water to Beaches

Bokhove, Onno

Pages: 103 –134

[The mathematical and numerical modelling of free-surface water waves is considered from the viewpoint of variational principles combined with finite-element discretisations. Luke’s classical variational principle (VP) is derived first, as opposed to Luke’s (ingenious) positing of his VP, and...
LitStream

Chapter 6Quasi-2D Turbulence in Shallow Fluid Layers

Clercx, Herman J. H.

Pages: 135 –165

[Flows in thin fluid layers, like in the Earth’s atmosphere or oceans, tend to behave as quasi-two-dimensional flows. Their dynamics is strikingly different from three-dimensional flows, and main features of the flow dynamics can be understood by considering two-dimensional (2D) fluid flows....
LitStream

Chapter 7Turbulent Dispersion

Cushman-Roisin, Benoit

Pages: 167 –196

[This chapter proposes a novel method for the modeling of turbulent dispersionTurbulent dispersion in the absence of buoyancy effects. Starting from a few salient observations, properties that an effective model should possess are identified, and a model is subsequently developed to incorporate...
LitStream

Chapter 8Spreading and Mixing in Near-Field River Plumes

Hetland, Robert D.

Pages: 197 –211

[Near-field plumes are supercritical, jet-like regions of rapid flow expansion and strong mixing. The characteristics of near-field river plumes are described based on our understanding from numerical ocean models and observations. A simple mathematical model is presented that demonstrates two...
LitStream

Chapter 9Lagrangian Modelling of Transport Phenomena Using Stochastic Differential Equations

Heemink, Arnold; Deleersnijder, Eric; Shah, Syed Hyder Ali Muttaqi; Gräwe, Ulf

Pages: 213 –242

[When modelling transport processes in marine waters one might have to solve the advection-diffusion equation or one can simulate the stochastic behaviour of individual particles of the constituent under study. By using the well-established theory of stochastic differential equations (SDEs) it is...
LitStream

Chapter 10Morphodynamic Modelling in Marine Environments: Model Formulation and Solution Techniques

Schuttelaars, H. M.; Zitman, T. J.

Pages: 243 –285

[The bathymetry and geometry of coastal seas, barrier coasts and estuaries strongly influence tides and currents, and the associated transport of sediments. In turn, these transports result in a constantly evolving bathymetry and geometry, thus resulting in a feedback loop between bathymetry and...

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