# Mathematical Model K-MODEL

### From BAWiki

## short description

The mathematical model k-model is a spectral wave model with non-linear dissipation which was developed at GKSS Research Center (Geesthacht). The model can be used to compute the development, propagation and dissipation of waves, sea and swell in the ocean, coastal waters or estuaries. It uses a source function which describes dissipation by wave turbulence interaction. The use of action density in (k,Θ)-co-ordinates as a prognostic field in the model enables a convenient treatment of instationary systems, e.g. systems with tidal influence.

The k-model is able to work on unstructured orthogonal grids (UOG). The modelling domain is covered by a grid consisting of a set of non-overlapping convex polygons, usually either triangles or quadrilaterals. The grid is said to be an unstructured orthogonal grid if within each polygon a point (hereafter called a center) can be identified in such a way that the segment joining the center of two adjacent polygons and the side shared by the two polygons, have a non-empty intersection and are orthogonal to each other.

Areas with pronounced variations in bathymetry as well as current velocity do often occur in coastal water bodies. Due to the use of an unstructured grid concept these areas of strong variations may be discretized with sufficiently high resolution in order to arrive at a good quality for simulated results related to processes like shoaling or current refraction of waves.

## physical processes

- conservation of wave action density (action density balance equation);
- advection of wave action density due to currents;
- shoaling of waves due to variation of water depth and/or current velocity;
- refraction of waves due to horizontal gradients of water depth and/or current velocity;
- wind forcing at the free surface;
- dissipation due to turbulent diffusion;
- dissipation due to bottom friction.

## computational results

- integral wave parameters for waves, sea and swell:

- significant wave height;
- wave peak period;
- wave mean period TM-1;
- wave period TM1;
- wave period TM2;
- wave mean direction;
- wave mean directional spread;
- acceleration (due to radiation stress).

- two-dimensional spectra for waves, sea and swell:

- frequency-direction wave spectrum.

## publications

- Schneggenburger, C. (1997) : Shallow Water Wave Modelling with Nonlinear Dissipation, Deutsche Hydrographische Zeitschrift, 49, 431--444.
- Schneggenburger, C. (1998) : Spectral Wave Modelling with Nonlinear Dissipation, Dissertation, 117 Seiten, Bericht Nr. GKSS 98/E/42, GKSS-Forschungszentrum Geesthacht, Germany.
- Schneggenburger, C., Günther, H. and Rosenthal, W. (1998) : Shallow Water Wave Modelling with Non-Linear Dissipation: Application to Small Scale Tidal Systems, in Proc. 5th Int. Workshop Wave Hindcasting and Forecasting, 242--255, Melbourne, FL, USA.
- Schneggenburger, C., Günther, H. and Rosenthal, W. (2000) : Shallow Water Wave Modelling with Non-Linear Dissipation: Validation and Applications in a Coastal Tidal Environment, Coastal Engineering, 41, 201--235.
- Werft, A. (2003) : Surface Wave Modelling in the Wadden Sea, Diplomarbeit, 83 Seiten, Institut für Chemie und Biologie des Meeres, Carl-von-Ossietzky Universität Oldenburg, Germany.

## validation document

An independent validation document is currently not available for the k-model. In this context the reader is referred to the above mentioned literature, i.e. Schneggenburger (1998).

A PDF-version of this dissertation is freely available for download:

## user interface description

Currently not available.

## users (in alphabetical order)

- Gayer. G., GKSS Helmholtz-Zentrum Geesthacht, Zentrum für Material- und Küstenforschung, Geesthacht, Germany;
- Günther, H., GKSS Helmholtz-Zentrum Geesthacht, Zentrum für Material- und Küstenforschung, Geesthacht, Germany; (meanwhile retired)
- Winkel, N., Bundesanstalt für Wasserbau, Dienststelle Hamburg - Wasserbau im Küstenbereich, Hamburg, Germany.

In all of the above mentioned organizations, k-model is applied by a larger number of users, compared to the people listed. People mentioned are the main contact persons and speakers for their respective organization concerning all questions related to applications of the k-model and related developments.

## BAW-specific informations

## grid generation

An unstructured orthogonal grid for UNTRIM can be prepared using JANET grid generator software, made by SmileConsult. For further informations related to the integration of JANET into BAW's programming environment please visit JANET program description.

## simulation

Actually the k-model can be used as a stand-alone postprocessor UNK as well as directly coupled to the three-dimensional mathematical model UNTRIM for hydrodynamics and transport processes.

## graphical presentation of computed results

To display UNTRIM results currently several methods are used at BAW. The more important ones are,

- HVIEW2D, for data available throughout the computational domain,
- VVIEW2D and/or LQ2PRO, for data at longitudinal- and/or cross-sections, as well as
- GVIEW2D, for data at specific locations.

## analyses of computational results

A great variety of methods for analyses of computational results is available which enables the user to respond to many different questions.

## coupling to independent sub-models

At BAW the k-model can be actually used in direct connexion to the following physical sub-models:

- three-dimensional hydrodynamic and transport model UNTRIM;
- sedimentological model SediMorph (see sedimorph.dat).

The above mentioned sub-models can be used together with the k-model.

back to Mathematical Models for Coastal Areas and Estuaries