1.3.7. Forcing/dissipation¶

1.3.7.1. Forcing¶

The forcing terms $$\mathcal{F}$$ on the rhs of the equations are provided by ‘physics packages’ and forcing packages. These are described later on.

1.3.7.2. Dissipation¶

1.3.7.2.1. Momentum¶

Many forms of momentum dissipation are available in the model. Laplacian and biharmonic frictions are commonly used:

(1.41)$D_{V}=A_{h}\nabla _{h}^{2}v+A_{v}\frac{\partial ^{2}v}{\partial z^{2}} +A_{4}\nabla _{h}^{4}v$

where $$A_{h}$$ and $$A_{v}\$$are (constant) horizontal and vertical viscosity coefficients and $$A_{4}\$$is the horizontal coefficient for biharmonic friction. These coefficients are the same for all velocity components.

1.3.7.2.2. Tracers¶

The mixing terms for the temperature and salinity equations have a similar form to that of momentum except that the diffusion tensor can be non-diagonal and have varying coefficients.

(1.42)$D_{T,S} = \nabla \cdot \left[ \boldsymbol{K} \nabla (T,S) \right] + K_{4} \nabla _{h}^{4}(T,S),$

where $$\boldsymbol{K}$$ is the diffusion tensor and $$K_{4}\$$ the horizontal coefficient for biharmonic diffusion. In the simplest case where the subgrid-scale fluxes of heat and salt are parameterized with constant horizontal and vertical diffusion coefficients, $$\boldsymbol{K}$$, reduces to a diagonal matrix with constant coefficients:

(1.43)$\begin{split}\qquad \qquad \qquad \qquad \boldsymbol{K} = \left( \begin{array}{ccc} K_{h} & 0 & 0 \\ 0 & K_{h} & 0 \\ 0 & 0 & K_{v} \end{array} \right) \qquad \qquad \qquad\end{split}$

where $$K_{h}\$$and $$K_{v}\$$are the horizontal and vertical diffusion coefficients. These coefficients are the same for all tracers (temperature, salinity … ).