# 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 … ).