forcing_dissip.rst

Forcing/dissipation

Forcing

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

Dissipation

Momentum

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

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

where A_h and A_v are (constant) horizontal and vertical viscosity coefficients and A₄ is the horizontal coefficient for biharmonic friction. These coefficients are the same for all velocity components.

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.

$$D_{T,S}=\nabla .[\underline{\underline{K}}\nabla (T,S)]+K_{4}\nabla _{h}^{4}(T,S)$$

where $\underline{\underline{K}}\ $is the diffusion tensor and the K₄  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, $\underline{\underline{K}}$, reduces to a diagonal matrix with constant coefficients:

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

where K_h and K_v are the horizontal and vertical diffusion coefficients. These coefficients are the same for all tracers (temperature, salinity ... ).