Dissipation
Description
In the LMD grid point model, nonlinear interactions between explicitly resolved scales and subgrid-scale processes are parameterized by applying a scale-selective horizontal dissipation operator based on an $$n$$ time iterated Laplacian $$\Delta^n$$. For the grid point model, for instance, this can be written:
\begin{align}
\label{def:Wns}
\frac{\partial q}{\partial t} = \frac{(-1)^n}{\tau_{diss}}(\delta x)^{2n}\Delta^nq
\end{align}
where $$q$$ is a field component on which disspation is applied, $$\delta x$$ is the smallest horizontal distance represented in the model and $$\tau_{diss}$$ is the dissipation timescale for a structure of scale $$\delta x$$. These operators are necessary to ensure the grid point model numerical stability. In practice, the operator is separately applied to three components :
- the divergence of the flow,
- the vorticity of the flow,
- potential temperature.
We classically use n = 2, n = 1,and n = 2.
How to change it in the model
In practise, the values of $$n$$ and $$\tau_{diss}$$ are prescribed in the run.def with the keys:
- nitergdiv
- nitergrot
- niterh
for the values of $$n$$ on each field, and the associated $$\tau$$:
- tetagdiv
- tetagrot
- tetatemp
In run.def, there is also a key idissip which is the frequency (in dynamical steps) at which to apply the dissipation.
Good to know rules and rules of thumb
- If your simulation shows numerical instabilities, a good idea is to increase dissipation. This means decreasing parameters $$\tau$$.
- Optimal values for the dissipation timescales depends on the resolution of the horizontal grid. The higher the resolution, the more dissipation we need.
