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.