# Lateral Dynamics¶

The lateral dynamics are controlled in the namelist.dynamics. We have decided to experiment with the lateral eddy viscosity rn_ahm_0_lap, the biharmonic operator ln_dynldf_bilap, and the lateral boundary conditions for momentum set in the namelist.lateral.

## Lateral Eddy Viscosity¶

The lateral eddy viscosity controls how dissipative the simulation is. Since we are forcing tides at the Juan de Fuca boundary we would like the visocisty to be as small as possible in order to prevent tidal phase lags within the Strait of Georgia. We have had some success at reducing the lateral viscosity as outlined in the table below.

Simulation rn_ahm_0_lap ln_apr_dyn rn_avevd Notes
$$\nu=100$$ 100 true or false 10 stable
$$\nu=60$$ 60 false 10 stable
$$\nu=60$$ 60 true 10 unstable near islands
$$\nu=60$$ 60 true 100 stable
$$\nu=50$$ 50 false 10 unstable
$$\nu=40$$ 40 true 60 stable
$$\nu=40$$ 40 true 50 unstable near islands

These simulations were run on salish with model time seven days. The boolean ln_apr_dyn in namelist.surface controls forcing at the free surface due to atmospheric pressure. We are having difficulty with stability when this is set to true and the viscosity is lower than 100. Unfortunately, this type of forcing is likely important when modelling storm surges.

The parameter rn_avevd in namelist.dynamics controls the vertical eddy viscosity only in areas where/when the stratification is statically unstable. When the model is presented with an unstable stratification it locally increases the amount of vertical diffusion which effectively mixes the unstable region (see Vertical Mixing). Through our analysis, we have observed that the stability of the model at lower viscosities depends on how it treats vertical mixing. Thus, this parameter is likely important for achieving stability at low lateral viscosity. This must be investigated further.

We are still having trouble with stability during our spin up runs. See Spin-up Runs.

## Biharmonic Operator¶

The biharmonic operator dissipates energy selectively at smaller scales. It is a fourth order diffusive operator in the momentum equations and is chosen by modifiying ln_dynldf_bilap in namelist.dynamics. It can be used in conjuction with the second order laplacian operator. The AMM configuration employs the bilaplacian with rn_ahm_0_blp=-1e10 and $$\nu=60$$ for the laplacian operator. Note that AMM also uses free slip lateral boundary conditions and s-coordinates.

The biharmonic operator can be used in conjunction with the second order laplacian operator. Under the current resolution, typical values for the operator coefficient should be around rn_ahm_0_blp=-2000. Decreasing the magnitude of this parameter has some stablizing effect with little change in the maximum currents. However, the simulations with this operator in use still display overturning and poor behaviour in the vertical salinity profiles. A summary of simulations is given below.

Simulation rn_ahm_0_lap rn_ahm_0_blp rn_avevd Notes
apr60_nu50 50 none 60 unstable near islands
apr60_nu50_bi2000 50 -2000 60 unstable near islands
apr60_nu50_bi4000 50 -4000 60 unstable near islands
apr60_nu50_bi1000 50 -1000 60 stable, poorly behaved salinity

## Lateral Boundary Conditions¶

Currently we are using partial slip boundary conditions with rn_shlat =0.5 in namelist.lateral. No slip conditions are applied when rn_shlat =2 and free slip when rn_shlat =0.

At $$\nu=50$$, we have seen some stablizing features as we take the lateral boundary torwards no slip. It seems that the no slip conditions change the location of the maximum velocities in the island regions, which can have an affect on the mixing. Our concern with no slip stems from resolving the boundary layer. We fear that using no slip BCs will leave the boundary layer unresolved, especially at lower viscosity.

Simulation rn_ahm_0_lap rn_shlat rn_avevd Notes
partial25/apr100_nu50 50 0.25 100 unstable at Stuart Island
apr60_nu50 50 0.5 60 unstable near islands
partial1/apr60_nu50 50 1 60 stable
noslip/apr60_nu50 50 2 60 stable