Freshwater cylinder test-case

Objectives To compare with Tartinville et al. 94 results of a similar test-case To compare with Tartinville et al. 94 results of a similar test-case To determine wether Mohid can produce similar results, and depthen the knowledge on baroclinic and barotropic instabilities To determine wether Mohid can produce similar results, and depthen the knowledge on baroclinic and barotropic instabilities To test-case the several advection schemes presents within Mohid To test-case the several advection schemes presents within Mohid

The model setup Domain Domain domain depth: 20 m domain depth: 20 m domain size: 30 x 30 km (without relaxation zone) domain size: 30 x 30 km (without relaxation zone) latitude: 52ºN latitude: 52ºN => Coriolis: f=1.15x10E-4 s-1 => Coriolis: f=1.15x10E-4 s-1 horizontal grid resolution: 1 km horizontal grid resolution: 1 km geometry: 20 levels (equally spaced?) geometry: 20 levels (equally spaced?) Cylinder Cylinder depth: 10 m depth: 10 m radius: 3 km radius: 3 km => S = 1.1 * (d/3)^ => S = 1.1 * (d/3)^

The model setup Density Density linear: rho = *(S-33.75) linear: rho = *(S-33.75) Simulation time Simulation time T = 144 h = 6 d T = 144 h = 6 d Vertical boundaries Vertical boundaries Bottom stress: none Bottom stress: none Surface stress (wind): none Surface stress (wind): none

The model setup Vertical viscosity Vertical viscosity none or minimal value none or minimal value Horizontal viscosity Horizontal viscosity none or minimal value none or minimal value Vertical diffusivity Vertical diffusivity none or minimal value none or minimal value Horizontal diffusivity Horizontal diffusivity none or minimal value none or minimal value Hydrodynamic Open boundary Hydrodynamic Open boundary Water level: four-points-wide relaxation to zero (coefficients of 1, , 0.25, ). Water level: four-points-wide relaxation to zero (coefficients of 1, , 0.25, ). momentum: no advection of momentum at the boundaries i.e. null-gradient(?) momentum: no advection of momentum at the boundaries i.e. null-gradient(?) Waterproperties Open boundary Waterproperties Open boundary Salinity: four-points-wide relaxation to psu (ambient salinity) (coefficients of 1, , 0.25, ). Salinity: four-points-wide relaxation to psu (ambient salinity) (coefficients of 1, , 0.25, ).

The model setup Hydrodynamic options: Hydrodynamic options: Coriolis: on Coriolis: on Baroclinic: on Baroclinic: on Inertial: on Inertial: on Advection: on Advection: on Diffusion: off or minimum Diffusion: off or minimum Waterproperties options: Waterproperties options: Salinity Salinity Advection: on Advection: on Diffusion: off Diffusion: off InitialCondition: ASCII InitialCondition: ASCII DefaultValue: DefaultValue: Temperature Temperature AdvectionDiffusion: off AdvectionDiffusion: off RemainConstant: on RemainConstant: on DefaultValue: To DefaultValue: To

The battery test RunMomentum_HorMomentum_VertSal_HorSal_Vert :424:4 334:434:4 44:44:44:44:4 case Method: *Upwind1 *Upwind22 *Upwind33 *CentralDif or LeapFrog5 or 6 *P2_TVD4 case TVD_Limitation(4): *MinMod1 *VanLeer2 *Muscl3 *PDM5 *SuperBee4

The descriptive results

Comparing with Tar94 2nd order instability

The energy study

Observations The results are quite good for KE The results are quite good for KE The results can become good for PE The results can become good for PE Reproducing the same amount of vorticity wasn’t yet accomplished by the modeler Reproducing the same amount of vorticity wasn’t yet accomplished by the modeler Decent extrema of salinity are yet to come if it is ever possible Decent extrema of salinity are yet to come if it is ever possible The behavior of the model is different between radiation and relaxation boundary conditions. Without radiation the gravity waves cannot leave and hence they sum up to the noise of the model. Radiative boundaries gave here better results The behavior of the model is different between radiation and relaxation boundary conditions. Without radiation the gravity waves cannot leave and hence they sum up to the noise of the model. Radiative boundaries gave here better results

Questions What is APE? What is the physical information behind PE? What is APE? What is the physical information behind PE? Why does the model gives different results for PE, ranging from 1 order of magnitude? Why does the model gives different results for PE, ranging from 1 order of magnitude? Why isn’t there the same amount of vorticity as for the other models? Why isn’t there the same amount of vorticity as for the other models?

Conclusions The model can reproduce the experiment under nearly the same conditions. It apparently requires radiative boundaries for such task. The model can reproduce the experiment under nearly the same conditions. It apparently requires radiative boundaries for such task. The model can develop fourth-order instabilities for less diffusive schemes. The model can develop fourth-order instabilities for less diffusive schemes. The model doesnt’ reproduces the same amount of enstrophy as predicted. The model doesnt’ reproduces the same amount of enstrophy as predicted. The treatment of the boundary conditions need to be further investigated The treatment of the boundary conditions need to be further investigated