Turbulence schemes in GOTM

"Big whorls have little whorls,
That feed on their velocity,
And little whorls have lesser whorls,
and so on to viscosity".

L.F. Richardson (1922)


In the turbulent module of GOTM, eddy mixing coefficients are calculated for momentum and tracers. It is assumed that all tracers have the same eddy diffusivity, which is based on the assumption of fully developed turbulence. In order to account for differential turbulent mixing of temperature and salinity in the low-turbulent bulk of the oceans, the group of Vittorio Canuto (New York) is currently working on a suitable algorithm.

The eddy viscosity for momentum and the eddy diffusivity for tracers is calculated as the product of a non-dimensional stability functions, normalised turbulent kinetic energy (TKE) k and macro length scale L. The stability functions are result of various second-moment closures, the TKE and the length scales are either calculated by dynamic equations (as in k-epsilon or Mellor-Yamada models) or algebraic formulations.

Mechanism
Parameterizations
BOUNDARY LAYER TURBULENCE
Isotropic turbulence generated by wind stirring, bottom friction, negative buoyancy fluxes, inhibated by stable stratification, and destroyed by dissipation. This type of turbulence occurs in boundary layers (surface mixed layer and bottom layer).
The eddy coefficient involves the product of :
  • "k": the TKE (Turbulent Kinetic Energy).
  • "L": a master length scale related to eddies' size.
  • "S": a stability function which represents the effects of stratification & velocity shear.
INTERNAL MIXING
Internal Wave Breaking
Gravity waves moving along the interior pycnocline can grow to unstability. The breaking of waves generate mixing in the cross-isopycnal direction.
Observations indicate that the intensity of mixing is directly related to the Brunt-Vaisalla frequency which measures the vertical gradient of density.

Shear Instability
Shear instability occurs in the thermocline when the destabilizing effect of the vertical shear of velocity overcomes the stabilizing effect of the buoyancy gradient.
The tendancy for unstability is measured by the Richardson number "Ri" which is the ratio of the Prandtl frequency "M" (measure of shear) and the Brunt Vaisalla frequency "N" (measure of stratification) and occurs when Ri overcomes a critical Richardson number "Ri_c".




Code key features

Modular model

GOTM is written with the following different modules. This modular form enables to easily embed GOTM in 3D ocean models.

Spatio-temporal discretisation

Implementation