Version 1 (modified by poddo, 9 years ago) (diff)

Last edited Timestamp?

Author : Paolo Oddo

ticket : #851

Branch : dev_r2802_INGV4_zdfRic


In the current version of the Richardson number vertical turbolence scheme eddy viscosities and diffusivities are estimated based on the local gradient Richardson number Ri, using a scheme similar to that of Pacanowski and Philander (1981).

Where Ri(x, y, z, t) is ≥0,

Av=Abv+ (v0) / (1+αRi)nn_ri


Kv=Kbv + (v0) / (1+ αRi)(nn_ric+1).

In this shear vertical mixing scheme, the adjustable parameters are:

the background coefficients, Abv and Kbv;

the shear eddy viscosity at Ri=0 denoted by v0

the exponent (nn_ric=2)

the alpha parameter (5).

This simple scheme has been largely used in numerical models (it is simple and robust) however it does not have any parameterization of the mixing layer.

The basic idea is to introduce near the surface, a mixing-layer model to transfer and dissipate the atmospheric forcings (̌wind-stress and buoyancy flux).

Following the scheme used in HOPS (Harvard Ocean Prediction System) and described in PFJ Lermusiaux (2001) we first evaluate the local depth of turbulent wind-mixing or “Ekman depth” hee(̌x, y, t).

This depth is assumed proportional to the “depth of frictional influence” that is limited by rotation:

hee=Ek u* / f0 (Rossby and Montgomery, 1935; Cushman-Roisin, 1994).

In this similarity height relationship, the turbulent friction velocity:

τ / ρ0)

is computed from the wind stress vector τ and reference density ρ0.

The coefficient Ek is an empirical factor (tunable) and f0 is the Coriolis parameter.

The final he is further constrained by adjustable bounds hemin≤ he ≤ hemax.

Once hee is computed, the vertical eddy coefficients within hee are set to the empirical values Ae and Ke. This vertical mixing-layer model is one of the common results of more complex models (̌e.g. Mofjeld and Lavelle, 1984; Garwood et al., 1985; Stigebrandt, 1985; Large et al., 1994).


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