Pacanowski-Philander
In the model proposed by Pacanowski and Philander (1981), turbulent fluxes are diffusive, so that
where the diffusivity for velocity fields, $K_U$, is
while the diffusivity for tracer fields is
In \eqref{momentumdiffusivity} and \eqref{tracerdiffusivity}, the local Richardson number $\Ri$ is defined
in terms of the buoyancy $B = - g \rho' / \rho_0$, where $g$ is gravitational acceleration, $\rho_0$ is a reference density, and $\rho'$ is the density deviation therefrom. With the linear equation of state
near some reference temperature $T_0$ and reference salinity $S_0$, buoyancy $B$ is given by
and its vertical derivative is
Parameters
Typical values for the model parameters in PP (see the text following equation 19 in chapter 3 of CV12) are
Parameter | Value | Units |
---|---|---|
$\nu_0$ | $10^{-4}$ | $\r{m^2 \, s^{-1}}$ |
$\nu_1$ | $10^{-2}$ | $\r{m^2 \, s^{-1}}$ |
$\kappa_0$ | $10^{-5}$ | $\r{m^2 \, s^{-1}}$ |
$\kappa_1$ | $10^{-2}$ | $\r{m^2 \, s^{-1}}$ |
$c$ | $5$ | none |
$n$ | $2$ | none |