Update internal wave mixing

INTERFACE:

   subroutine internal_wave(nlev,NN,SS)

DESCRIPTION:

Imposes eddy viscosity and diffusivity characteristic of internal wave activity and shear instability when there is extinction of turbulence as suggested by Kantha and Clayson (1994). In this case, the new values of $\nu_t$ and $\nu'_t=\nu^B_t$, defined in (43), are used instead of those computed with the model.

When k is small (extinction of turbulence, diagnosed by $k<$klimiw), $\nu_t$ and $\nu'_t$ are set to empirical values typical in the presence of internal wave activity (IW) and shear instability (SI). This model is described by

$$\nu_t = \nu_t^{IW} + \nu_t^{SI} \; , \quad \nu'_t= \nu'^{IW}_t + \nu'^{SI}_t \; , \quad$$ (204)

where

$$\nu_t^{IW} = 10^{-4} \; , \quad \nu'^{IW}_t = 5 \cdot 10^{-5} \quad .$$ (205)

The `SI' parts are functions of the Richardson number according to

$$\nu_t^{SI} = \nu'^{SI}_t = 0 \; , \quad R_i>0.7 \; , \quad$$ (206)

$$\nu_t^{SI} = \nu'^{SI}_t = 5 \cdot 10^{-3} \left( 1-\left(\frac {R_i} {0.7}\right)^2\right)^3 \; , \quad 0<R_i<0.7 \; , \quad$$ (207)

$$\nu_t^{SI} = \nu'^{SI}_t = 5 \cdot 10^{-3} \; , \quad R_i < 0 \quad .$$ (208)

The unit of all diffusivities is m$^2$s$^{-1}$.

USES:

   use turbulence,    only:            iw_model,alpha,klimiw,rich_cr
   use turbulence,    only:            numiw,nuhiw,numshear
   use turbulence,    only:            tke,num,nuh
   IMPLICIT NONE

INPUT PARAMETERS:

   integer,  intent(in)                :: nlev
   REALTYPE, intent(in)                :: NN(0:nlev),SS(0:nlev)

REVISION HISTORY:

   Original author(s): Karsten Bolding, Hans Burchard,
                       Manuel Ruiz Villarreal