Internal wave-driven mixing (key_ zdftmx_new)

!-----------------------------------------------------------------------
&namzdf_tmx_new    !   new tidal mixing parameterization                ("key_zdftmx_new")
!-----------------------------------------------------------------------
   nn_zpyc     = 1         !  pycnocline-intensified dissipation scales as N (=1) or N^2 (=2)
   ln_mevar    = .true.    !  variable (T) or constant (F) mixing efficiency
   ln_tsdiff   = .true.    !  account for differential T/S mixing (T) or not (F)
/

The parameterization of mixing induced by breaking internal waves is a generalization of the approach originally proposed by St. Laurent et al. [2002]. A three-dimensional field of internal wave energy dissipation $\epsilon(x,y,z)$ is first constructed, and the resulting diffusivity is obtained as

$$A^{vT}_{wave} = R_f \frac{ \epsilon }{ \rho N^2 }$$ (10.47)

where $R_f$ is the mixing efficiency and $\epsilon$ is a specified three dimensional distribution of the energy available for mixing. If the ln_mevar namelist parameter is set to false, the mixing efficiency is taken as constant and equal to 1/6 [Osborn, 1980]. In the opposite (recommended) case, $R_f$ is instead a function of the turbulence intensity parameter $Re_b = \frac{ \epsilon}{\nu N^2}$, with $\nu$ the molecular viscosity of seawater, following the model of Bouffard and Boegman [2013] and the implementation of de Lavergne et al. [2016]. Note that $A^{vT}_{wave}$ is bounded by $10^{-2} m^2/s$, a limit that is often reached when the mixing efficiency is constant.

In addition to the mixing efficiency, the ratio of salt to heat diffusivities can chosen to vary as a function of $Re_b$ by setting the ln_tsdiff parameter to true, a recommended choice). This parameterization of differential mixing, due to Jackson and Rehmann [2014], is implemented as in de Lavergne et al. [2016].

The three-dimensional distribution of the energy available for mixing, $\epsilon(i,j,k)$, is constructed from three static maps of column-integrated internal wave energy dissipation, $E_{cri}(i,j)$, $E_{pyc}(i,j)$, and $E_{bot}(i,j)$, combined to three corresponding vertical structures (de Lavergne et al., in prep):

$$F_{cri}(i,j,k) \propto e^{-h_{ab} / h_{cri} }$$

$$F_{pyc}(i,j,k) \propto N^{n\_p}$$

$$F_{bot}(i,j,k) \propto N^2 e^{- h_{wkb} / h_{bot} }$$

In the above formula, $h_{ab}$ denotes the height above bottom, $h_{wkb}$ denotes the WKB-stretched height above bottom, defined by

$$h_{wkb} = H \frac{ \int_{-H}^{z} N dz' } { \int_{-H}^{\eta} N dz' } \; ,$$

The $n_p$ parameter (given by nn_zpyc in namzdf_tmx_new namelist) controls the stratification-dependence of the pycnocline-intensified dissipation. It can take values of 1 (recommended) or 2. Finally, the vertical structures $F_{cri}$ and $F_{bot}$ require the specification of the decay scales $h_{cri}(i,j)$ and $h_{bot}(i,j)$, which are defined by two additional input maps. $h_{cri}$ is related to the large-scale topography of the ocean (etopo2) and $h_{bot}$ is a function of the energy flux $E_{bot}$, the characteristic horizontal scale of the abyssal hill topography [Goff, 2010] and the latitude.