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

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

$\displaystyle F_{cri}(i,j,k)$ $\displaystyle \propto e^{-h_{ab} / h_{cri} }$    
$\displaystyle F_{pyc}(i,j,k)$ $\displaystyle \propto N^{n\_p}$    
$\displaystyle F_{bot}(i,j,k)$ $\displaystyle \propto N^2   e^{- h_{wkb} / h_{bot} }$    

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

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

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.

Gurvan Madec and the NEMO Team
NEMO European Consortium2017-02-17