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Timestamp:
2019-10-11T00:15:18+02:00 (13 months ago)
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agn
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started on flux-gradient relationship

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  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex

    r11674 r11675  
    548548Much of the time the turbulent motions in the ocean surface boundary 
    549549layer (OSBL) are not given by 
    550 classical shear turbulence. Instead they are in a regime dominated by an 
    551 interaction between the currents and the Stokes drift of the surface waves known as 
    552 `Langmuir turbulence' \citep[e.g.][]{mcwilliams.ea_JFM97}. 
     550classical shear turbulence. Instead they are in a regime known as 
     551`Langmuir turbulence',  dominated by an 
     552interaction between the currents and the Stokes drift of the surface waves \citep[e.g.][]{mcwilliams.ea_JFM97}. 
     553This regime is characterised by strong vertical turbulent motion, and appears when the surface Stokes drift $u_{s0}$ is much greater than the friction velocity $u_{\ast}$. More specifically Langmuir turbulence is thought to be crucial where the turbulent Langmuir number $\mathrm{La}_{t}=(u_{\ast}/u_{s0}) > 0.4$. 
     554 
    553555The OSMOSIS model is fundamentally based on results of Large Eddy 
    554556Simulations (LES) of Langmuir turbulence and aims to fully describe 
     
    561563$h_{\mathrm{BL}}$ and a turbulent velocity scale, is imposed throughout the  
    562564boundary layer 
    563 $-h_{\mathrm{BL}}<z<\eta$. 
    564 However, rather than the OSBL 
     565$-h_{\mathrm{BL}}<z<\eta$. The turbulent closure model 
     566also includes fluxes of tracers and momentum that are``non-local'' (independent of the local property gradient). 
     567 
     568Rather than the OSBL 
    565569depth being diagnosed in terms of a bulk Richardson number criterion, 
    566570as in KPP, it is set by a prognostic equation that is informed by 
     
    570574of the pycnocline (the stratified region at the bottom of the OSBL). 
    571575 
     576 
    572577\subsubsection{The flux gradient model} 
    573  
    574 The turbulent closure model 
    575 also includes ``non-local'' (independent of the local property gradient) 
    576 fluxes of tracers and momentum. 
     578The flux-gradient relationships used in the OSMOSIS scheme take the form, 
     579\begin{equation}\label{eq:flux-grad-gen} 
     580\overline{w^\prime\chi^\prime}=-K\frac{\partial\overline{\chi}}{\partial z} + N_{\chi,s} +N_{\chi,b} +N_{\chi,t} 
     581\end{equation}  
     582where $\chi$ is a general variable and $N_{\chi,s}, N_{\chi,b} \mathrm{and} N_{\chi,t}$  are the non-gradient terms, and represent the effects of the different terms in the turbulent flux-budget on the transport of $\chi$. $N_{\chi,s}$ represents the effects that the Stokes shear has on the transport of $\chi$, $N_{\chi,b}$  the effect of buoyancy, and $N_{\chi,t}$ the effect of the turbulent transport.  The same general form for the flux-gradient relationship is used to parametrize the transports of momentum, heat and salinity. 
     583 
    577584 
    578585%% ================================================================================================= 
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