Changeset 11680
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 20191011T00:15:47+02:00 (5 years ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_ZDF.tex
r11679 r11680 658 658 659 659 \subsubsection{Evolution of the boundary layer depth} 660 660 661 The prognostic equation for the depth of the neutral/unstable boundary layer is given by \citep{grant+etal18}, 661 662 … … 671 672 + G\left(\delta/h_{\mathrm{ml}} \right)\left[\alpha_{\mathrm{S}}e^{1.5\, \mathrm{La}_t}\alpha_{\mathrm{L}} \frac{w_{\mathrm{*L}}^3}{h_{\mathrm{ml}}}\right] 672 673 \end{equation} 673 where the factor $G\equiv 1  \exp (25\delta/h_{\mathrm{bl}})(14\delta/h_{\mathrm{bl}})$ takes care of the lesser efficiency of Langmuir mixing when the mboundarylayer depth is much greater than the Stokes depth, and $\alpha_{\mathrm{B}}$, $\alpha_{S}$ and $\alpha_{\mathrm{L}}$ depend on the ratio of the appropriate eddy turnover time to the inertial timescale $f^{1}$. Results from the LES suggest $\alpha_{\mathrm{B}}=0.18 F(fh_{\mathrm{bl}}/w_{*C})$, $\alpha_{S}=0.15 F(fh_{\mathrm{bl}}/u_*}$ and $\alpha_{\mathrm{L}}=0.035 F(fh_{\mathrm{bl}}/u_{*L})$, where $F(x)\equiv\tanh(x^{1}))^{0.69}$. 674 where the factor $G\equiv 1  \mathrm{e}^ {25\delta/h_{\mathrm{bl}}}(14\delta/h_{\mathrm{bl}})$ models the lesser efficiency of Langmuir mixing when the boundarylayer depth is much greater than the Stokes depth, and $\alpha_{\mathrm{B}}$, $\alpha_{S}$ and $\alpha_{\mathrm{L}}$ depend on the ratio of the appropriate eddy turnover time to the inertial timescale $f^{1}$. Results from the LES suggest $\alpha_{\mathrm{B}}=0.18 F(fh_{\mathrm{bl}}/w_{*C})$, $\alpha_{S}=0.15 F(fh_{\mathrm{bl}}/u_*}$ and $\alpha_{\mathrm{L}}=0.035 F(fh_{\mathrm{bl}}/u_{*L})$, where $F(x)\equiv\tanh(x^{1})^{0.69}$. 675 676 For the stable boundary layer, the equation for the depth of the OSBL is: 677 678 \begin{equation}\label{eq:dhdtstable} 679 \max\left(\Delta B_{bl},\frac{w_{*L}^2}{h_\mathrm{bl}}\right)\frac{\partial h_\mathrm{bl}}{\partial t} = \left(0.06 + 0.52\,\frac{ h_\mathrm{bl}}{L_L}\right) \frac{w_{*L}^3}{h_\mathrm{bl}} +\left<\overline{w^\prime b^\prime}\right>_L. 680 \end{equation} 681 682 Equation. \ref{eq:dhdtunstable} always leads to the depth of the entraining OSBL increasing (ignoring the effect of the mean vertical motion), but the change in the thickness of the stable OSBL given by Eq. \ref{eq:dhdtstable} can be positive or negative, depending on the magnitudes of $\left<\overline{w^\prime b^\prime}\right>_L$ and $h_\mathrm{bl}/L_L$. The rate at which the depth of the OSBL can decrease is limited by choosing an effective buoyancy $w_{*L}^2/h_\mathrm{bl}$, in place of $\Delta B_{bl}$ which will be $\approx 0$ for the collapsing OSBL. 674 683 675 684
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