Changeset 10092 for NEMO/trunk/doc/tex_sub
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 20180905T18:53:05+02:00 (3 years ago)
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NEMO/trunk/doc/tex_sub/chap_SBC.tex
r9407 r10092 756 756 757 757 % ================================================================ 758 % Tidal Potential759 % ================================================================ 760 \section{ Tidal potential(\protect\mdl{sbctide})}758 % Surface Tides Forcing 759 % ================================================================ 760 \section{Surface tides (\protect\mdl{sbctide})} 761 761 \label{sec:SBC_tide} 762 762 … … 765 765 % 766 766 767 A module is available to compute the tidal potential and use it in the momentum equation. 768 This option is activated when \np{ln\_tide} is set to true in \ngn{nam\_tide}. 769 770 Some parameters are available in namelist \ngn{nam\_tide}: 771 772  \np{ln\_tide\_load} activate the load potential forcing and \np{filetide\_load} is the associated file 773 774  \np{ln\_tide\_pot} activate the tidal potential forcing 775 776  \np{nb\_harmo} is the number of constituent used 777 778  \np{clname} is the name of constituent 779 780 The tide is generated by the forces of gravity ot the EarthMoon and EarthSun sytem; 781 they are expressed as the gradient of the astronomical potential ($\vec{\nabla}\Pi_{a}$). \\ 782 783 The potential astronomical expressed, for the three types of tidal frequencies 784 following, by : \\ 785 Tide long period : 767 The tidal forcing, generated by the gravity forces of the EarthMoon and EarthSun sytems, is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \np{.true.} in \ngn{nam\_tide}. This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that: 768 \begin{equation} \label{eq:PE_dyn_tides} 769 \frac{\partial {\rm {\bf U}}_h }{\partial t}= ... 770 +g\nabla (\Pi_{eq} + \Pi_{sal}) 771 \end{equation} 772 where $\Pi_{eq}$ stands for the equilibrium tidal forcing and $\Pi_{sal}$ a selfattraction and loading term (SAL). 773 774 The equilibrium tidal forcing is expressed as a sum over the chosen constituents $l$ in \ngn{nam\_tide}. The constituents are defined such that \np{clname(1) = 'M2', clname(2)='S2', etc...}. For the three types of tidal frequencies it reads : \\ 775 Long period tides : 786 776 \begin{equation} 787 \Pi_{ a}=gA_{k}(\frac{1}{2}\frac{3}{2}sin^{2}\phi)cos(\omega_{k}t+V_{0k})777 \Pi_{eq}(l)=A_{l}(1+kh)(\frac{1}{2}\frac{3}{2}sin^{2}\phi)cos(\omega_{l}t+V_{l}) 788 778 \end{equation} 789 diurnal Tide:779 diurnal tides : 790 780 \begin{equation} 791 \Pi_{ a}=gA_{k}(sin 2\phi)cos(\omega_{k}t+\lambda+V_{0k})781 \Pi_{eq}(l)=A_{l}(1+kh)(sin 2\phi)cos(\omega_{l}t+\lambda+V_{l}) 792 782 \end{equation} 793 Semidiurnal tide :783 Semidiurnal tides: 794 784 \begin{equation} 795 \Pi_{ a}=gA_{k}(cos^{2}\phi)cos(\omega_{k}t+2\lambda+V_{0k})785 \Pi_{eq}(l)=A_{l}(1+kh)(cos^{2}\phi)cos(\omega_{l}t+2\lambda+V_{l}) 796 786 \end{equation} 797 798 799 $A_{k}$ is the amplitude of the wave k, $\omega_{k}$ the pulsation of the wave k, $V_{0k}$ the astronomical phase of the wave 800 $k$ to Greenwich. 801 802 We make corrections to the astronomical potential. 803 We obtain : 787 Here $A_{l}$ is the amplitude, $\omega_{l}$ is the frequency, $\phi$ the latitude, $\lambda$ the longitude, $V_{0l}$ a phase shift with respect to Greenwich meridian and $t$ the time. The Love number factor $(1+kh)$ is here taken as a constant (0.7). 788 789 The SAL term should in principle be computed online as it depends on the model tidal prediction itself (see \citet{Arbic2004} for a discussion about the practical implementation of this term). Nevertheless, the complex calculations involved would make this computationally too expensive. Here, practical solutions are whether to read complex estimates $\Pi_{sal}(l)$ from an external model (\np{ln\_read\_load=.true.}) or use a ``scalar approximation'' (\np{ln\_scal\_load=.true.}). In the latter case, it reads:\\ 804 790 \begin{equation} 805 \Pi g\delta = (1+kh) \Pi_{A}(\lambda,\phi)791 \Pi_{sal} = \beta \eta 806 792 \end{equation} 807 with $k$ a number of Love estimated to 0.6 which parameterised the astronomical tidal land, 808 and $h$ a number of Love to 0.3 which parameterised the parameterisation due to the astronomical tidal land. 809 810 A description of load potential can be found in \citet{Arbic2010} 793 where $\beta$ (\np{rn\_scal\_load}, $\approx0.09$) is a spatially constant scalar, often chosen to minimize tidal prediction errors. Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to false removes the SAL contribution. 811 794 812 795 % ================================================================
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