# Changeset 10092 for NEMO/trunk/doc/tex_sub

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Timestamp:
2018-09-05T18:53:05+02:00 (3 years ago)
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Update Tidal forcing documentation

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 r9407 % ================================================================ %        Tidal Potential % ================================================================ \section{Tidal potential (\protect\mdl{sbctide})} %        Surface Tides Forcing % ================================================================ \section{Surface tides (\protect\mdl{sbctide})} \label{sec:SBC_tide} %----------------------------------------------------------------------------------------- A module is available to compute the tidal potential and use it in the momentum equation. This option is activated when \np{ln\_tide} is set to true in \ngn{nam\_tide}. Some parameters are available in namelist \ngn{nam\_tide}: - \np{ln\_tide\_load} activate the load potential forcing and \np{filetide\_load} is  the associated file - \np{ln\_tide\_pot} activate the tidal potential forcing - \np{nb\_harmo} is the number of constituent used - \np{clname} is the name of constituent The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem; they are expressed as the gradient of the astronomical potential ($\vec{\nabla}\Pi_{a}$). \\ The potential astronomical expressed, for the three types of tidal frequencies following, by : \\ Tide long period : The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun 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: \label{eq:PE_dyn_tides} \frac{\partial {\rm {\bf U}}_h }{\partial t}= ... +g\nabla (\Pi_{eq} + \Pi_{sal}) where $\Pi_{eq}$ stands for the equilibrium tidal forcing and $\Pi_{sal}$ a self-attraction and loading term (SAL). 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 : \\ Long period tides : \Pi_{a}=gA_{k}(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{k}t+V_{0k}) \Pi_{eq}(l)=A_{l}(1+k-h)(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{l}t+V_{l}) diurnal Tide : diurnal tides : \Pi_{a}=gA_{k}(sin 2\phi)cos(\omega_{k}t+\lambda+V_{0k}) \Pi_{eq}(l)=A_{l}(1+k-h)(sin 2\phi)cos(\omega_{l}t+\lambda+V_{l}) Semi-diurnal tide: Semi-diurnal tides: \Pi_{a}=gA_{k}(cos^{2}\phi)cos(\omega_{k}t+2\lambda+V_{0k}) \Pi_{eq}(l)=A_{l}(1+k-h)(cos^{2}\phi)cos(\omega_{l}t+2\lambda+V_{l}) $A_{k}$ is the amplitude of the wave k, $\omega_{k}$ the pulsation of the wave k, $V_{0k}$ the astronomical phase of the wave $k$ to Greenwich. We make corrections to the astronomical potential. We obtain : 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 $(1+k-h)$ is here taken as a constant (0.7). 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:\\ \Pi-g\delta = (1+k-h) \Pi_{A}(\lambda,\phi) \Pi_{sal} = \beta \eta with $k$ a number of Love estimated to 0.6 which parameterised the astronomical tidal land, and $h$ a number of Love to 0.3 which parameterised the parameterisation due to the astronomical tidal land. A description of load potential can be found in  \citet{Arbic2010} 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. % ================================================================