From 47cd83f4e89e5c93a204413e1b9f59a6e20c44e1 Mon Sep 17 00:00:00 2001
From: Thierry Fouquet <thierry.fouquet@edf.fr>
Date: Tue, 14 Jan 2025 10:33:52 +0100
Subject: [PATCH] [doc] replace modelisation by modeling in documentation
---
.../tomawac/user/latex/numerical.tex | 39 ++++++++++++++-----
1 file changed, 30 insertions(+), 9 deletions(-)
diff --git a/documentation/tomawac/user/latex/numerical.tex b/documentation/tomawac/user/latex/numerical.tex
index 5e5dea350b..88e09a4a07 100644
--- a/documentation/tomawac/user/latex/numerical.tex
+++ b/documentation/tomawac/user/latex/numerical.tex
@@ -231,25 +231,46 @@ Non-linear transfers & non-lin & & $\Lambda^*$ & $Q_{tr}^{*} $ \\
As regards the wave frequencies that are discretized, the minimum and maximum frequency markers are considered as ``open boundary limits'', where the energy can be transferred to lower or higher frequencies, exiting the discretized frequency range.
-\section{ A set of different models: BAJ modelisation. }
+\section{ A set of different models: BAJ modeling. }
\label{se:baj}
-In \cite{Bidlot2007}, the authors proposed a new formulation in terms of mean wave parameters to emphasis the high frequency part in interaction between windsea and swell. That formula has been implemented in Tomawac. It consist firstly in choosing a set of formulation in term of simulation. This modelisation includes WAM 4 for Janssen wind modelisation, (i.e. option 1 in \ref{WIND_INPUT}), Komen whitecapping dissipation (i.e. option 1 in \ref{WHITECAPPING},% 4.2.3.3.1,
-with $C_{dis}=2.1$ and $\delta=0.4$). In the initial paper, BAJ formulation also includes Discrete Integration Approximation for non linear resonant quadruplet interactions, (i.e. option 1 in \ref{Quadruplet}% see 4.2.3.6.1
-), but since \telemac v8.2, it doesn't include automatically this modele, which allows user to use BAJ with another formulation for Non Linear Interaction.
+In \cite{Bidlot2007}, the authors proposed a new formulation in terms of mean
+wave parameters to emphasis the high frequency part in interaction between
+windsea and swell. That formula has been implemented in Tomawac. It consist
+firstly in choosing a set of formulation in term of simulation. This modeling
+includes WAM 4 for Janssen wind modeling, (i.e. option 1 in \ref{WIND_INPUT}),
+Komen whitecapping dissipation (i.e. option 1 in \ref{WHITECAPPING},
+% 4.2.3.3.1,
+with $C_{dis}=2.1$ and $\delta=0.4$). In the initial paper, BAJ formulation also
+includes Discrete Integration Approximation for non linear resonant quadruplet
+interactions, (i.e. option 1 in \ref{Quadruplet}), % see 4.2.3.6.1
+but since \telemac v8.2, it doesn't include automatically this modele, which
+allows user to use BAJ with another formulation for Non Linear Interaction.
In those formulations the mean wave number $\sqrt{k}$
- and the mean angular frequency $\sigma$ are defined using weighted spectral integrals that put more emphasis on the high frequencies:
+ and the mean angular frequency $\sigma$ are defined using weighted spectral
+ integrals that put more emphasis on the high frequencies:
$$
\barr{l}
-\dsp \sqrt{<k>}=\frac{\int d \vec{k}\sqrt{\vec{k}}F(\vec{k})}{\int d \vec{k}F(\vec{k})} \\[12pt]
+\dsp \sqrt{<k>}=\frac{\int d \vec{k}\sqrt{\vec{k}}F(\vec{k})}{\int d
+ \vec{k}F(\vec{k})} \\[12pt]
\dsp <\sigma>=\frac{\int d \vec{k}\sigma F(\vec{k})}{\int d \vec{k}F(\vec{k})}
\earr
$$
- Another point is the frequency cut off to calculate the discrete integration. This frequency is no longer a function of the mean frequency but the mean frequency of the windsea only, denoted by $f_{meanWS}$, where only frequency with $S_{input}>0$ or $\frac{28}{c}u_*cos(\Delta \theta) \ge 1$ are considered. Where $S_{input}$ is the wind input source term, $c$ is the wave phase speed, $u_*$ is the friction velocity and $\Delta \theta$ is the difference between the wind direction and the wave propagation direction. Then only frequencies such that:
+Another point is the frequency cut off to calculate the discrete integration.
+This frequency is no longer a function of the mean frequency but the mean
+frequency of the windsea only, denoted by $f_{meanWS}$, where only frequency
+with $S_{input}>0$ or $\frac{28}{c}u_*cos(\Delta \theta) \ge 1$ are
+considered. Where $S_{input}$ is the wind input source term, $c$ is the wave
+phase speed, $u_*$ is the friction velocity and $\Delta \theta$ is the
+difference between the wind direction and the wave propagation direction. Then
+only frequencies such that:
$$
f_{min}\le f \le min(2.5 f_{meanWS},f_{max})
$$
- will be considered for the integration. Frequencies above will follow a $f^{-5}$ shape. The consequence of that choice is the modification of the charnock constant in the wind generation (0.0095).
+will be considered for the integration. Frequencies above will follow a
+$f^{-5}$ shape. The consequence of that choice is the modification of the
+charnock constant in the wind generation (0.0095).
- The last point concern the wave growth limiter that will use the mean frequency of the windsea (option 3 in \ref{se:growthlimiter}).
+The last point concern the wave growth limiter that will use the mean
+frequency of the windsea (option 3 in \ref{se:growthlimiter}).
--
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