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.
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}
\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,
In \cite{Bidlot2007}, the authors proposed a new formulation in terms of mean
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
wave parameters to emphasis the high frequency part in interaction between
), 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.
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 $\sqrt{k}$
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}
\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})}
\dsp <\sigma>=\frac{\int d \vec{k}\sigma F(\vec{k})}{\int d \vec{k}F(\vec{k})}
\earr
\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 $\frac{28}{c}u_*cos(\Delta\theta)\ge1$ 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 $\frac{28}{c}u_*cos(\Delta\theta)\ge1$ 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})
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}).
