mmcp-19-gerstner

commit c6c94b450d0058d102b792c10f06c6f98e8a2c9e
parent 70d4cd983be8a044c0180250a9842e1c548b672b
Author: Ivan Gankevich <igankevich@ya.ru>
Date:   Fri, 19 Jul 2019 22:46:59 +0300

Wave groups.

Diffstat:
main.tex
 | 
18
++++++++++++++++++

1 file changed, 18 insertions(+), 0 deletions(-)
diff --git a/main.tex b/main.tex
@@ -175,6 +175,12 @@ for breaking waves.
 
 \section{Trochoidal wave groups}
 
+In our modified model we simulate two wavy surfaces simultaneously: one for
+regular waves with normal length and one for waves with nine times higher
+length, that propagate under the same laws but with two times less speed
+(fig.~\ref{fig-group}). The product of these surfaces allows to simulate wave
+groups.
+
 \begin{figure}
 	\centering
 	\includegraphics[width=\textwidth]{graphics/06-group-wave.png}
@@ -182,6 +188,18 @@ for breaking waves.
 	field.\label{fig-group}}
 \end{figure}
 
+On the first entry the profile of the long wave is given by specific smoothing
+function, the form of which is close to phase wave profile. This function
+defines continuous change of wave front phase, which is needed to simulate
+waves produced by the ship.
+
+There is also a simpler approach to simulate wave groups: a superposition of
+regular waves with slightly different periods propagating in the opposite
+directions. Interference of waves of comparable lengths produces beats, in
+which ninth waves has double height and are standing waves. This approach
+generally gives satisfactory wavy surface, but does not work for waves produced
+by the ship, because they have complex wave front.
+
 \section{Direct numerical simulation for the simulation of sea waves}
 
 \begin{figure}