commit 449235f476c155c0e1b3dd3962b4aca0372c5fec
parent f5465a31ecc4f417cf657a8596a8ac2423286a35
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Sun, 14 Jul 2019 14:33:41 +0300
Formulae and bibliography.
Diffstat:
| main.tex | | | 43 | ++++++++++++++++++++++++++++++++++++++++--- |
| refs.bib | | | 47 | ++++++++++++++++++++++++++++++++++++----------- |
2 files changed, 76 insertions(+), 14 deletions(-)
diff --git a/main.tex b/main.tex
@@ -56,9 +56,46 @@ that uses added masses.
\maketitle
\section{Introduction}
-\section{Methods}
-\section{Results}
-\section{Conslusion}
+\section{Computational model of intense sea waves}
+
+\(r_W=1.134\lambda_Wh_W/4\pi\text{ }\left[\text{m}\right]\)
+
+\begin{equation*}
+ \zeta_Z = r_W \cos x_W \exp\left(-2\pi z_W / \lambda_W\right)
+ \qquad \left[\text{m}\right]
+\end{equation*}
+
+\begin{equation*}
+ \zeta_X = -r_W \sin x_W \exp\left(-2\pi z_W / \lambda_W\right)
+ \qquad \left[\text{m}\right]
+\end{equation*}
+
+\(^{A}R_W=^{A}Kr_W\left(\cos{}x_W-1\right)\), where \(^{A}K=[1,0..\sqrt{2}]\)
+\(^{W}R_W=^{W}Kr_W\left(\sin{}x_W-1\right)\), where \(^{W}K=[0..1]\)
+
+\begin{equation*}
+ \begin{aligned}
+ \zeta_Z &= r_W \cos x_W \exp\left(
+ 2\pi \left[
+ -z_W + r_W ^{A} K \left( \cos x_W - 1\right) + r_W ^{W} K\sin x_W
+ \right] / \lambda_W
+ \right) \\
+ \zeta_X &= -r_W \sin x_W
+ 2\pi \left[
+ -z_W + r_W ^{A} K \left( \cos x_W - 1\right) + r_W ^{W} K\sin x_W
+ \right] / \lambda_W
+ \right)
+ \end{aligned}
+\end{equation*}
+
+\begin{equation*}
+ \frac{\rho V^2}{2} + \rho g \zeta_W = \text{const},
+ \qquad \left[\text{N}/\text{m}^2\right]
+\end{equation*}
+
+\section{Group structures of trochoidal waves}
+\section{Direct numerical simulation for the simulation of sea waves}
+\section{Conclusion}
\begin{acknowledgement}
Research work is supported by Saint Petersburg State University (grant
diff --git a/refs.bib b/refs.bib
@@ -1,13 +1,38 @@
-@Article{ nouguier2015,
- title = {Second-order Lagrangian description of tri-dimensional
- gravity wave interactions},
- volume = {772},
- doi = {10.1017/jfm.2015.179},
- journal = {Journal of Fluid Mechanics},
- publisher = {Cambridge University Press},
- author = {Nouguier, Frédéric and Chapron, Bertrand and Guérin,
- Charles-Antoine},
- year = {2015},
- pages = {165--196}
+@Article{ gerstner1809,
+ author = {Gerstner, Franz},
+ title = {Theorie der Wellen},
+ journal = {Annalen der Physik},
+ volume = {32},
+ number = {8},
+ pages = {412--445},
+ doi = {10.1002/andp.18090320808},
+ url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.18090320808},
+ year = {1809}
+}
+
+@Book{ sommerfeld1945mechanik,
+ title = {Mechanik der deformierbaren Medien},
+ author = {Sommerfeld, A.},
+ series = {Vorlesungen {\"u}ber theoretische Physik},
+ year = {1945},
+ publisher = {Akademische Verlagsgesellschaft Becker \& Erler}
+}
+
+@Book{ shuleikin1968,
+ author = {Shuleikin, V.},
+ title = {Physics of the sea},
+ publisher = {Moscow, Science},
+ year = {1968}
+}
+
+@Article{ poplavskii1997,
+ title = {Operational forecast of the tsunami on the sea shores of the
+ Far East of Russia},
+ author = {Poplavskii, A. and Khramushin, V. and Nepop, K. and Korolev,
+ Yu.},
+ journal = {Yuzhno-Sakhalinsk: Institute of Marine Geology and Geophysics
+ Far Eastern Branch Russian Academy of Sciences},
+ year = {1997},
+ note = {in Russian}
}
