next up previous
Next: Steady ship waves, wave Up: Free-surface waves: linear superposition, Previous: Energy Propagation - Group

Conservation of energy equation


\begin{figure} \begin{center} \epsfig{file=lfig2013.eps,height=1.7in,clip=} \end{center} \end{figure}

\begin{align}& \left( {\overline F _1 - \overline F _2 } \right)\Delta t = \Del... ...\partial }{\partial x}\left( {V_g \overline E } \right) = 0 \notag \end{align}

1.
$\frac{\partial \overline E }{\partial t} = 0, V_g \overline E = $ constant in $x$ for any $h( x)$.
2.
$V_g = $ constant (i.e. constant depth, $\delta k < < k)$

\begin{displaymath}\left( {\frac{\partial }{\partial t} + V_g \frac{\partial }{\... ... - V_g t} \right)\mbox{ or } A = A\left( {x - V_g t} \right) \end{displaymath}

i.e. wave packet moves at $V_{g}$.

Keyword Search