Dispersed

For a $6-$second wave with a height of $H=1\mathrm{.}5m,$ estimate the orbital velocity $(u$ and $v$ component$)$ at a depth of

$4$ m from the surface based on linear wave theory.

For an $8$ sec and $1\mathrm{.}8$ m high wave propagating in water that is $500$ m deep, estimate the wave properties when

the wave reaches a point where the water depth is $2\mathrm{.}3$ m $,$ e$.$g$.,1)$ Wave celerity, $2)$ wavelength, $3)$ wave

steepness, $4)$ water particle speed at the wave crest, and $5)$ calculate the wave celerity and length.