Assignment No$.2$

$(10\%)$ A wave train approaches the same shore that has straight parallel nearshore bottom

contours oriented in a north$-$south direction. The deep$-$water wave crests form an angle with

the shoreline of $50.$ If the wave period is $11s$ and the deep$-$water height is $2m$ what is the

wave height and angle between the wave crest and shoreline where the water depth is $8m?$ At

what depth will the wave break?

$(10\%)$ A wave train has a period of $8\mathrm{.}6s$ and propagates toward the shore over straight

shore$-$parallel bottom contours. Plot the wave crest angle $($with respect to the shoreline

orientation$)$ in deep water versus the wave crest angle at a water depth of $5m$ for deep water

angles ranging from zero to $80.$ How would this curve differ if the incident wave period were

$6s?$

$(10\%)$ Consider the $L-$shaped breakwater that protects a small harbor dredged to a

uniform depth of $6m.$ For a $2m$ high, $10s$ period incident wave at the head of the breakwater

having the direction shown, what length $x$ must the seaward arm of the breakwater have to

diminish the wave height to $0\mathrm{.}5m$ at point $A?$

$(10\%)$ With $x=300m$ in Problem $11$ and the same incident wave direction, what are the

values of $K_d$ at point A for a $2,4,6,8$ and $10s$ wave? From this, discuss the effect of wave

diffraction on a spectrum of waves all arriving from the same direction and diffracting to the

lee of a breakwater.

$(10\%)$ A $7s,2\mathrm{.}5m$ high deep water wave approaches the shore in a normal direction. At a

distance of $300m$ from the shore a $700m$ long breakwater is constructed parallel to the shore

and the area leeward of the breakwater is dredged to a depth of $5m,$ which is the natural depth

at the breakwater. What is the maximum wave height that will occur at the center of the

breakwater on the leeward side?

$(10\%)$ If the deep water incident wave direction in Problem $13$ is $30$ off a line normal to

the breakwater axis and the nearshore bottom contours are all straight and parallel to the shore,

what is the maximum wave height at the center of the breakwater on the leeward side? Draw

the wave crest pattern in the vicinity of the breakwater. Assume the breakwater has a reflection

coefficient of zero.

$(10\%)$ In Problem $11,$ for the same incident wave height, period, and direction and a

breakwater length of $x=400m,$ what is the wave height at point $A$ if the water depth in the lee

of the breakwater decreases linearly from $-6m$ at the offshore arm to $-2m$ at point $A?$

$(10\%)$ In Problem $11,$ for the same incident wave height, period, and direction and a

breakwater length of $x=300m$ draw the diffracted and reflected wave crest pattern in the

harbor. Assume that the shoreline is a bulkhead with a reflection coefficient of $0\mathrm{.}8$ and that the

interior sides of the breakwater are stone mound with a reflection coefficient that is essentially

zero. What will the reflected wave height be at point $A?$

$(10\%)$ Consider the situation depicted in Figure $4\mathrm{.}14$ and assume the water depth

throughout is $5m.$ If the incident wave height and period are $2\mathrm{.}2m$ and $4s,$ respectively, what

is the reflected wave height at point A which is $20m$ from each of the barriers? The barrier that

reflects the wave has a $C_r=0\mathrm{.}75.$

$(10\%)$ The offshore arm of the breakwater in Problem $11$ has a reflection coefficient of

$0\mathrm{.}65$ on the seaward side. Consider the incident wave period, height, and incident direction

given in Problem $11$ and assume that the water depth immediately seaward of the breakwater

is also $6m.$ What is the reflected wave height at a point $100m$ from the head of the breakwater

along a line that extends out from the axis of the offshore arm? Show the reflected wave crest

pattern out to this point.