Question: 2. The flow-field under a sinusoidal wave, which travels to -x, is considered, as shown in the figure. It can be shown that the

2. The flow-field under a sinusoidal wave, which travels to -x, is

2. The flow-field under a sinusoidal wave, which travels to -x, is considered, as shown in the figure. It can be shown that the velocity potential corresponding to this problem is given as follows (-00 0): (x, z, t) = Rcosh[Ak + B2] sin(kx + wt) (2) t is the time, and k and w are the wave number and the wave frequency, respectively. d is the water depth. R is a given constant. A and B are positive constants to be determined. Do the following: (a) Determine the constant B so that this flow-field is physically meaningful everywhere and at all times. (10 points) (b) Determine the constant A by requiring that the vertical (i.e. in the z direction) fluid particle velocity, w, at the sea-floor (z = -d) is zero at all points (-00 < x < +o0) and at all times. (8 points)

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