COMPUTATIONAL HYDRAULICS CIVE 572
Assignment No. 1
The wave speed of the tidal waves (of long wave length and small-amplitude) is
where λ = wave length, τ = wave period, g = 981 cm/s2 = gravity constant and h = water depth. The water surface profile is superposition of a progressive wave train in the positive direction, asin(kx − ωt), and a progressive wave train in the negative direction, bsin(kx + ωt), as follows:
ζ(x,t) = asin(kx − ωt)+ bsin(kx + ωt) (1)
where (a, b) = constants, k = 2π/λ = wave number and ω = 2π/τ = wave frequency.
(a) Write a computer program to plot on screen the profile of a progressive wave along a xmax = 50 m long channel of water depth h = 10.2 cm. Find the values of a,b,k and ω in Eq. 1 for a progressive wave of wave height H = 4 cm and wave length λ = 10 m.
(b) Draw the axes of the wave-amplitude and the spatial coordinate. Provide labels and scales on the axes.
(c) Plot the profile of a standing wave of the same wave height, same wave length and same water depth as the progressive wave in (a). What are the values of a and b for this standing wave.
(d) Plot the profile of a wave obtained from superposition of the progressive wave in (a) and the standing wave in (c). Find the wave height of this new wave obtained from the superposition? Provide your answer in cm with an accuracy of one decimal place.
Submit the relevant VB6 computer programs. Summarize the numerical and graphic results in a power-point presentation.