hw6 - e = 5 rad/s H = 0.5 m a = 0.1 m f = 4 rad/s H = 0.5 m...

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2.016 HW #6 Out: November 1, 2005 Due: November 8, 2005 1) Concept questions: a. The majority of ocean waves are caused by what force? Discuss. b. On the “Motion of a Fluid Particle” slide in the Free-Surface Waves handout, (call him Bob): . What do they mean? Why are these equations valid? u = d " p dt , w = d # p dt two equations are given for the velocities of a fluid particle (Hint: your answer should use the words: “Eulerian” and “Lagrangian”…) c. For linear deep water waves, sketch the particle orbits. How deep must a scuba diver go before he or she doesn’t notice any motion due to the waves? d. For linear shallow water waves, describe what a scuba diver on the bottom experiences. 2) For each of the following scenarios, determine whether the waves are linear or not. If so, determine the wavelength, " . a. " " " " " " = 10 rad/s, H = 1 m, a = 0.02 m b. = 10 rad/s, H = 0.1 m, a = 0.06 m c. = 2 rad/s, H = 100 m, a = 5 m d. = 1 rad/s, H = 100 m, a = 2 m
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Unformatted text preview: e. = 5 rad/s, H = 0.5 m, a = 0.1 m f. = 4 rad/s, H = 0.5 m, a = 0.05 m 3) Consider a cylinder of radius, R, and length, L, held in place a distance, d, under the surface of the water by a slender post. The axis of the cylinder is parallel to the sea floor and perpendicular to incoming linear free-surface waves. Given , , a , and H, calculate the added mass forces on the cylinder, F 1 and F 3 , as a function of time. (Hint: the cylinder is not moving, so the simple added mass equation applies.) 4) A packet of waves 1 , k 1 , a 1 2 , k 2 < k 1 2 1 , a 2 # $ % & ’ ( ( ) are send down a wavetank of height, H << 1 , 2 . A second packet is generated seconds later. At what time will the second packet overtake the first? 5) Compare and contrast the vertical Foude-Krylov force to the restoring force due to buoyancy. What causes each force, and why are they different?...
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