Equation (10.10) is for a single disturbance wave. For periodic small-amplitude surface

Chapter 10, Problem p10.9

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Equation (10.10) is for a single disturbance wave. For periodic small-amplitude surface waves of wavelength and period T, inviscid theory [8 to 10] predicts a wave propagation speed c2 0 5 g 2 tanh 2y where y is the water depth and surface tension is neglected. (a) Determine if this expression is affected by the Reynolds number, Froude number, or Weber number. Derive the limiting values of this expression for (b) y ! and (c) y @ . (d ) For what ratio y/ is the wave speed within 1 percent of limit (c)?

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