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Surface Waves

Surface Waves. Water surface is not fixed. Behaves elastically Based on surface tension Surface tension can be measured in a thin cylinder. Acts at boundary Balanced by gravity. Surface Tension. for a cylinder with walls at radius r :. Water surface is not fixed.

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Surface Waves

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  1. Surface Waves

  2. Water surface is not fixed. Behaves elastically Based on surface tension Surface tension can be measured in a thin cylinder. Acts at boundary Balanced by gravity Surface Tension for a cylinder with walls at radius r:

  3. Water surface is not fixed. Use a dynamic boundary condition. Pressure balanced by tension Dynamic Boundary z y(x) T T x x+Dx Can be extended to a 2-D surface

  4. Make assumptions about flow to approximate fluid motion. Incompressible Inviscid Irrotational Force from gravity Apply to Navier-Stokes The result is Bernoulli’s equation. Bernoulli’s Equation

  5. Vertical Motion • Consider surface motion. • Constant pressure • Velocity relatively small • Vertical velocity w • Vertical deflection h • The homogeneous equation has solutions. • Two constants B, C at z = h

  6. A sinusoidal surface wave is used to get the speed. Separable velocity potential Continuity implies Laplace’s equation Find constants of integration Surface Wave A h x

  7. Problem Find the wavelength L and speed c of a wave in deep water with a period of 3 s. Begin with a deep water approximation, h>> L. The speed, period and wavelength are all related. L = cT Speed c = 4.7 m/s Wavelength L = 14.1 m Deep Water

  8. Complicated fluid motion requires experimental verification. Release a bump of water at t = 0 Sloped shore stops reflections Compare the expected period to experiment. Discrepancy due to finite depth Prins Experiment (1958) R Q H next

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