APPH 4200 Physics of Fluids - Columbia...

21
APPH 4200 Physics of Fluids Waves (Ch. 7) 1. Waves 2. Linear gravity waves at a free surface 1

Transcript of APPH 4200 Physics of Fluids - Columbia...

Page 1: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-16.pdf · APPH 4200 Physics of Fluids Waves (Ch. 7) 1.!Waves 2.!Linear gravity waves

APPH 4200 Physics of Fluids

Waves (Ch. 7)

1. Waves2. Linear gravity waves at a free surface

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Page 14: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-16.pdf · APPH 4200 Physics of Fluids Waves (Ch. 7) 1.!Waves 2.!Linear gravity waves

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15

Page 16: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-16.pdf · APPH 4200 Physics of Fluids Waves (Ch. 7) 1.!Waves 2.!Linear gravity waves

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16

Page 17: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-16.pdf · APPH 4200 Physics of Fluids Waves (Ch. 7) 1.!Waves 2.!Linear gravity waves

Velocity §

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17

Page 18: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-16.pdf · APPH 4200 Physics of Fluids Waves (Ch. 7) 1.!Waves 2.!Linear gravity waves

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18

Page 19: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-16.pdf · APPH 4200 Physics of Fluids Waves (Ch. 7) 1.!Waves 2.!Linear gravity waves

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19

Page 20: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-16.pdf · APPH 4200 Physics of Fluids Waves (Ch. 7) 1.!Waves 2.!Linear gravity waves

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20

Page 21: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-16.pdf · APPH 4200 Physics of Fluids Waves (Ch. 7) 1.!Waves 2.!Linear gravity waves

Summary• Waves: phase fronts, phase velocity, wave

packets, group velocity.

• Linear waves (vs. nonlinear)

• Surface gravity wave:

- Velocity potential, Laplace’s Equation

- Assume top surface varies as η0cos(kx - ωt)

- Bernoulli’s Principle at surface

- No vertical flow at bottom

21