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Waves

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Waves

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    1. Waves

    5. Qualitative aspects of water waves

    6. What are waves? A wave is a disturbance that travels from one part of a material to another The disturbance is propagated through the material without any substantive overall motion of the material itself The disturbance if propagated without any significant distortion of the wave form The distortion appears to propagate with constant speed What is being transported?

    7. If energy, and not material, is being transported, what is the nature of the movement observed when the ripples cross a pond?

    10. Internal waves

    11. Planetary (Rossby) waves

    15. Wind generated waves in the ocean Frictional stress exerted by a moving fluid is proportional to the square of the speed of the fluid So the wind stress exerted upon a surface is proportional to the (wind speed)2 At sea surface, most of the transferred energy results in waves, although a small proportion is manifest as wind-driven currents

    17. Wind generated waves in open ocean Sheltering effect is at a maximum when wind speed ~ 3x wave speed The greater the amount by which wind speed exceeds wave speed, the steeper the wave Steepness (H/L) = 0.03 - 0.06 (max 0.1) Wave speed in deep water is not related steepness but to wavelength The greater the wavelength the greater the speed (c = L/T) Calm weather to gale force sequence: waves grow in H and L , and appropriate to a speed which corresponds to 1/3 wind speed Never as fast as wind, why?

    18. The Fully Developed Sea Size of waves in deep water is governed not only by actual wind speed, but also by the length of time the wind has been blowing at that wind speed Wave size also depends on fetch, the unobstructed distance of sea over which wind blows An equilibrium is eventually reached: energy is dissipated by the waves at the same rate as the waves receive energy from the wind A fully developed sea: size and characteristics of waves not changing Wind speed variable = so ideal FDS rarely occurs. Usually consist of wave fields.

    20. Attenuation of wave energy White capping Viscous attenuation (capillary waves only dissipation into heat by fiction between molecule) Air resistance Non-linear wave - wave interactions

    21. Wave height Significant wave height , H1/3 = ave. ht. of the highest one-third of all waves Maximum wave ht., Hmax [Hmax(25 years)] As wind speed increases, so H1/3 in fully developed sea increases Relationship between sea state, H1/3, and wind speed is expressed by the Beaufort Scale, which can be used to estimate wind speed at sea

    23. Wave steepness (H/L) important to sailors!

    24. Wave theory

    26. Motion of water particles

    27. Wave speed c = celerity of propagation c = L/T (speed = distance/time) Wave number, k = 2p/L (m-1, number of waves per meter) Angular frequency, ? = 2p/T (s-1, number of cycles - waves - per second) Both relate to the sinusoidal nature of idealized wave form

    28. In deep water:

    29. When d lies between L/20 and L/2, need to use full equation C = ? (gL/2p)tanh(2pd/L) Other relationships to be aware of: With c, T, or L: L = gT2/ 2p c = gT/ 2p With constants developed: L = 1.56T2 c = 1.56T

    30. Assumptions made in surface wave theory Shapes are sinusoidal Wave amplitudes << L and d Viscosity and surface tension can be ignored Coriolis force can be ignored Dept his uniform and bottom has no bumps of hummocks Waves are not constrained or deflected by land masses That real 3-d waves behave like 2-d models

    31. Wave dispersion and group speed

    32. Wave dispersion and group speed

    33. Waves approaching shore

    34. Wave refraction

    35. Waves breaking upon the shore

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