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Linear Wave Theory fundamental description: L - wave length H - wave height T - period

Overview of Waves and Sediment Transport Most energy on continental shelf - gravity waves consisting of sea and swell. Linear Wave Theory fundamental description: L - wave length H - wave height T - period d - water depth. Shore Protection Manual, 1984. (Jeff Parsons’ web site).

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Linear Wave Theory fundamental description: L - wave length H - wave height T - period

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  1. Overview of Waves and Sediment Transport Most energy on continental shelf - gravity waves consisting of sea and swell Linear Wave Theory fundamental description: L - wave length H - wave height T - period d - water depth Shore Protection Manual, 1984

  2. (Jeff Parsons’ web site)

  3. Wave theory characteristics that affect what we see in the bottom boundary layer: • When wave is in “deep” water - d/L > 1/2 • orbits circular • waves don’t feel the bottom (and the seabed doesn’t feel the waves) • When wave is in “shallow” water - d/L < 1/25 • orbits flatten, become elliptical • wave speed is dependent upon depth, c =(gd)1/2 • wave-orbital velocities are felt at the seabed

  4. Linear Wave Theory: Shore Protection Manual, 1984

  5. Key Linear Wave equations for sediment transport: (At bottom, z = -d ) Wavelength: Maximum wave-orbital velocity, cos(Θ) = 1 : Orbital Excursion:

  6. Example: On the Washington shelf, a winter storm could produce waves of 7 m in height with period of 15 seconds. At what depths are these waves felt on the shelf?

  7. Shallow water waves • Speed is dependent on water depth • wave speed, c=(gd)1/2 Leads to wave refraction as shoreline is approached.

  8. Wave boundary layer • Linear wave theory assumed inviscid flow (no friction at bed). We can use linear wave theory above the BBL and develop a viscous boundary layer at seabed. • Because waves oscillate, there is limited time for viscous effects to build. Therefore, the wave boundary layer is thin relative to the current boundary layer. • Results in high shear in u • high u*w • high b • Wave boundary layer thickness is seldom > 10 cm

  9. How do we determine shear stress due to waves? • 1. Eddy viscosity concept • Az =  u*w z • (time invariant) • 2. Wave friction factor (analogous to a drag coefficient) • Time averaged over a wave cycle

  10. What is fw a function of: • bed roughness, ks • orbital excursion, ab • R* In rough turbulent region,

  11. Alternatively, we can write the Shield’s entrainment function using fw: Plot with the uni-directional threshold curve

  12. Suspended sediment concentration profile under waves: • (combined waves and currents) • Rouse Equation: for z < cw for z > cw

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