Background

Evidence for the existence in the nearshore surf zone of alongshore propagating waves with periods O(100s) and wavelengths O(100m) was found from observations (Oltman-Shay et al. 1989).

• The wavelengths are too short at observed periods to be surface gravity edge wave modes.
• The existence and properties of the waves were found to be related to the presence, strength and direction of a mean alongshore current in the surf zone.
• Based on a linear stability analysis about a mean alongshore current with offshore scale O(100m), Bowen and Homan (1989) described these oscillations as unstable waves associated with a shear instability.
• Good agreement of wavelengths and wavespeeds from observations and from predictions based on the most unstable linear wave mode was obtained by Dodd et al. (1992).
• Allen et al. (JFM, 1996) showed that long wavelength, propagating finite amplitude disturbances with properties not related to results of linear theory can develop on plane beaches.

Questions

• If the observed oscillations are related to a shear instablity, why doesn't the instability grow so that the flow breaks down into vorticies and loses wave-like properties?
• What is the nature of the finite amplitude nonlinear behavior and how does it depend on the forcing, the frictional dissipation, and the beach geometry?
  

Plan

• Pursue answers to these questions with studies using numerical finite-difference solutions to the shallow-water equations for forced, dissipative, initial-value problems.

Shallow-Water Equations

linear bottom friction, rigid lid:

( t_0 = L / V, V^2 << g h_0 )

forcing in alongshore momentum equation:

EQ??

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PART 1 PART 2 PART 3 PART 4 PART 5

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