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Miller & Barcilon 1978
Miller, C. and Barcilon, A. (1978). Hydrodynamic instability in the Surf Zone as a Mechanism for the Formation of Horizontal Gyres. Journal of Geophysical Research 83: doi: 10.1029/JC083iC08p04107. issn: 0148-0227.

We model analytically the wave-induced horizontal circulation on a mildly sloping beach. We are specifically interested in the cellular flow that is induced when monochromatic waves come in normal to straight, parallel, and nondeformable bottom contours, and we wish to determine the longshore dimension of the observed uniformly spaced cells as a function of the physical parameters of the problem. The energy for these motions is derived from the potential energy stored in the wave-induced sea surface setup. We postulate that infinitesimal perturbations of the proper wavelength will extract the energy associated with this setup and convert it into the circulation velocities of the gyres. A steady, linear stability analysis is performed, based on an appropriate nondimensional set of depth-integrated and time-averated equations which contain parameterizations for the effects of bottom friction and wave breaking. Lateral friction effects are not incorporated. Two distinct dynamic regions are considered: the zones seaward and shoreward of the breaker line. They are linked together by matching conditions at the breaker line. We find that the eigen-wave numbers are a function of the rate at which the wave energy is dissipated across the surface zone (which is controlled by the beach slope) and of the magnitude of the bottom friction coefficient. The eigenvalues decrease with increasing beach slope and increase with an increasing bottom friction factor. The range of eignevalues computed agrees with field observations, although the data are not complete enough to verify the parametric trends.

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Journal
Journal of Geophysical Research
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American Geophysical Union
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