Theory
When waves propagate through a vegetation field, wave energy is dissipated due to the work carried out by the waves on the vegetation. When assuming normally incident waves, and neglecting wave growth, refraction and dissipation due to friction and wave breaking, the wave energy conservation equation can be written as:
where E is the wave energy density, cgis the wave group velocity and εv is the time-averaged vegetation-induced rate of energy dissipation per unit horizontal area. A widely used method is to compute the time-averaged wave energy loss as the actual work carried out by the waves on the vegetation as function of the wave-induced drag force (e.g. Dalrymple et al., 1984):
where h is the water depth, αh is the vegetation height, F is the horizontal component of the force acting on the vegetation per unit volume, and u is the horizontal velocity. The overbar indicates averaging over time. When neglecting the plant swaying motion and inertial forces, the plant-induced force can be expressed with a Morison-type equation (Morison et al., 1950):
where ρ is the water density, CD is a drag coefficient, bv is the vegetation stem diameter, and N is the vegetation density. By applying linear wave theory to compute the horizontal component of the velocity, Dalrymple et al. (1984) found an expression for the time-averaged energy dissipation for regular waves propagation through a vegetation field on a uniform bed. This expression was extended by Mendez and Losada (2004) to include random waves, and waves propagating over a sloping bed, given by:
where k is the wave number, g is the gravitational acceleration, σ is the wave frequency, h is the water depth, CD is the (bulk) drag coefficient and Hrms is the root mean square wave height.
Typical applications
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How to use it?
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Further readings
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