Quantifying the length-scale dependence of surf zone advection

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Abstract

[1] We investigate the momentum balance in the surf zone, in a setting which is weakly varying in the alongshore direction. Our focus is on the role of nonlinear advective terms. Using numerical experiments, we find that advection tends to counteract alongshore variations in momentum flux, resulting in more uniform kinematics. Additionally, advection causes a shifting of the kinematic response in the direction of flow. These effects are strongest at short alongshore length scales, and/or strong alongshore-mean velocity. The length-scale dependence is investigated using spectral analysis, where the effect of advective terms is treated as a transfer function applied to the solution to the linear (advection-free) equations of motion. The transfer function is then shown to be governed by a nondimensional parameter which quantifies the relative scales of advection and bottom stress, analogous to a Reynolds Number. Hence, this parameter can be used to quantify the length scales at which advective terms, and the resulting effects described above, are important. We also introduce an approximate functional form for the transfer function, which is valid asymptotically within a restricted range of length scales.

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