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Nonlinear Shear Instabilities of Alongshore Currents Over Barred Beaches

Donald Slinn, John Allen, Priscilla Newberger, Robert Holman

College of Oceanic and Atmospheric Sciences

Phase velocities of the shear (or vorticity) waves in the experiments are determined in two ways.

**Figure.** Time- and space-lagged correlations $C(y_L, t_L)$ for the across-shore velocity component $u(x_0,y,t)$ from beach 1 experiments with different values of $\mu$ (ms$^{-1}$). ($x_0 = 125$ m for $\mu = 0.00145$ and 0.00116 ms$^{-1}$; $x_0 = 100$ m for $\mu = 0.00060$ ms$^{-1}$).
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Linear stability analysis applied to the time mean alongshore currents predict alongshore phase velocities and wavelengths in reasonable agreement with both the observations from the experiments and from linear analysis of the forced V_TGE velocity profiles even when the v and V_TGE velocity profiles are substantially different.

**Figure.** Results of the linear stability calculations for the time- and alongshore-averaged alongshore velocity $ \left< \overline{ v } \right> $ in terms of growth rate $kc_i$ versus alongshore wavenumber $k$ for beach 1 at different values of $\mu$ (ms$^{-1}$). The values of the wavelength $\lambda = 2 \pi / k$ m at the maximum growth rate are indicated.

*Note that the highest friction experiment predicts a stable flow, in agreement with the observed equilibrated shear wave flow behavior.*
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**Figure.** Phase velocities $c_{rm}$ of the most unstable mode from linear stability theory applied to $V_{TGE}$ and $ \left< \overline{ v } \right> $ and the observed phase velocities $c_0$ for experiments on beach 1 (top) and beach 2 (bottom) for different values of $\mu$.
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Results

Alongshore currents forced by the Thornton and Guza (TG) submodel are unstable for moderate values of the bottom friction coefficient $mu$
For decreasing values of $mu$, the resulting flow becomes increasingly unsteady exhibiting a transition from equilibrated hear waves to a turbulent shear flow.
For lower values of $mu$, the averaged across-shelf flux of potential vorticity supports a mean alongshore current with cross-shore structure in substantially better qualitative agreement with observations than given by TG forcing.
The results point to the possible existence in the nearshore region of an energetic eddy field associated with instabilities of the alongshore current.

PART 1 PART 2 PART 3 PART 4 PART 5

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