No abstract

No abstract

A numerical method based on spectral expansions is given for the computation of vorticity waves arising from shear instability of a longshore current. This method allows for any mean flow profile and any beach topography (remaining constant alongshore and with a straight shoreline). The shallow‐water equations are considered without any assumption about the sea surface (such as rigid lid), and dissipative terms accounting for bottom friction and/or eddy viscosity are included. A numerical simulation for some flow profiles that are quite realistic in the surf zone and for several bathymetries is presented. For inviscid flow the predictions of the Bowen and Holman (1989) analytical model for a very simplified geometry are found to give rise to the main features. However, the details in the flow and depth profiles are found to significantly influence the instability curves, especially for a barred beach. For the fastest growing mode, the wavelength is between 1.7 and 2.7 times the width of the mean current l. Frequencies of about 0.09ƒs, where ƒs is the maximum shear at the sea face of the current profile, and an e‐folding time of the exponential growth that is roughly equal to the wave period are obtained. The phase speed is between 0.5 and 0.7 of the mean current peak. Dissipation has a considerable effect on the wavenumber span and the growth rate of the instability, so reasonably constant values of the eddy viscosity and realistic values of the Chezy coefficient can entirely remove the instability. The phase speed of neutral shear waves is analytically found to be equal to the mean flow velocity at the cross‐shore location where the potential vorticity has an extremum. This velocity is found to give an estimate of the phase speed of growing modes. We found that the rigid‐lid assumption tends to overestimate the growth rates by an amount which depends on the maximum Froude number of the mean flow. The instability curves and the dispersion lines for a free surface converge towards the rigid‐lid ones when the Froude number decreases, and the rigid‐lid assumption is therefore valid for a low Froude number.

Abstract. The present state of research into and understanding of shear waves is appraised. In this paper these motions, which result from an instability of an alongshore, wave-driven current, are described, their theoretical explanation is recounted, and the history of their discovery is related. The various investigations into their genesis, which attempted to develop an understanding of when and why they occur, are summarized, and more recent research into their finite amplitude development is discussed, focusing on the understanding gained. Attention is also given to observations of shear waves made in the field and attempts to observe them in the laboratory. Finally, work that still needs to be done is described. INTRODUCTIONThe nearshore region called the surf zone has been so intensively investigated over the last 30 years, in theoretical and numerical studies, laboratory experiments, and field campaigns, that it is rare nowadays for a completely new phenomenon to be discovered. It was therefore a great surprise to the "nearshore community" to discover that precisely such an event was unfolding when preliminary results of the analysis of data from the SUPERDUCK experiment of 1986 were presented at the The observations were noteworthy for a number of reasons: (1) They were highly coherent, low-frequency, wave-like motions; (2) they occurred apparently only when the longshore current was present; (3) their kinematics were dependent on the longshore current orientation and strength; and (4) these kinematics revealed them to be distinct from any other previously observed nearshore motion.The observations, which were soon presented in a full particularly, velocity components (see Figure 1).However, these motions only occurred in the presence of a strong longshore current, and the stronger the current was, the more energetic the motions were. Furthermore, the motions were remarkable for possessing an alongshore speed of propagation proportional to the longshore current strength and orientation (i.e., they would propagate with the current), and interestingly, all such frequencies would propagate at the same speed, given constant current conditions (i.e., they were nondispersive). Finally, the observed alongshore wavelengths (periods) were between about 50 and 300 m (50 and 1000 s). These properties distinguished the motions from previously recognized IG waves, most notably alongshore propagating edge waves and oblique leaky modes [see, e.g., Oltman-Shay and Guza, 1987; OltmanShay and Howd, 1993]. In fact, these motions possessed a very distinct position in frequency-wavenumber (cok) space, as can be seen in Figure 2, and are clearly not (known) leaky or trapped surface gravity modes. (In this