A Generation Mechanism for Very Low Frequency Surf Zone Eddies

Abstract We examine an instability mechanism for generating very low frequency (VLF) vortical motions in the surf zone that oscillate with periods of O (10) min and associated alongshore wavelengths of O (100) m. The instability arises due to the mutual, dynamic interaction of wave and current. The mathematical formulation of the instability analysis follows the previous studies for generating rip current circulations. The unstable modes of the instability are examined for two classes of beach profiles, each of which is generalized from the realistic bathymetry of its kind: a fringing reef beach and a sandy beach with a well-defined alongshore bar. In each case, we find the unstable modes with temporal periods and alongshore wavelengths in the ranges of scales of the observed VLF surf zone eddies. Since we consider the stability of a basic state that is steady and alongshore uniform, there are no prescribed temporal or spatial scales in the system. Therefore, the wavenumber–frequency relationship of the unstable VLF modes is intrinsic to the coupling dynamics of wave and current. Since the central physics is the transfer of wave momentum to the current as the wave breaks and wave refraction by the current, which similarly exists regardless of beach and wave conditions, we expect that the intrinsic dynamics to generate VLF surf zone eddies applies more generally. We do not imply that the instability mechanism is necessary for surf zone VLF eddies but call attention to the intrinsic physics that manifest in the mutual, dynamic wave–current coupling and can interact and/or resonate with other excitation forces to influence VLF generation.