Vortical surf zone velocity fluctuations with 0(10) min period

Abstract

Observations of velocity fluctuations with periods between about 4 and 30 min, thus longer than infragravity waves and referred to as very low frequency (VLF) surf zone motions, are described and compared with numerical simulations. The VLF motions discussed here exclude instabilities (generated by the wave-driven alongshore current velocity shear) that occur in the same frequency range by selecting cases with weak alongshore currents only. Numerical simulations are based on the linear shallow water equations including friction and forced by nonlinear difference-frequency interactions between incident sea and swell waves. The model is initialized with sea and swell frequency directional spectra observed seaward of the surf zone. Modeled and observed VLF velocity fluctuation magnitudes agree within a factor of 2; both increase approximately linearly with increasing incident wave height and rapidly decay seaward of the surf zone. Observed frequency-wave-number, f-ky, spectra of VLF velocity fluctuations, estimated with instrumented alongshore arrays, are energetic in a broad range of ky in the vortical band. Observed and modeled VLF pressure fluctuations are relatively weak. Still, the model momentum balance suggests that VLF pressure gradients are as important as the nonlinear wave group forcing by sea and swell in accelerating/decelerating the VLF velocities. Model calculations demonstrate that the VLF-f-ky response is a function of the modulations of short-wave forcing associated with the frequency directional distribution of the incident sea and swell spectra. This results in VLF motions which span the surf zone and have O(50–1000 m) alongshore scales with O(200–2000 s) time scales. Given the fact that modulations of short waves resulting from directionally spread incident waves are common during field conditions we expect VLFs to be ubiquitous.