A vortex force analysis of the interaction of rip currents and surface gravity waves

Abstract

We use the vortex force formalism to analyze the effect of rip currents on their own wave forcing. The vortex force formalism allows us to decompose the wave forcing into the nonconservative flux of momentum due to wave breaking and the conservative vortex force. Following Yu and Slinn (2003), we consider rip currents initially generated by alongshore variation of wave breaking due to a perturbation of a barred bottom topography. This variation is reduced in magnitude by two current effects on waves: wave ray bending and the flux of wave energy by currents. We compute the change in wave energy caused by these two effects on their own and use this to show that their relative magnitude scales with the square of the ratio of the length to width of the rip current. Both effects increase the wave height over the channels of the longshore bar, which leads to more wave breaking and counterbalances its longshore variation due to bottom refraction. In comparison to wave breaking, the change in the vortex force is negligible. Next, we show how the reduction in wave breaking is similar to an enhanced bottom friction. We then analyze the dependence of this relationship on the breaking parameterization, angle of incidence of the waves, and bottom drag law.

Three-dimensional modelling of wave-induced current from the surf zone to the inner shelf

“…Moreover, our rip currents are more extended offshore and are narrower in the channel than in the other simulations. The effects of the currents on waves not represented here, could be responsible of these differences (Smith, 2006), as Yu and Slinn (2003); Weir et al (2011) have shown that rip currents reduce the flux of momentum from waves to currents due to wave breaking. Finally, intensities of depth-integrated currents are comparable to the data, with a maximum value equal to 0.25 m s −1 .…”

“…Uchiyama et al, 2010;Haas and Warner, 2009;Weir et al, 2011). Few studies and measurements have been dedicated to the mid-shelf zone (with water depths of order 100 m), or at least to the inner shelf (between the surf zone and mid shelf): Lentz et al (1999Lentz et al ( , 2008 were one of the first to study the influence of waves on the inner shelf.…”

On tridimensional rip current modeling

“…The wave model uses the parameterization of Church and Thornton (1993), which has the particularly of producing more shoaling of the incoming wave before breaking and thus more intense breaking than other choices (Weir et al, 2011). It relies on two empirical constants: the breaking wave parameter γ b (wave height-to-depth ratio) and Bb the percentage of the wave face that is broken.…”

“…Clear identification of these terms is thus of primary interest. Another advantage of the VF formalism is numerical since it requires taking one less derivative in space and thus produces fewer numerical approximations (Weir et al, 2011). The coupled system is applied to the nearshore surf zone during the 2007 Biscarosse field measurement campaign (see Bathymetry in Figure 2).…”

“…An innovative modeling approach for 3D wave-current interactions (McWilliams et al, 2004) was implemented in the Regional Oceanic Modeling System (ROMS; Shchepetkin and McWilliams, 2005) by Uchiyama et al (2010) and used for idealized rip current studies (Weir et al, 2011). An upgraded version of this implementation is proposed here based on the AGRIF version of ROMS (Debreu et al, 2012;Penven et al, 2006).…”