A dissipative point-vortex model for nearshore circulation

Abstract

The hydrodynamic circulation of a nearshore region with complex bathymetry is inves- tigated by means of a point-vortex approach similar, but more complete and suited to practical applications, to that of Kennedy (J. Fluid Mech. vol. 497, 2003, p. 225). The generation and dissipation of each single-point vortex are analysed in detail to obtain a complete description of the vortex dynamics. In particular, we clarify how the mechanism for the generation of breaking-wave-induced macrovortices (large-scale two-dimensional horizontal vortices) can be practically implemented and we discuss in detail the mechanism leading to the dissipation of the circulation assigned to each vortex. Available approximate relations for the rate of generation of bar vortices are placed in context and discussed in detail, and novel approximate relations for the shore vortex generation and for the vortex viscous dissipation are proposed, the latter largely improving the description of the point vortex dynamics. Results have been obtained using three ‘typical’ rip-current bathymetries for which we also test qualitatively and quantitatively the model comparing the vorticity dynamics with the results obtained by means of both wave-resolved and wave-averaged circulation models. A comparison of dynamically equivalent flow configurations shows that the dissipative point-vortex model solutions, neglecting any influence of the wave field, provide rip current velocities in good agreement with both types of numerical solution. A more complete description of the rip current system, not limited to the rip-neck region as given by Kennedy (2003) by mean of an inviscid model, has been achieved by including dissipative effects.

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

“…Nonlinear model results [ Johnson and Pattiaratchi , 2006; Reniers et al , 2004, 2007; Long and Özkan‐Haller , 2009] suggest that VLF vortices can interact and travel offshore, thus transferring VLF energy to the outer surf zone or beyond. This offshore flux of VLF energy is likely to be associated with a combination of the nonlinear eddy‐eddy interactions, the life time of the eddies, which is subject to bottom friction, viscous damping, and adverse wave forcing [ Reniers et al , 2004; Terrile and Brocchini , 2007; Long and Özkan‐Haller , 2009], and the underlying topography such as rip channels [ Brocchini et al , 2004; Kennedy et al , 2006; Reniers et al , 2007], barred beaches [ Buhler and Jacobson , 2001; Reniers et al , 2004] or planar beaches [ Johnson and Pattiaratchi , 2006]. To qualify the importance of nonlinear effects on the generation and spatial distribution of the VLF's at SandyDuck, calculations were performed using nonlinear Delft3D model described by Reniers et al [2004].…”

Shoreline response to a single shore-parallel submerged breakwater

“…In the presence of submerged structures and sandbars, wave-resolving numerical models have been successfully used to simulate the generation of circulation patterns due to breaking induced vortical motions (i.e. start-up macro-vortices) (Terrile and Brocchini, 2007;Kennedy et al, 2006;Brocchini et al, 2004;Bühler and Jacobson, 2001), while wave-averaged models have been successfully used to simulate the associated time averaged circulation patterns (Zanuttigh, 2007;Martinelli et al, 2006;Ranasinghe et al, 2004. Shoreline response to SBWs has also been successfully simulated, albeit for a very limited number of scenarios, using depth-averaged (2DH) morphodynamic models with full hydrodynamic and morphological feedback (Zanuttigh, 2007;Martinelli et al, 2006;Zyserman et al, 2005;van der Biezen et al, 1998).…”

Interaction between breaking-induced vortices and near-bed structures. Part 1. Experimental and theoretical investigation

“…Considering the two-dimensional domain reported in figure 6, the interaction and migration of vortices due to mutual and self-advection can be simulated with the point-vortex method (Batchelor 1971), used in the literature in finite domains with periodic boundary conditions to study the vortex-vortex interactions (Meunier, Le Dizes & Leweke 2005;Kuvshinov & Schep 2016) and the interactions with the free surface (Curtis & Kalisch 2017). This approach has been used in various contexts: an example is the vortex ring theory applied to the dynamics of breaking-wave-induced macrovortices in the near shore (Bühler & Jacobson 2001;Brocchini et al 2004;Kennedy et al 2006;Terrile & Brocchini 2007). In our case, the point-vortex method has been used to reproduce the dynamics of the vortices due to mutual and self-advection only, using the available experimental data as initial conditions.…”

“…2004; Kennedy et al. 2006; Terrile & Brocchini 2007). In our case, the point-vortex method has been used to reproduce the dynamics of the vortices due to mutual and self-advection only, using the available experimental data as initial conditions.…”