Abstract
Abstract. This study investigates the linear and non-linear instability of a buoyant coastal current flowing along a sloping topography. In fact, the bathymetry strongly impacts the formation of meanders or eddies and leads to different dynamical regimes that can both enhance or prevent the cross-shore transport. We use the Regional Ocean Modeling System (ROMS) to run simulations in an idealized channel configuration, using a fixed coastal current structure and testing its unstable evolution for various depths and topographic slopes. The experiments are integrated beyond the linear stage of the instability, since our focus is on the non-linear end state, namely the formation of coastal eddies or meanders, to classify the dynamical regimes. We find three non-linear end states, whose properties cannot be deduced solely from the linear instability analysis. They correspond to a quasi-stable coastal current, the propagation of coastal meanders, and the formation of coherent eddies. We show that the topographic parameter Tp, defined as the ratio of the topographic Rossby wave speed over the current speed, plays a key role in controlling the amplitude of the unstable cross-shore perturbations. This result emphasizes the limitations of linear stability analysis to predict the formation of coastal eddies, because it does not account for the non-linear saturation of the cross-shore perturbations, which is predominant for large negative Tp values. We show that a second dimensionless parameter, the vertical aspect ratio γ, controls the transition from meanders to coherent eddies. We suggest the use of the parameter space (Tp, γ) to describe the emergence of coastal eddies or meanders from an unstable buoyant current. By knowing the values of Tp and γ for an observed flow, which can be calculated from hydrological sections, we can identify which non-linear end state characterizes that flow – namely if it is quasi-stable, meanders, or forms eddies.
Highlights
Coastal currents can act either as a source of coherent eddies or as a dynamical barrier to the offshore redistribution of coastal waters, controlling the cross-shelf transport in a local or regional circulation
In this paper we have studied the non-linear evolution of an unstable buoyant current, flowing along a coastal slope, for various depths and sloping topographies
We determined the properties of the linear instability from the direct integration of the primitive equations forward in time
Summary
Coastal currents can act either as a source of coherent eddies or as a dynamical barrier to the offshore redistribution of coastal waters, controlling the cross-shelf transport in a local or regional circulation. Experimental studies (using a two-layer stratification) of coastal fronts or coastal currents over linear shelf slopes (Pennel et al, 2012; Geheniau et al, 2017) have shown that there are no large meanders or any eddy detachments when the topographic parameter reaches values below T0 −3. This is evidence that the non-linear saturation of the linear instability becomes important when the topographic slopes are comparable to the isopycnal slopes. Discussions and conclusions are given in the final Sect. 7
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