Meanders and eddy formation by a buoyant coastal current flowing over a sloping topography

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.

Meanders and eddies formation by a buoyant coastal current flowing over a sloping topography

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 states characterizes that flow, namely if it is quasi-stable, meanders, or forms eddies.

Energetics of Bottom Ekman Layers during Buoyancy Arrest

Turbulent bottom Ekman layers are among the most important energy conversion sites in the ocean. Their energetics are notoriously complex, in particular near sloping topography, where the feedback between cross-slope Ekman transports, buoyancy forcing, and mixing affects the energy budget in ways that are not well understood. Here, the authors attempt to clarify the energy pathways and different routes to mixing, using a combined theoretical and modeling approach. The analysis is based on a newly developed energy flux diagram for turbulent Ekman layers near sloping topography that allows for an exact definition of the different energy reservoirs and energy pathways. Using a second-moment turbulence model, it is shown that mixing efficiencies increase for increasing slope angle and interior stratification, but do not exceed the threshold of 5% except for very steep slopes, where the canonical value of 20% may be reached. Available potential energy generated by cross-slope advection may equal up to 70% of the energy lost to dissipation for upwelling-favorable flow, and up to 40% for downwelling-favorable flow.

Diapycnal Transport and Mixing Efficiency in Stratified Boundary Layers near Sloping Topography

The interaction of shear, stratification, and turbulence in boundary layers on sloping topography is investigated with the help of an idealized theoretical model, assuming uniform bottom slope and homogeneity in the upslope direction. It is shown theoretically that the irreversible vertical buoyancy flux generated in the boundary layer is directly proportional to the molecular destruction rate of small-scale buoyancy variance, which can be inferred, for example, from microstructure observations. Dimensional analysis of the equations shows that, for harmonic boundary layer forcing and no rotation, the problem is governed by three nondimensional parameters (slope angle, roughness number, and ratio of forcing and buoyancy frequencies). Solution of the equations with a second-moment closure model for the turbulent fluxes reveals the periodic generation of gravitationally unstable boundary layers during upslope flow, consistent with available observations. Investigation of the nondimensional parameter space with the help of this model illustrates a systematic increase of the bulk mixing efficiencies for (i) steep slopes and (ii) low-frequency forcing. Except for very steep slopes, mixing efficiencies are substantially smaller than the classical value of Γ = 0.2.