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

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 crossshore 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 nonlinear 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 T p , 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 crossshore 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 T p 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 (T p , γ ) to describe the emergence of coastal eddies or meanders from an unstable buoyant current. By knowing the values of T p 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.

Scalings for Eddy Buoyancy Fluxes Across Prograde Shelf/Slope Fronts

“…In particular, K θ is of ( 10 3 − 10 4 m 2 /s) shoreward of y = 118 and seaward of y = 348 km, decays almost monotonically to 146 and 60 m 2 /s at the shelf break (y = 150 km) and at the junction of slope to open ocean regions (y = 250 km), respectively, and reaches its minimum of 13 m 2 /s near the mid-slope position (y = 197 km). This spatial distribution of K θ is consistent with previous findings that a sloping bottom suppresses baroclinic eddy fluxes across prograde fronts (Blumsack & Gierasch, 1972;Brink, 2012Brink, , 2016Brink & Cherian, 2013;Chen et al, 2020;Cimoli et al, 2017;Ghaffari et al, 2018;Hetland, 2017;Isachsen, 2011;Mechoso, 1980;Pennel et al, 2012;Poulin et al, 2014;Spall, 2004;Trodahl & Isachsen, 2018).…”

“…The main conclusions of this work are as follows: The eddy buoyancy diffusivity varies by approximately three orders of magnitude from the continental shelf toward the open ocean regions, and is suppressed where the bottom slope is steepened (Figure 2), consistent with previous findings of the suppression effects of the sloping seafloor on baroclinic eddy fluxes (Hetland, 2017; Isachsen, 2011). Scalings based on QG linear theories (e.g., K S04 defined in Equation ), which treat the bulk ratio between the topographic and isopycnal slopes as the key control parameter for capturing the topographic suppression on baroclinic eddy fluxes (Blumsack & Gierasch, 1972; Cimoli et al., 2017; Mechoso, 1980; Spall, 2004), are limited in quantifying the cross‐slope eddy buoyancy diffusivity across prograde fronts (Figure 3a). Scalings depending on the mesoscale eddy energy and the slope Burger number (e.g., K B12 in Equation , K BC13 in Equation , and K B16 in Equation ) (Brink, 2012, 2016; Brink & Cherian, 2013) can perform quantitatively better than linear theory‐based scalings in capturing the eddy buoyancy diffusivity across prograde fronts (Figures 3b and 3d), though significant scaling‐diagnosis mismatches remain. The GEOMETRIC scheme (see Equation ) developed by D. P. Marshall et al.…”

“…2. Scalings based on QG linear theories (e.g., K S04 defined in Equation 10), which treat the bulk ratio between the topographic and isopycnal slopes as the key control parameter for capturing the topographic suppression on baroclinic eddy fluxes (Blumsack & Gierasch, 1972;Cimoli et al, 2017;Mechoso, 1980;Spall, 2004), are limited in quantifying the cross-slope eddy buoyancy diffusivity across prograde fronts (Figure 3a). 3.…”

“…Brink (2016) quantified the eddy buoyancy diffusivities at locations of maximum eddy energy in simulations of wind‐forced continental shelf flows. For studies addressing initial value problems (e.g., by focusing on the “spin‐down” flow phases; see Brink, 2012, 2016; Brink & Cherian, 2013; Chen et al., 2020; Cimoli et al., 2017; Hetland, 2017; Pennel et al., 2012; Zhang & Gawarkiewicz, 2015), these calculations must also be temporally confined. Here we focus on the dynamically equilibrated eddy fluxes across both sloping‐ and relatively flat‐bottomed regions.…”

Structure, variability, and dynamics of the West Greenland Boundary Current System

“…A similar asymmetry is observed in the Agulhas Current, where submesoscale meanders are observed only on the offshore side of the jet and are hypothesized to be topographically-constrained (Elipot and Beal, 2015). Cimoli et al (2017) used a model shelfbreak jet to derive a parameter space that distinguishes between regions of stable flow, meandering flow, and eddying flow. The parameter space is a function of 𝛾, which is a measure of the baroclinicity of the flow, and 𝑇 𝑝 , which is a measure of the bottom topography, WGC speed, and stratification.…”