Steep Shelf Stabilization of the Coastal Bransfield Current: Linear Stability Analysis

F J Poulin,A Stegner,M Hernández-Arencibia,A Marrero-Díaz,P Sangrà

doi:10.1175/jpo-d-13-0158.1

Abstract

Abstract In situ measurements obtained during the 2010 COUPLING cruise were analyzed in order to fully characterize the velocity structure of the coastal Bransfield Current. An idealized two-layer shallow-water model was used to investigate the various instability processes of the realistic current along the coastal shelf. Particularly studied is how the topographic parameter To (ratio between the shelf slope and the isopycnal slope of the surface current) impacts the growth and the wavelength of the unstable perturbations. For small bottom slopes, when the evolution of the coastal current is controlled by the baroclinic instability, the increase of the topographic parameter To yields a selection of smaller unstable wavelengths. The growth rates increase with small values of To. For larger values of To (To ≳ 10, which is relevant for the coastal Bransfield Current), the baroclinic instability is strongly dampened and the horizontal shear instability becomes the dominant one. In this steep shelf regime, the unstable growth rate and the wavelength selection of the baroclinic coastal current remains almost constant and weakly affected by the amplitude of the bottom velocity or the exact value of the shelf slope. Hence, the linear stability analysis of an idealized Bransfield Current predicts a typical growth time of 7.7 days and an alongshore scale of 47 km all along the South Shetland Island shelf. The fact that these large growth times are identical to the typical transit time of water parcels along the shelf may explain why the current does not exhibit any unstable meanders.

Highlights

Coastal currents are important features of the local or the regional circulation that control the cross-shelf transport
This study revealed that retrograde topography is strictly stabilizing in comparison with the flat-bottom case, whereas prograde topography will first destabilize the jet and stabilize it when the topographic slope increases beyond a critical value
We note that in the range 220 # To # 210, which is relevant for the Bransfield Current, the growth time is tmax ’ 7.7 days and the alongshore scale is lmax ’ 47 km for the most unstable perturbations

Summary

Introduction

Coastal currents are important features of the local or the regional circulation that control the cross-shelf transport. In the framework of quasigeostrophic (QG) models, both the two-layer model (Mysak 1977) and the continuously stratified Eady model (Blumsack and Gierasch 1972; Mechoso 1980) show that a prograde current, which corresponds to a negative shelf slope (i.e., shelf slope and isopycnals tilt in the opposite sense), reduces the unstable growth of baroclinic modes These idealized studies demonstrate that the central parameter of the problem is To 5 s/a, the ratio of the bottom slope s over the isopycnal slope a. Recent studies generally used two-layer shallow-water equations or the hydrostatic primitive equations to model the unstable dynamics of the coastal current over sloping bathymetry In this context, the linear stability analyses of Lozier et al (2002) and Lozier and Reed (2005) show that a negative shelf slope may amplify the unstable growth.

Characteristics of the Coastal Bransfield Current

A two-layer model

Findings

Discussion