Radiating Instability of a Meridional Boundary Current

Abstract

A linear stability analysis of a meridional boundary current on the beta plane is presented. The boundary current is idealized as a constant-speed meridional jet adjacent to a semi-infinite motionless far field. The far-field region can be situated either on the eastern or the western side of the jet, representing a western or an eastern boundary current, respectively. It is found that when unstable, the meridional boundary current generates temporally growing propagating waves that transport energy away from the locally unstable region toward the neutral far field. This is the so-called radiating instability and is found in both barotropic and two-layer baroclinic configurations. A second but important conclusion concerns the differences in the stability properties of eastern and western boundary currents. An eastern boundary current supports a greater number of radiating modes over a wider range of meridional wavenumbers. It generates waves with amplitude envelopes that decay slowly with distance from the current. The radiating waves tend to have an asymmetrical horizontal structure-they are much longer in the zonal direction than in the meridional, a consequence of which is that unstable eastern boundary currents, unlike western boundary currents, have the potential to act as a source of zonal jets for the interior of the ocean.

Low‐frequency interaction between horizontal and overturning gyres in the ocean

“…The lateral eddy heat flux terms are concentrated in the eastern basin, where the vertical shear in the meridional velocity is the largest, but the perturbations are able to penetrate westward all the way to the western boundary. This is similar to the radiation from unstable meridional eastern boundary currents recently discussed by Hristova et al [2008].…”

Energy pathways and structures of oceanic eddies from the ECCO2 state estimate and simplified models

“…Afanasyev et al, 2011), radiating instabilities of the eastern boundary current (e.g. Hristova et al, 2008;Wang et al, 2012), stationary Rossby waves (e.g. Maximenko et al, 2008), and the nonlinear self-interactions of the linear eigenmodes (e.g.…”

“…We term this hypothesis the "vortex-propagation mechanism". Other formation mechanisms include, but are not limited to, stationary Rossby waves (Maximenko et al, 2008), beta plumes (Afanasyev et al, 2011), radiating instabilities of the eastern boundary current (Hristova et al, 2008;Wang et al, 2012), and the nonlinear self-interactions of the linear eigenmodes (Berloff, 2005;Berloff et al, 2009). …”

On quartet interactions in the California Current system

“…Alternative hypotheses based on three-dimensional models have been proposed to explain mechanisms of QZJ generation; see Hristova et al (2008), Berloff et al (2009Berloff et al ( , 2011, Tanaka and Akitomo (2010), Wang et al (2012) and Qiu at al. (2013), among others.…”

“…(2013), among others. For example, Hristova et al (2008) hypothesized that QZJs observed in the eastern region of subtropical gyres may be related to radiating instabilities of eastern boundary currents. Connaugton et al (2010) have suggested using a modulational instability concept for explanation of quasi-zonal jets observed in the ocean and atmosphere.…”