Interaction between Rossby Waves and a Jet Flow: Basic Equations and Verification for the Antarctic Circumpolar Current

2019 ◽  
Vol 55 (5) ◽  
pp. 412-422 ◽  
Author(s):  
V. G. Gnevyshev ◽  
A. V. Frolova ◽  
A. A. Kubryakov ◽  
Yu. V. Sobko ◽  
T. V. Belonenko
Keyword(s):  
Antarctic Circumpolar Current ◽  
Rossby Waves ◽  
Jet Flow ◽  
Circumpolar Current ◽  
Basic Equations ◽  
The Antarctic

scholarly journals Interaction of Rossbi waves with a jet flow: basic equations and verification for Antarctic circumpolar current

2019 ◽  
Vol 55 (5) ◽  
pp. 39-50
Author(s):  
V. G. Gnevyshev ◽  
A. V. Frolova ◽  
A. A. Kubryakov ◽  
Yu. V. Sobko ◽  
T. V. Belonenko
Keyword(s):  
Dispersion Relation ◽  
Antarctic Circumpolar Current ◽  
Rossby Waves ◽  
Jet Flows ◽  
Altimetry Data ◽  
Sea Level Anomalies ◽  
Nonlinear Approach ◽  
Circumpolar Current ◽  
Basic Equations ◽  
Long Wave Approximation

The article focuses on the interaction of Rossby waves in the ocean with zonal jet flows. A new approach is proposed to show that nonlinearity in the long-wave approximation exactly compensates the Doppler shift. A new dispersion relation for the Rossby waves interacting with the jets is deduced from the nonlinear theory. The conclusion is verified using satellite altimetry data of the Antarctic Circumpolar Current (ACC). For the ACC area, we compare empirical velocities obtained from the altimetry data with theoretical phase velocities of Rossby waves calculated from nonlinear dispersion relation using the equivalent beta effect. The comparison shows that the new dispersion relation based on the nonlinear approach is capable of describing both the westward and the eastward propagation of mesoscale eddies in the field of sea level anomalies that can be identified as manifestation of Rossby waves in the ocean.

scholarly journals Submesoscale Rossby waves on the Antarctic circumpolar current

2018 ◽  
Vol 4 (3) ◽  
pp. eaao2824 ◽  
Author(s):  
John R. Taylor ◽  
Scott Bachman ◽  
Megan Stamper ◽  
Phil Hosegood ◽  
Katherine Adams ◽  
...  
Keyword(s):  
Antarctic Circumpolar Current ◽  
Rossby Waves ◽  
Circumpolar Current ◽  
The Antarctic

Waveguide for Rossby waves in the Antarctic Circumpolar current based on the altimetry data

2020 ◽  
Author(s):  
Anastasiia Frolova ◽  
Tatyana Belonenko
Keyword(s):  
Antarctic Circumpolar Current ◽  
Large Scale ◽  
Rossby Waves ◽  
Ocean Current ◽  
Altimetry Data ◽  
Wave Approximation ◽  
Long Wave ◽  
Circumpolar Current ◽  
Long Wave Approximation ◽  
The Antarctic

<p>Rossby waves in the ocean play a crucial role in large-scale ocean circulation and global climate. However, the interaction of Rossby waves with large-scale currents in the ocean is still a relatively little studied issue. The Antarctic Circumpolar Current (ACC) is the largest ocean current in the World Ocean. The ACC is a waveguide for Rossby waves where wave kinetic energy is captured by jets, and where Rossby waves interact with the flow. The purpose of this research is to analyze a manifestation of Rossby waves in the ACC based on satellite altimetry data. We propose a new approach to determining the boundaries of the waveguide. We analyze the variability of sea level anomalies and examine the latitude where the zonal velocity of Rossby waves is zero. For calculating Rossby waves velocities we use Radon and cross-correlation methods. We detect the Northern and the Southern Waveguide Boundaries for the ACC and compare them to the climatological fronts in the ACC. The linear theory of Rossby waves doesn’t work within the waveguide due to that we should consider nonlinear in the long-wave approximation. It follows from the theory of shallow water that nonlinearity in the long-wave approximation compensates exactly for the Doppler shift. The nonlinear dispersion equation agrees well with altimetry data.</p><p>The investigation is supported by the Russian Foundation for Basic Research grant (17-05-00034).</p>

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

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