Rossby waves and zonal momentum redistribution induced by localised forcing in the rotating shallow-water model

The aim of this study is to understand the dynamics of Rossby waves induced by a localised and periodic ‘plunger’ forcing – imposed on a background flow – which is intended as an elementary representation of transient mesoscale eddy forcing in the ocean. We consider linearised dynamics and its quasi...

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Bibliographic Details
Published in:Journal of fluid mechanics 2020-02, Vol.885, Article A43
Main Authors: Haigh, Michael, Berloff, Pavel
Format: Article
Language:English
Subjects:
Dependence
Dynamics
Eddies
Elongation
Fluid dynamics
Geometry
Gravitational waves
Mesoscale eddies
Methods
Momentum
Momentum transfer
Ocean circulation
Ocean currents
Physical simulation
Planetary waves
Reynolds number
Reynolds stresses
Rotation
Shallow water
Vortices
Waves
Wind shear
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Summary:The aim of this study is to understand the dynamics of Rossby waves induced by a localised and periodic ‘plunger’ forcing – imposed on a background flow – which is intended as an elementary representation of transient mesoscale eddy forcing in the ocean. We consider linearised dynamics and its quasi-nonlinear extension, and focus on the rotating shallow-water model. The plunger induces a spectrum of Rossby waves that drive zonal momentum flux convergence at the forced latitudes. This behaviour has a robust and significant dependence on the background flow, which we treat as zonal and uniform. We systematically analyse this dependence using two methods. First, we use the eddy geometry formulation, in which Reynolds stresses are expressed in terms of eddy elongation and eddy tilt parameters, and consider the relationship between eddy geometry and zonal momentum redistribution. Second, we implement decompositions of flow responses into linear dynamical eigenmodes and compare with expectations from linear Rossby wave theory. Both methods compliment each other and aid the understanding of zonal momentum redistribution and its dependence on uniform background flow. We find that this dependence is determined by two factors: (i) dispersion-constrained resonance with the plunger forcing and (ii) efficiency of nonlinear eddy self-interactions. These results significantly improve our understanding of shallow-water Rossby waves, and may also be applied towards the development of parameterisations of oceanic mesoscale eddies.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.1032