Baroclinic instability of timedependent currents
Citable URI
https://hdl.handle.net/1912/154As published
https://doi.org/10.1017/S0022112003005007DOI
10.1017/S0022112003005007Keyword
Baroclinic instability; Baroclinic wavesAbstract
The baroclinic instability of a zonal current on the betaplane is studied in the context of the twolayer model when the shear of the basic current is a periodic function of time. The basic shear is contained in a zonal channel and is independent of the meridional direction. The instability properties are studied in the neighbourhood of the classical steadyshear threshold for marginal stability. It is shown that the linear problem shares common features with the behaviour of the wellknown Mathieu equation. That is, the oscillatory nature of the shear tends to stabilize an otherwise unstable current while, on the contrary, the oscillation is able to destabilize a current whose timeaveraged shear is stable. Indeed, this parametric instability can destabilize a flow that at every instant possesses a shear that is subcritical with respect to the standard stability threshold. This is a new source of growing disturbances. The nonlinear problem is studied in the same near neighbourhood of the marginal curve. When the timeaveraged flow is unstable, the presence of the oscillation in the shear produces both periodic finiteamplitude motions and aperiodic behaviour. Generally speaking, the aperiodic behaviour appears when the amplitude of the oscillating shear exceeds a critical value depending on frequency and dissipation. When the timeaveraged flow is stable, i.e. subcritical, finiteamplitude aperiodic motion occurs when the amplitude of the oscillating part of the shear is large enough to lift the flow into the unstable domain for at least part of the cycle of oscillation. A particularly interesting phenomenon occurs when the timeaveraged flow is stable and the oscillating part is too small to ever render the flow unstable according to the standard criteria. Nevertheless, in this regime parametric instability occurs for ranges of frequency that expand as the amplitude of the oscillating shear increases. The amplitude of the resulting unstable wave is a function of frequency and the magnitude of the oscillating shear. For some ranges of shear amplitude and oscillation frequency there exist multiple solutions. It is suggested that the nature of the response of the finiteamplitude behaviour of the baroclinic waves in the presence of the oscillating mean flow may be indicative of the role of seasonal variability in shaping eddy activity in both the atmosphere and the ocean.
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Author Posting. © Cambridge University Press, 2003. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 490 (2003): 189215, doi:10.1017/S0022112003005007.
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