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Three-dimensional instabilities of oscillatory equatorial zonal shear flows

Published online by Cambridge University Press:  06 March 2009

ANDREI NATAROV  and
KELVIN J. RICHARDS
ANDREI NATAROV*
Affiliation:
International Pacific Research Center, University of Hawaii at Mānoa, Honolulu, Hawaii
KELVIN J. RICHARDS
Affiliation:
International Pacific Research Center, University of Hawaii at Mānoa, Honolulu, Hawaii
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we investigate the linear stability of oscillating zonal flows on the equatorial β-plane in the presence of fully three-dimensional disturbances. To exclude inflection point effects, we focus on the simplest case of a linear meridional shear with time-mean and oscillating components. For purely oscillatory background flows we find that in addition to resonant excitation of ‘additive’ type that occurs in the zonally invariant case, resonant excitation of ‘difference’ type is also possible. For flows with an oscillatory shear superimposed on an unstable time-mean shear it is shown that while the oscillatory shear has a stabilizing influence on disturbances with a small zonal wave number k, at higher k the effect of the oscillating shear diminishes and can even be destabilizing. Overall, a small oscillatory shear tends to reduce the fastest growth rate in the system and pushes the dominant k to higher values. Calculation of dominant zonal and vertical modes shows that the zonally asymmetric modes dominate a large portion of the parameter space, especially at high time-mean background shear and low oscillatory shear. As a result, the dominant vertical mode can have a somewhat larger vertical scale than in the zonally invariant case. At intermediate values of the time-mean shear the growth rate is relatively flat with respect to the zonal mode number, with maximum growth rate occurring in bands of high and low k. We have uncovered a rich assortment of vertical and zonal modes which are likely to play a role in the nonlinear evolution of equatorial flows.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 623 , 25 March 2009 , pp. 59 - 74
Copyright
Copyright © Cambridge University Press 2009

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References

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