Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-22T10:46:51.088Z Has data issue: false hasContentIssue false
  • English
  • Français

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: natarov@hawaii.edu
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Dunkerton, T. J. 1981 On the inertial stability of the equatorial middle atmosphere. J. Atmos. Sci. 38, 2354–2364.2.0.CO;2>CrossRefGoogle Scholar
Dunkerton, T. J. 1983 A nonsymmetric equatorial inertial instability. J. Atmos. Sci. 40, 807–813.2.0.CO;2>CrossRefGoogle Scholar
Lee, H. & Richards, K. J. 2004 The three-dimensional structure of the interleaving layers in the western equatorial pacific ocean. Geophys. Res. Lett. 31, L07301. Doi:10.1029/2004GL019441.CrossRefGoogle Scholar
Natarov, A. & Boyd, J. P. 2001 Beyond-all-orders instability in the equatorial kelvin wave. Dyn. Atmos. Ocean. 33, 191–200.CrossRefGoogle Scholar
Natarov, A., Richards, K. J. & McCreary, J. P. 2008 Two-dimensional instabilities of time-dependent zonal flows: linear shear. J. Fluid Mech. 599, 29–50.CrossRefGoogle Scholar
d'Orgeville, M. & Hua, B. L. 2005 Equatorial inertial-parametric instability of zonally symmetric oscillating shear flows. J. Fluid Mech. 531, 261–291.CrossRefGoogle Scholar
Philander, G. 1990 El Niño, la Niña, and the Southern Oscillation. Academic Press.Google Scholar
Poulin, F., Flierl, G. & Pedlosky, J. 2003 The instability of time-dependent shear flows. J. Fluid Mech. 481, 329–353.CrossRefGoogle Scholar
Richards, K. J. & Banks, H. 2002 Characteristics of interleaving in the western equatorial pacific. J. Geophys. Res. 107 (C12), 3231. Doi:10.1029/2001JC000971.Google Scholar
Ripa, P. 1982 Nonlinear wave-wave interactions in a one-layer reduced-gravity model on the equatorial β plane. J. Phys. Oceanogr. 12, 97–111.2.0.CO;2>CrossRefGoogle Scholar
Taniguchi, H. & Ishiwatari, M. 2006 Physical interpretation of unstable modes of a linear shear flow in shallow water on an equatorial beta-plane. J. Fluid Mech. 567, 1–26.CrossRefGoogle Scholar