HR: 09:45h
AN: OS41A-08    [Abstracts]
TI: Stability of Internal Gravity Waves in Sheared Inertial Currents
AU: * Winters, K
EM: kraig@coast.ucsd.edu
AF: UCSD, Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, CA 92093-0209, United States
AB: Observations of the oceanic internal wave field exhibit characteristic spectral peaks near the local inertial frequency. Near-inertial internal gravity waves are characterized by nearly horizontal currents with a flow direction that oscillates at the inertial frequency. In this work, we consider the stability of near-inertial waves in the limit of infinite horizontal scale and constant shear and stratification and pose the question: Are there small-scale internal gravity waves of infinitesimal amplitude that grow exponentially within such a flow? The stability problem is addressed using Floquet theory and the results are examined within a three-dimensional parameter space defined by the characteristic frequencies of the problem; the buoyancy frequency, the shear and the free-wave frequency of an infinitesimal test-wave, all normalized by the inertial frequency. Growth rates are computed numerically and distinct zones of instability are identified. A principal finding is that for particular combinations of shear, stratification and rotation, internal wave disturbances of all frequencies grow exponentially on the inertial time scale even when the neccessary condition for steady KH instability (N² / S² < ¼) is not satisfied. In the limit of vanishing shear, the zones of instability collapse to a discrete set of unstable waves. These waves further divide into those with frequencies such that they are periodic at the inertial period and those that are periodic at twice the inertial period.
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
DE: 3367 Theoretical modeling
DE: 4534 Hydrodynamic modeling
DE: 4544 Internal and inertial waves
DE: 4568 Turbulence, diffusion, and mixing processes (4490)
SC: Ocean Sciences [OS]
MN: 2007 Joint Assembly