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Jeffrey A. Proehl

Abstract

The instability of zonally and temporally invariant, equatorial, zonal flow is found to be tied directly to the presence of critical layers within the fluid. Insight into the mechanism of instability can, therefore, be gained through the use of the ideas of wave over-reflection. For idealized flows, where it can be directly applied, over-reflection successfully predicts the phase speed and wavelength of the most unstable waves. In complex flows, where application is difficult, the character of the energy exchanges is consistent with the ideas of over-reflection. Whereas at the scales of the tropical instability waves, instability arises by extracting energy from the background state through varying mixes of baroclinic, barotropic, and Kelvin-Helmholtz mechanisms (depending upon the details of the flow), the importance of the critical layer as the root of instability suggests that attempting to classify the instability through these energy conversions is misleading.

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Jeffrey A. Proehl

Abstract

The interaction of long equatorial Rossby waves with mean zonal currents in the ocean is investigated in a continuously stratified finite difference numerical model. The model allows for realistic specification of the mean state including both vertical and meridional shear of the mean flow. In addition to changing of wave scales expected from slowly varying wave theory, the effect of strongly sheared mean flows is to cause strong scattering of wave energy. This scattering can cause large structural and dispersional changes to the wave solutions. As a result, for realistic mean flows, wave energy input near the equator appears at higher latitudes and a shadow zone occurs below the Equatorial Undercurrent in the near equatorial zone. The lateral shear of the undercurrent also causes subundercurrent equatorial focusing of wave energy input at higher latitudes.

Results for westward flow show that changes in resonant phase speeds and wave structures can be very large. Due to the scattering nature of rapidly varying flow, the presence of an equatorial confined critical layer does not preclude the radiation of wave activity into the deep ocean as it does for the Kelvin waves. The wave induced mean accelerations for both the resting ocean and for an eastward undercurrent in this model are dominated by Fictional dissipation of wave energy and are relatively weak. The induced accelerations for westward flows, where the intrinsic phase speed (cU) ?? 0, show that large divergences of the wave action flux exist leading to large momentum transfers from wave to mean states. The primary difference from the Kelvin waves is that the wave-induced residual circulation is important locally and leads to significant accelerations. These accelerations are primarily due to Coriolis torque with a lesser contribution from the residual advection of mean momentum.

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Jeffrey A. Proehl
and
Maurice Ratrray Jr.

Abstract

An analytic linearized continuously stratified model which explains low-frequency response of wide deep estuaries to non-local forcing is developed. The dynamic model used for the coastal ocean is similar to that of McCreay with the effects of vertical friction and vertical and horizontal diffusion included. The response in the estuary, to lowest order, is governed by the free-wave equations. In the present study, the channel is not assumed to be narrow when compared to the local internal Rossby deformation radii. Therefore, rotation is included in the dynamics in the estuary which allows the propagation or energy up-channel as a Kelvin wave. Once obtained, the oceanic solution is matched to that in the estuary using the Green's-function matching technique of Buchwald. The results show that the response in the estuary is geostrophically controlled by the flow on die continental shelf. Additionally, the adjustment is strongest in the entrance and consists primarily of the first baroclinic mode. A simulation for real winds is run and results compared to current meter data collected in the Strait of Juan de Fuca, Washington. The comparisons show good agreement between observed and simulated response in the fjord.

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Eric S. Johnson
and
Jeffrey A. Proehl

Abstract

Shipboard acoustic Doppler current profiler (ADCP)-derived zonal currents from 170° to 110°W are assembled into composite seasonal and ENSO cycles to produce detailed representations of large-scale ocean flow regimes that favor tropical instability waves (TIWs). The instability-favorable portion of these cycles, namely, the August– October period of the seasonal cycle and the pre-December period of the ENSO cold phase, both have intense westward flow in the South Equatorial Current, most particularly the branch north of the equator (SECN), and strengthened eastward flows in the North Equatorial Countercurrent (NECC) and the Equatorial Undercurrent (EUC). Taken together these flows enhance current shear in the two regions generally associated with TIW activity, namely, the cyclonic and anticyclonic shear regions located to the south and north of the SECN, respectively. Direct correlation of ADCP currents and CTD densities to an instability index derived from equatorial 13–30-day meridional velocities confirms the importance of the strengths of the SECN and NECC in determining the timing of TIW events. Very little correlation was found in the EUC, implying that its strength is not a determining factor in such timing. Reynolds stress and density flux calculations indicate that in a time-averaged sense TIWs derive energy from both the cyclonic and anticyclonic flanks of the SECN, and from both sides of the equatorial cold tongue. During low-instability periods these Reynolds stresses and fluxes substantially vanish, indicating that eddy energy production ceases. This is in marked contrast to Baturin and Niller's study, which indicated that eddy energy production was relatively continuous at 110°W. The current structures of individual months associated with TIW activity show substantial variability among themselves. Combined with previous findings of multiple modes of instabilities, this indicates that caution is required when attempting to model instabilities from averages of observed background flows such as those presented here.

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Zuojun Yu
,
Julian P. McCreary Jr.
, and
Jeffrey A. Proehl

Abstract

One of the striking features of tropical instability waves (TIWs) is that they appear to be more prominent north of the equator. A linearized, 2½-layer ocean model is used to investigate effects of various asymmetric background states on structures of equatorial, unstable waves. Our results suggest that the meridional asymmetry of TIWs is due to asymmetries of the two branches of the South Equatorial Current (SEC) and of the equatorial, sea surface temperature front; it is not due to the presence of the North Equatorial Countercurrent. Energetics analyses indicate that frontal instability associated with the equatorial, SST front, as well as barotropic instability due to shear associated with the SEC, are energy sources for the model TIWS.

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Lewis M. Rothstein
,
Michael J. McPhaden
, and
Jeffrey A. Proehl

Abstract

A numerical model is designed to study the effects of the strong, near-surface associated with the equatorial current system on energy transmission of time-periodic equatorial waves into the deep mean. The present paper is confined to long wavelength, low-frequency Kelvin waves forced by a longitudinally confined patch of zonal wind. Energy transmission into the deep ocean is investigated as a function of mean current shear amplitude and geometry and the forcing frequency.

Solutions form well-defined beams of energy that radiate energy eastward and vertically toward the deep ocean in the absence of mean flow. However, the presence of critical surfaces associated with mean currents inhibits low-frequency energy from reaching the deep ocean. For a given zonal wavenumber, longitudinal propagation through mean currents will be less inhibited as the frequency increases (phase speed increases). When the mean current amplitude is large enough, the beam encounters multiple critical surfaces (i.e., critical surfaces for different wavenumber components of the beam) where significant and momentum can take place with the men currents via Reynolds stress transfers. Work against the dominant vertical shear is the dominant wave energy loss for the case of a mean South Equatorial Current–Equatorial Undercurrent system, illustrating the need for high vertical resolution in equatorial ocean models.

The model also describes the possible induction of a mean zonal acceleration as well as a mean meridional circulation. Eliassen-Palm fluxes are used to diagnose these dynamics. The presence of critical surfaces result in mean field accelerations on the equator above the core of the Equatorial Undercurrent. Implications of these results with regard to observations in the equatorial waveguide are discussed.

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