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Analytical Theory for the Quasi-Steady and Low-Frequency Equatorial Ocean Response to Wind Forcing: The “Tilt” and “Warm Water Volume” Modes

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  • 1 Department of Oceanography, The Florida State University, Tallahassee, Florida
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Abstract

Analytical theory is used to examine the linear response of a meridionally unbounded stratified ocean to large-scale, low-frequency wind forcing. The following results, applied mainly to the equatorial Pacific, were obtained.

(i) Provided that the wind stress curl vanishes at large distance from the equator, a general Sverdrup solution is valid in the quasi-steady (frequency ω → 0) limit. The meridionally averaged zonal flow toward the western boundary layer is zero so that there is no net mass flow into the boundary layer and the large-scale boundary condition is therefore satisfied. This solution predicts a zero pycnocline response in the eastern equatorial Pacific. It therefore predicts that, for the eastern equatorial Pacific, a slow weakening of the equatorial trade winds will not lead to long-term El Niño conditions there.

(ii) Consistent with observations and other previous work, for finite but small frequencies there are two modes of equatorial motion. One is a “tilt” mode in which the equatorial sea level and thermocline are tilted by the in-phase zonal wind stress and the other is an equatorial warm water volume (WWV) mode in which the discharge of equatorial warm water (negative WWV anomaly) lags the wind stress forcing by a quarter of a period.

(iii) The amplitude of the WWV mode approaches zero like ω1/2. Therefore, as ω → 0, the equatorial solution reduces to the tilt mode.

(iv) The WWV mode is not due to a dominant meridional divergence driven by the wind, as suggested by some previous work. Meridional and zonal divergence approximately cancel. Reflection of energy at both ocean boundaries together with the strong dependence of long Rossby wave speed on latitude is crucial to the existence of the disequilibrium WWV mode. Because higher-latitude Rossby waves travel so much more slowly, the Rossby waves reflecting from the western ocean boundary are not in phase. This gives rise to a reflected equatorial Kelvin wave and a WWV that is not in phase with the wind stress forcing.

(v) Observations from past work have shown that much low-frequency wave energy, particularly westward propagating Rossby wave energy poleward of about 5°N and 5°S, is damped out before it reaches the western ocean boundary. In this way dissipation likely has a strong influence on the equatorial Kelvin wave reflection and hence the disequilibrium WWV.

Corresponding author address: Allan Clarke, Department of Oceanography, The Florida State University, Tallahassee, Florida 32306-4320. Email: aclarke@ocean.fsu.edu

Abstract

Analytical theory is used to examine the linear response of a meridionally unbounded stratified ocean to large-scale, low-frequency wind forcing. The following results, applied mainly to the equatorial Pacific, were obtained.

(i) Provided that the wind stress curl vanishes at large distance from the equator, a general Sverdrup solution is valid in the quasi-steady (frequency ω → 0) limit. The meridionally averaged zonal flow toward the western boundary layer is zero so that there is no net mass flow into the boundary layer and the large-scale boundary condition is therefore satisfied. This solution predicts a zero pycnocline response in the eastern equatorial Pacific. It therefore predicts that, for the eastern equatorial Pacific, a slow weakening of the equatorial trade winds will not lead to long-term El Niño conditions there.

(ii) Consistent with observations and other previous work, for finite but small frequencies there are two modes of equatorial motion. One is a “tilt” mode in which the equatorial sea level and thermocline are tilted by the in-phase zonal wind stress and the other is an equatorial warm water volume (WWV) mode in which the discharge of equatorial warm water (negative WWV anomaly) lags the wind stress forcing by a quarter of a period.

(iii) The amplitude of the WWV mode approaches zero like ω1/2. Therefore, as ω → 0, the equatorial solution reduces to the tilt mode.

(iv) The WWV mode is not due to a dominant meridional divergence driven by the wind, as suggested by some previous work. Meridional and zonal divergence approximately cancel. Reflection of energy at both ocean boundaries together with the strong dependence of long Rossby wave speed on latitude is crucial to the existence of the disequilibrium WWV mode. Because higher-latitude Rossby waves travel so much more slowly, the Rossby waves reflecting from the western ocean boundary are not in phase. This gives rise to a reflected equatorial Kelvin wave and a WWV that is not in phase with the wind stress forcing.

(v) Observations from past work have shown that much low-frequency wave energy, particularly westward propagating Rossby wave energy poleward of about 5°N and 5°S, is damped out before it reaches the western ocean boundary. In this way dissipation likely has a strong influence on the equatorial Kelvin wave reflection and hence the disequilibrium WWV.

Corresponding author address: Allan Clarke, Department of Oceanography, The Florida State University, Tallahassee, Florida 32306-4320. Email: aclarke@ocean.fsu.edu

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