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 ω ^1/2. 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.

Abstract

Previous work has shown that the near-surface tropospheric response to anomalous heating can be described in terms of damped equatorial Rossby waves and a damped equatorial Kelvin wave. The zonal and meridional extent of the dominant ENSO heating/cooling region is such that the westward decaying Rossby waves dominate the response. Consequently, eastward of the forcing region the flow is small. Zonal convergence caused by the heating and small zonal flow to the cast together imply that winds must be anomalously westerly in the beating region.

Abstract

Turbulent flow is considered in a narrow, constant-depth channel connecting two basins having a time-dependent sea-level difference. The bosom stress is taken to be linear rather than quadratic in velocity, even when flows are quite strong. This approximation is justified theoretically by comparing appropriate linear and nonlinear solutions. Simple formulae are available for the depth-averaged current speed ū along the channel axis in terms of the sea-level gradient along that axis. Application of suitable mixing length theory shows that the stress should vary linearly with depth even for time-dependent flows. The mixing length theory predicts the current profile to be logarithmic near the bottom and slightly greater than logarithmic near the surface.

The theory was applied to sea level tidal constants and some acoustic Doppler and ship drift measurements recently made in the Prince of Wales Channel, Torres Strait. Sea level gradients and tidal flows in the channel are large because the channel joins two very different tidal regions, one in the Gulf of Carpentaria and the other in the Coral Sea. In accordance with theory, the channel is short enough that tidal constants vary linearly down the channel. The simple formulae for ū model the data reasonably well and clarity and improve previous tide table estimates. Depth averaged currants peak at about 2 m s⁻¹ and have a root mean squared depth averaged velocity of 0.74 m s⁻¹. The bottom r, resistance coefficient r, the drag coefficient C_D and roughness length z_o take the large values 4.8 × 10^&minus:1 m s⁻¹, 5.3 × 10^-3 and 0.029 m.

Abstract

Analytical theory and wind, sea level, and atmospheric pressure data were used to examine low-frequency dynamics near the equatorial eastern Pacific Ocean boundary. The analytical technique involves linking low-frequency solutions near a nonmeridional boundary with the deep ocean equatorial Kelvin wave for both unforced and wind-forced flows using an equatorial wave orthogonality condition. The following results were obtained.

• Mathematical and physical arguments show that nonmeridional boundaries should be less reflective than meridional ones, and that the poleward coastal Kelvin wave energy flux should be greater the more the boundary tilts from north to south. The eastern Pacific Ocean boundary is more nonmeridional in the Northern Hemisphere and, as a consequence, calculations for the intraseasonal, semiannual, annual, and interannual frequencies an indicated that poleward coastally trapped energy flux is greater in the Northern Hemisphere than in the Southern Hemisphere. For most frequencies the asymmetry is small, however. Although the Pacific eastern boundary is far from being meridional, only for the higher intraseasonal frequencies was it substantially less reflective than a meridional boundary.

• The eastern ocean boundary is a special place where it is comparatively easy to determine the equatorial Kelvin wave signal. The sea level at the nonmeridional boundary is partly due to incoming equatorial Kelvin waves and partly due to an alongshore tilt associated with the local wind forcing. A simple formula enables the extraction of the equatorial Kelvin wave sea level signal from the boundary sea level. When there is no forcing, this formula indicates that the boundary sea level is 2^1/2 times the equatorial Kelvin wave signal at the intersection of the equator and an appropriate average boundary meridian.

• In agreement with previous analysis, the theory indicates that the intraseasonal sea level signal in the eastern tropical Pacific is due to remotely forced equatorial Kelvin waves, while the annual sea level signal is due to the local alongshore winds. In contrast with earlier work, remote and local semiannual sea level contributions are comparable. The interannual signal is primarily due to remotely forced equatorial Kelvin waves, although on average during El Niño the sea level at Balboa (9°N) is reduced by an anomalous southward wind associated, it seems, with an anomalous southward displacement of the intertropical convergence zone (ITCZ) near the eastern Pacific boundary.

• Using the interannual sea levels at the eastern boundary it is possible to estimate the interannual equatorial Kelvin wave signal at the equator and eastern boundary since October 1908. This interannual equatorial Kelvin wave signal can be regarded as an El Niño index. According to this index the Largest El Niños since 1908 occurred in 1982–83 with other major El Niños in 1957 and 1941. Numerically, one obtains the interannual equatorial Kelvin wave index by multiplying the interannual La Libertad signal by 0.57 or the interannual Balboa signal by 0.85.

Abstract

Freely propagatiug coastally trapped waves (CTWs) dominated the large alongshore-scale low-frequency variability in the Australian Coastal Experiment (ACE). Two analytical models are used to demonstrate that these waves are not due to wave energy propagating freely through Bass Strait from the Southern Australian wave guide, but rather are largely generated by the very strong low-frequency winds in Bass Strait. The first model shows that the considerable CTW energy flux from the Southern Australian shelf wave guide does not propagate through Bass Strait. It is either frictionally dissipated at the northwest entrance to Bass Strait or travels southward along the western Bass Strait escarpment as “escarpment” waves and then southward along Tasmania's west coast as coastally trapped waves. The second model is used to calculate the eastward energy flux at the eastern end of Bass Strait assuming that all of this flux is generated by the very strong winds in Bass Strait. The calculations show that the size of this flux is consistent with the amount entering the ACE region.

Abstract

Theory is developed to discuss the reflection of long equatorial waves from ocean boundaries. The main results are as follows:

1) Energy flux reflection coefficients for the reflection of equatorial waves from meridional eastern and western ocean boundaries have been plotted as a function of frequency. The coefficients enable one to determine, for example, how much energy of an incoming equatorial wave of frequency ω is transmitted along an eastern oceanic boundary as poleward propagating Kelvin waves. The coefficients are useful for, both modal and vertically propagating descriptions of equatorial waves. As an example, the reflection of the Yanai wave observed in the equatorial Pacific is discussed in connection with poleward propagating sea levels along the South American coast.

2) Moore (1968) showed that the reflection of an incoming equatorial wave to an eastern meridional boundary consists, in part, of poleward propagating Kelvin waves. Here the same result is generalized to non-meridional small curvature boundaries. The analytic formula associated with this result is useful for determining whether energy of equatorial origin will have Kelvin-like characteristics along a strongly non-meridional boundary.

3) Low-frequency reflection near a non-meridional small curvature eastern boundary can be described analytically. If there is effectively no wind forcing new the boundary, linear solutions near the boundary shores that no matter how complicated the interior motion, near the boundary the motion can be described in terms of long westward propagating Rossby waves (low enough frequency) or poleward propagating Kelvin waves (high enough latitude). The Rossby waves are unaffected by coastline curvature at first order. When the Rossby wave solution is valid, there is no phase propagation along the coast and this result is discussed with reference to the poleward propagating low-frequency “El Niño" sea level signals recently reported in the literature. It seems that in the El Niño frequency band (2π/2 to 2π/5 year⁻¹) the coastal sea level is partly described by Rossby waves and partly by poleward propagating Kelvin waves. There is also some discussion of eastern boundaries with severe bending (the Atlantic eastern boundary) and the seasonal propagation of an upwelling signal along that boundary. Observations indicate that the signal is in the form of a poleward, vertically propagating Kelvin wave and this is consistent with the theory. In both Atlantic and Pacific low-frequency coastal poleward propagating phenomena, dissipation does not appear to play a fundamental role.

Abstract

A nonlinear model is developed and analytical results obtained to discuss the response of the Antarctic Circumpolar Current to wind forcing over a wide range of frequencies. The main results are as follows:

(i) The nonlinear equations of motion can be conveniently separated into one “baroclinic” and one “barotropic” mode.

(ii) For forcing with period T equal to less than a few years, wind-driven fluctuations in the Antarctic Circumpolar Current are barotropic and governed by the linearized Laplace tidal equations. Theory suggests that fluctuations in the transport should lag, and be most strongly correlated with, the circumpolar-averaged wind stress. These theoretical results are consistent with recent measurements made in Drake Passage. An interesting untested theoretical prediction is that the sea level fluctuations measured at the southern side of Drake Passage with T between one month and a few years should be coherent at zero lag with sea level fluctuations at the same latitude around the earth.

(iii) For longer period forcing, baroclinic fluctuations are important. The baroclinic pressure, current and associated density variations all decrease exponentially with depth. Exponential depth decay of these baroclinic fields is in fact observed, the decay scale being about 1 km.

(iv) The theory indicates that significant large-scale, wind-driven fluctuations in the strength of the baroclinic Antarctic Circumpolar Current can only occur at frequencies with periodicity ≳ 70 years. Climatic changes associated with such variability must therefore consist of oscillations of similar or longer period. This is consistent with limited observations which suggest that wind and sea-surface temperature in the region of the Antarctic Circumpolar Current have fluctuated through one “cycle” over the last 100 years.

(v) The spin-down time scale for barotropic motions appears to be short (observed to be ∼9 days) while that for the baroclinic motions is several years or more. The barotropic spin-down may be largely associated with Rossby wave drag over topographic irregularities while the baroclinic spin-down is most likely due to baroclinic instability.

(vi) Sverdrup balance does not hold.

Abstract

Recent work has shown that the linear, wind-forced quasi-geostrophic motion of stratified water over shelf topography can be described by a sum of modes, the amplitude of each of these modes satisfying a forced, first-order wave equation. The analysis presented suggests that this forced wave equation can qualitatively explain a wide range of observational and numerical results.

Abstract

The interannual, equatorial Pacific, 20°C isotherm depth variability since 1980 is dominated by two empirical orthogonal function (EOF) modes: the “tilt” mode, having opposite signs in the eastern and western equatorial Pacific and in phase with zonal wind forcing and El Niño–Southern Oscillation (ENSO) indices, and a second EOF mode of one sign across the Pacific. Because the tilt mode is of opposite sign in the eastern and western equatorial Pacific while the second EOF mode is of one sign, the second mode has been associated with the warm water volume (WWV), defined as the volume of water above the 20°C isotherm from 5°S to 5°N, 120°E to 80°W. Past work suggested that the WWV led the tilt mode by about 2–3 seasons, making it an ENSO predictor. But after 1998 the lead has decreased and WWV-based predictions of ENSO have failed. The authors constructed a sea level–based WWV proxy back to 1955, and before 1973 it also exhibited a smaller lead. Analysis of data since 1980 showed that the decreased WWV lead is related to a marked increase in the tilt mode contribution to the WWV and a marked decrease in second-mode EOF amplitude and its contribution. Both pre-1973 and post-1998 periods of reduced lead were characterized by “mean” La Niña–like conditions, including a westward displacement of the anomalous wind forcing. According to recent theory, and consistent with observations, such westward displacement increases the tilt mode contribution to the WWV and decreases the second-mode amplitude and its WWV contribution.

Abstract

Observations of TRITON moored array salinity and temperature in the very wet western equatorial Pacific at 137°E, 147°E, and 156°E since the late 1990s reveal the importance of rainfall to the interannual flow and El Niño–Southern Oscillation (ENSO) dynamics. Past work has shown that in this region a fresher surface isohaline layer is embedded in a thicker isothermal layer. Array estimates of dynamic height relative to the 50–70-m isothermal layer depth (ILD) indicate a near-surface salinity-driven contribution to the monthly sea level anomaly that is uncorrelated with, and smaller than, monthly anomalous sea surface height (SSH) estimated from altimeter data. Despite the smaller size of , its meridional gradient dominates the total sea level meridional gradient. Thus, the corresponding shallow equatorially trapped interannual freshwater jet dominates the near-surface zonal interannual flow. This jetlike flow has a meridional scale of only about 2°–3° of latitude, an amplitude of 23 cm s⁻¹, and is associated with the zonal back and forth displacement of the western equatorial warm/fresh pool that is fundamental to El Niño. The jet is not directly forced by the interannual freshwater surface flux but rather by wind stress anomalies that are mostly east of the warm/fresh pool edge during La Niña and mostly west of it during El Niño. A conceptual coupled ocean–atmosphere instability model is proposed to understand these observations. Calculations show that Aquarius satellite sea surface salinity (SSS) data match the TRITON in situ data well and that the satellite SSS can be used to estimate , and hence , geostrophically.