Free Rossby Waves Research Articles

Effect of Overturning Circulation on Long Equatorial Waves: A Low-Frequency Cutoff

Zonally long tropical waves in the presence of a large-scale meridional and vertical overturning circulation are studied in an idealized model based on the intraseasonal multiscale moist dynamics (IMMD) theory. The model consists of a system of shallow-water equations describing barotropic and first baroclinic vertical modes coupled to one another by the zonally symmetric, time-independent background circulation. To isolate the effects of the meridional circulation alone, an idealized background flow is chosen to mimic the meridional and vertical components of the flow of the Hadley cell; the background flow meridionally converges and rises at the equator. The resulting linear eigenvalue problem is a generalization of the long-wave-scaled version of Matsuno’s equatorial wave problem with the addition of meridional and vertical advection. The results demonstrate that the meridional circulation couples equatorially trapped baroclinic Rossby waves to planetary, barotropic free Rossby waves. The meridional circulation also causes the Kelvin wave to develop an equatorially trapped barotropic component, imparting a westward-tilted vertical structure to the wave. The total energy of the linear system is positive definite, so all waves are shown to be neutrally stable. A critical layer exists at latitudes where the meridional background flow vanishes, resulting in a minimum frequency cutoff for physically feasible waves. Therefore, linear Matsuno waves with periods longer than the vertical transport time of the meridional circulation do not exist in the equatorial waveguide. This implies a low-frequency cutoff for long equatorial waves.

Multi-scale variability of the tropical Indian Ocean circulation system revealed by recent observations

The tropical Indian Ocean circulation system includes the equatorial and near-equatorial circulations, the marginal sea circulation, and eddies. The dynamic processes of these circulation systems show significant multi-scale variability associated with the Indian Monsoon and the Indian Ocean dipole. This paper summarizes the research progress over recent years on the tropical Indian Ocean circulation system based on the large-scale hydrological observations and numerical simulations by the South China Sea Institute of Oceanology (SCSIO), Chinese Academy of Sciences. Results show that: (1) the wind-driven Kelvin and Rossby waves and eastern boundary-reflected Rossby waves regulate the formation and evolution of the Equatorial Undercurrent and the Equatorial Intermediate Current; (2) the equatorial wind-driven dynamics are the main factor controlling the inter-annual variability of the thermocline in the eastern Indian Ocean upwelling; (3) the equatorial waves transport large amounts of energy into the Bay of Bengal in forms of coastal Kelvin and reflected free Rossby waves. Several unresolved issues within the tropical Indian Ocean are discussed: (i) the potential effects of the momentum balance and the basin resonance on the variability of the equatorial circulation system, and (ii) the potential contribution of wind-driven dynamics to the life cycle of the eastern Indian Ocean upwelling. This paper also briefly introduces the international Indian Ocean investigation project of the SCSIO, which will advance the study of the multi-scale variability of the tropical Indian Ocean circulation system, and provide a theoretical and data basis to support marine environmental security for the countries around the Maritime Silk Road.

A note on free and forced Rossby wave solutions: The case of a straight coast and a channel

The free Rossby wave (RW) solutions in an ocean with a straight coast when the offshore wavenumber of incident (l1) and reflected (l2) wave are equal or complex are discussed. If l1=l2 the energy streams along the coast and a uniformly valid solution cannot be found; if l1,2 are complex it yields the sum of an exponentially decaying and growing (away from the coast) Rossby wave. The channel does not admit these solutions as free modes.If the wavenumber vectors of the RWs are perpendicular to the coast, the boundary condition of no normal flow is trivially satisfied and the value of the streamfunction does not need to vanish at the coast. A solution that satisfies Kelvin's theorem of time-independent circulation at the coast is proposed.The forced RW solutions when the ocean's forcing is a single Fourier component are studied. If the forcing is resonant, i.e. a free Rossby wave (RW), the linear response will depend critically on whether the wave carries energy perpendicular to the channel or not. In the first case, the amplitude of the response is linear in the direction normal to the channel, y, and in the second it has a parabolic profile in y. Examples of these solutions are shown for channels with parameters resembling the Mozambique Channel, the Tasman Sea, the Denmark Strait and the English Channel. The solutions for the single coast are unbounded, except when the forcing is a RW trapped against the coast. If the forcing is non-resonant, exponentially decaying or trapped RWs could be excited in the coast and both the exponentially “decaying” and exponentially “growing” RW could be excited in the channel.

The Vertical Structure of Large-Scale Unsteady Currents

AbstractA linear model based on the quasigeostrophic equations is constructed in order to predict the vertical structure of Rossby waves and, more broadly, of anomalies resolved by altimeter data, roughly with periods longer than 20 days and with wavelengths larger than 100 km. The subsurface field is reconstructed from sea surface height and climatological stratification. The solution is calculated in periodic rectangular regions with a 3D discrete Fourier transform. The effect of the mean flow on Rossby waves is neglected, which the authors believe is a reasonable approximation for low latitudes. The method used has been tested with an idealized double-gyre simulation [performed with the Miami Isopycnal Coordinate Ocean Model (MICOM)]. The linear model is able to give reasonable predictions of subsurface currents at low latitudes (below approximately 30°) and for relatively weak mean flow. However, the predictions degrade with stronger mean flows and higher latitudes. The subsurface velocities calculated with this model using AVISO altimetric data and velocities from current meters have also been compared. Results show that the model gives reasonably accurate results away from the top and bottom boundaries, side boundaries, and far from western boundary currents. This study found, for the regions where the model is valid, an energy partition of the traditional modes of approximately 68% in the barotropic mode and 25% in the first baroclinic mode. Only 20% of the observed kinetic energy can be attributed to free Rossby waves of long periods that propagate energy to the west.

Eddy-Driven Recirculations from a Localized Transient Forcing

Abstract The generation of time-mean recirculation gyres from the nonlinear rectification of an oscillatory, spatially localized vorticity forcing is examined analytically and numerically. Insights into the rectification mechanism are presented and the influence of the variations of forcing parameters, stratification, and mean background flow are explored. This exploration shows that the efficiency of the rectification depends on the properties of the energy radiation from the forcing, which in turn depends on the waves that participate in the rectification process. The particular waves are selected by the relation of the forcing parameters to the available free Rossby wave spectrum. An enhanced response is achieved if the parameters are such to select meridionally propagating waves, and a resonant response results if the forcing selects the Rossby wave with zero zonal group velocity and maximum meridional group velocity, which is optimal for producing rectified flows. Although formulated in a weakly nonlinear wave limit, simulations in a more realistic turbulent system suggest that this understanding of the mechanism remains useful in a strongly nonlinear regime with consideration of mean flow effects and wave–mean flow interaction now needing to be taken into account. The problem presented here is idealized but has general application in the understanding of eddy–eddy and eddy–mean flow interactions as the contrasting limit to that of spatially broad (basinwide) forcing and is relevant given that many sources of oceanic eddies are localized in space.

Large-Scale Rossby Normal Modes during Some Recent Northern Hemisphere Winters

Abstract Large-scale Rossby normal modes are studied for the Northern Hemisphere winters of 2005, 2006, 2008, and 2009 using global observational meteorological analyses spanning the 0–92-km altitude range. Spectral analysis of geopotential height fields shows pronounced peaks at westward-propagating zonal wavenumber 1 near the theoretical locations of the free Rossby waves at 25, 16, 10, and 5 days that, in some cases, have amplitudes significantly larger than the estimated background spectrum. Evidence is also found for a wavenumber-2 free mode near 4 days. A coherence analysis is used to extract the amplitude and phase of the waves, and to isolate those regions of the latitude/altitude plane where the signals are statistically significant. Although the spectral location, temporal evolution, and vertical structure of several of these waves are suggestive of the presence of Rossby normal modes, this study shows that in the real atmosphere the waves only occasionally have the global properties of classical normal modes. Moreover, no evidence is found that the amplitudes of these modes are enhanced during stratospheric sudden warmings.

The interaction of free Rossby waves with semi-transparent equatorial waveguide – wave-mean flow interaction

Abstract. Nonlinear interactions of the barotropic Rossby waves propagating across the equator with trapped baroclinic Rossby or Yanai modes and mean zonal flow are studied within the two-layer model of the atmosphere, or the ocean. It is shown that the equatorial waveguide with a mean current acts as a resonator and responds to barotropic waves with certain wavenumbers by making the trapped baroclinic modes grow. At the same time the equatorial waveguide produces the barotropic response which, via nonlinear interaction with the mean equatorial current and with the trapped waves, leads to the saturation of the growing modes. The excited baroclinic waves can reach significant amplitudes depending on the magnitude of the mean current. In the absence of spatial modulation the nonlinear saturation of thus excited waves is described by forced Landau-type equation with one or two attracting equilibrium solutions. In the latter case the spatial modulation of the baroclinic waves is expected to lead to the formation of characteristic domain-wall defects. The evolution of the envelopes of the trapped Rossby waves is governed by driven Ginzburg-Landau equation, while the envelopes of the Yanai waves obey the "first-order" forced Ginzburg-Landau equation. The envelopes of short baroclinic Rossby waves obey the damped-driven nonlinear Schrodinger equation well studied in the literature.

Blocking systems over an aqua planet

It is well established that forced planetary waves are critically important for blocking formation. To test whether blocking can be generated and maintained in the absence of topographic forcing, we carry out aqua‐planet simulations using NCAR CAM2. Results show that blockings occur frequently under the aqua‐planet conditions which have no forcing such as land‐sea contrast, orography and stationary remote tropical forcing. Features of simulated blockings well resemble that in the real atmosphere, showing typical Ω‐like patterns, persistence, and quasi‐stationary behavior with occasionally westward shifting. It is found that the onset and maintenance of simulated blockings are due to interaction between quasi‐stationary free Rossby waves and baroclinic eddies. For 10‐year simulations, the blocking frequency is slightly higher than that in the Northern Hemisphere (NH) in the real atmosphere. These suggest that blocking is a natural consequence of rotating and baroclinic atmospheres, while locally topographic forcing and remote tropical forcing are not necessary conditions.

Free and Forced Rossby Waves in the Western South China Sea Inferred from Jason-1 Satellite Altimetry Data.

Data from a subsurface mooring deployed in the western South China Sea shows clear intra-seasonal oscillations (ISO) at the period of 40~70 days. Analysis of remotelysensed sea surface height (SSH) anomalies in the same area indicates that these ISO signals propagate both eastward and westward. Time-longitude diagrams of ISO signals in SSH anomalies and wind-stress curl indicate that the eastward propagating SSH anomalies is forced by wind-stress curl. This is also confirmed by lag correlation between SSH anomalies and the wind-stress-curl index (wind stress curl averaged over 109.5ºE -115ºE and 12ºN -13.5ºN). Lag correlation of SSH anomaly suggests that the westward propagating signals are free Rossby waves.

Free and Forced Rossby Waves in the Western South China Sea Inferred from Jason-1 Satellite Altimetry Data

Data from a subsurface mooring deployed in the western South China Sea shows clear intra-seasonal oscillations (ISO) at the period of 40∼70 days. Analysis of remotely-sensed sea surface height (SSH) anomalies in the same area indicates that these ISO signals propagate both eastward and westward. Time-longitude diagrams of ISO signals in SSH anomalies and wind-stress curl indicate that the eastward propagating SSH anomalies is forced by wind-stress curl. This is also confirmed by lag correlation between SSH anomalies and the wind-stress-curl index (wind stress curl averaged over 109.5°E -115°E and 12°N -13.5°N). Lag correlation of SSH anomaly suggests that the westward propagating signals are free Rossby waves.

Free and Forced Rossby Waves in the Western South China Sea Inferred from Jason-1 Satellite Altimetry Data

Data from a subsurface mooring deployed in the western South China Sea shows clear intra-seasonal oscillations (ISO) at the period of 40~70 days. Analysis of remotelysensed sea surface height (SSH) anomalies in the same area indicates that these ISO signals propagate both eastward and westward. Time-longitude diagrams of ISO signals in SSH anomalies and wind-stress curl indicate that the eastward propagating SSH anomalies is forced by wind-stress curl. This is also confirmed by lag correlation between SSH anomalies and the wind-stress-curl index (wind stress curl averaged over 109.5ºE -115ºE and 12ºN -13.5ºN). Lag correlation of SSH anomaly suggests that the westward propagating signals are free Rossby waves.

On long baroclinic Rossby waves in the tropical North Atlantic observed from profiling floats

Argo float data (subsurface tracks and temperature profiles collected from March 2004 through May 2005) are used to detect signatures of long Rossby waves in the velocity of the currents at 1000‐m depth and temperature, between the ocean surface and 950 m, in the zonal band of 4°N–24°N in the tropical North Atlantic. Different types of long Rossby waves (with the characteristic scales between 1000 and 2500 km) are identified in the western [west of the Mid‐Atlantic Ridge (MAR)] and eastern [east of the MAR] subbasins. Along‐shore wind fluctuations and an equatorially forced coastal Kelvin wave were found to be responsible for the excitation of annual‐ and semiannual‐propagating Rossby waves in the eastern subbasin. These waves are transmitted along a waveguide formed by the African shelf and the MAR. The speed of their propagation varies in magnitude and direction because of bottom topography and irregularity of the coastline. Unstable standing Rossby waves with annual and semiannual periods are shown in both the subbasins. All unstable waves, decaying, radiate shorter free Rossby waves propagating both westward and northwestward, with speeds of up to 10 cm/s. The standing Rossby waves are probably excited by the wind‐driven Ekman pumping alone or in combination with linear and nonlinear resonance mechanisms. The additional analysis of subsurface float tracks from May 2005 through May 2006 supports the obtained results.

Optical altimetry: a new method for observing rotating fluids with applications to Rossby and inertial waves on a polar beta-plane

The entire free-surface elevation field of a rotating fluid in the laboratory can be imaged and analysed, by using it as a parabolic Newtonian telescope mirror. This ‘optical altimetry’ readily achieves a precision of better than 1 μm of surface elevation. The surface topography corresponds to the pressure field just beneath the surface. It is the streamfunction for the geostrophic hydrostatic circulation, which can be resolved to better than 0.1 mm s−1. Still and animated images thus produced, of the entire surface elevation field, are of value in themselves, and using a projected image (a speckle pattern), have the promise of providing quantitative slope and height field data recovered by PIV (particle imaging velocimetry) techniques. With homogeneous fluid, geostrophic flow is the same at all depths. Yet of equal interest are sheared stratified rotating flows where the surface pressure is associated with inertial waves, convection, and other motions, geostrophic or ageostrophic.Although the technique is designed for experiments in which Coriolis effects are strong, it is possible to use reflective imaging for flows at such high Rossby number that Coriolis effects are negligible, and hence this becomes a tool of more general interest in non-rotating fluid dynamics (for example, illuminating surface gravity waves).Examples are given, involving (i) the Taylor–Proudman effect with very slow flows over topography; (ii) quasi-geostrophic and inertial-wave flows over a mountain (f-plane); (iii) inertial waves generated by oscillatory forcing; (iv) Kelvin waves (v) free oscillatory Rossby waves on a polar β-plane; and (vi) stationary waves, blocking, jets and wakes with β-plane zonal flow past a mountain. Movies are available with the online version of the paper.

Intraseasonal variability near 10°N in the eastern tropical Pacific Ocean

New in situ observations from 10°N, 125°W during 1997–1998 show strong intraseasonal variability in meridional velocity and sea surface temperature. The 50‐ to 100‐day oscillations in sea surface height (SSH) have long been recognized as a prominent aspect of oceanic variability in the region of 9–13°N in the eastern Pacific Ocean. We use in situ and satellite data to more fully characterize this variability. The oscillations have zonal wavelengths of 550–1650 km and propagate westward in a manner consistent with the dispersion relation for first baroclinic mode, free Rossby waves in the presence of a mean westward flow. Analysis of 9 years of altimetry data shows that the amplitude of the 50‐ to 100‐day SSH variability at 10°N is largest on 90–115°W, with peak amplitudes occurring around April. Some eddies traveling westward at 10–13°N emanate from near the gulfs of Tehuantepec and Papagayo, but eddies sometimes also appear to intensify well away from the coast while in the North Equatorial Current (NEC). The hypothesis that the intraseasonal variability and its annual cycle are associated with baroclinic instability of the NEC is supported by a spatiotemporal correlation between the amplitude of 50‐ to 100‐day variability and the occurrence of westward zonal flows meeting an approximate necessary condition for baroclinic instability. The notion that baroclinic instability may be involved is further corroborated by the tendency of the NEC to weaken while the eddies intensify, even as the wind works to strengthen the current.

On zonal jets in oceans

We find that in parameter regimes relevant to the recently observed alternating zonal jets in oceans, the formation of these jets can be explained as due to an arrest of the turbulent inverse‐cascade of energy by free Rossby waves (as opposed to Rossby basin modes) and a subsequent redirection of that energy into zonal modes. This mechanism, originally studied in the context of alternating jets in Jovian atmospheres and two dimensional turbulence in zonally‐periodic configurations survives in spite of the presence of the meridional boundaries in the oceanic context.

Coastal transition zone off Chile

Seven years of subsurface current observations at deep‐sea and continental slope moorings off Chile (30°S), satellite sea surface anomaly, and satellite wind stress are used to examine space, time, and propagation characteristics of the mesoscale eddy activity in the coastal transition zone off Chile. This zone off Chile extends from the coast to ∼600–800 km offshore and can be separated into two latitudinal regions. The first region, between 29° and 39°S off central Chile, is characterized by high eddy kinetic energy and strong but variable equatorward wind stress. The second region, between 19° and 29°S off northern Chile, is characterized by low eddy kinetic energy and weak but persistent equatorward wind stress. Low‐frequency mesoscale variability off central Chile is mainly associated with baroclinic instability of coastal currents and westward propagation of Rossby waves from the eastern boundary and is strongly modulated over El Niño/La Niña cycles. Application of a new rotary wavelet spectrum method to the recording current meter data and the use of current estimates from satellite altimeter data show that mesoscale eddies and meanders in the coastal transition zone fluctuate with periods centered on 120 days and with length scales centered on ∼200 km. Cross‐rotary wavelet analyses of currents and wind stress indicate that fluctuations of coastal currents with periods longer than 220 days propagated westward as free Rossby waves during 1995–1996 and as forced Rossby waves during 1999–2001.

Mechanisms for ENSO Phase Change in a Coupled GCM

The mechanisms leading to El Niño onset and termination in the ECHAM4/OPA coupled GCM are assessed and compared to observations and existing ENSO paradigms. At the equator as well as off equator, the patterns and timing of modeled El Niño composites are in good agreement with those observed. Heat content of the west Pacific is confirmed as a precursor to ENSO phase change, and the present work emphasizes the role of its northern off-equator part [west North Pacific (WNP) region, 5°–15°N, 120°–170°E]. The associated heat content changes appear to be dominated by a local Ekman pumping (or forced Rossby waves) rather than the accumulation of remotely generated free Rossby waves, as proposed by many theories. The heat content decrease in the WNP region, which triggers El Niño termination, is due to the negative feedback of the atmospheric Gill's response to the increased equatorial SST in the east Pacific, in agreement with most paradigms (delayed, recharged, west Pacific oscillators). The present study introduces the advection of the off-equator signal to the equatorial waveguide by the mean currents of the western Pacific as an additional process. A similar feedback (with opposite sign) also seems to drive the modeled El Niño onset, favoring a too strong and regular biennial ENSO in the model. This is due to the stronger-than-observed Walker circulation that isolates the WNP region from other remote influences (like monsoons). The model also exhibits “aborted” ENSO events where the warming peaks in late spring instead of late autumn and is quickly terminated by the Gill's negative feedback. The abort event occurs too frequently in the coupled model due to too strong and too zonal a convergence zone south of the equator (“double ITCZ”). It bears some resemblance to the spring 1993 warming, when the southern Tropics were also warm. The results of this paper provide additional insight into the El Niño seasonal phase lock mechanisms.

The Gill Model and the Weak Temperature Gradient Approximation

The authors investigate the accuracy of the weak temperature gradient (WTG) approximation, in which the divergent flow is computed by an assumed balance between adiabatic cooling and diabatic heating, for a prototype linear problem, the Gill model of a localized tropical heat source in a zonally periodic domain. As in earlier work by Neelin using a realistic, spatially distributed forcing, WTG is found to be a reasonable approximation to the full Gill model even when fairly large values of the thermal damping are used. Use of the local forcing and consideration of the different dispersion relations of free modes in the WTG and full Gill systems helps to clarify differences between the two solutions. WTG does not support an equatorial Kelvin wave. Instead, the Kelvin wave speed can be regarded as infinite in WTG. Hence, WTG becomes highly accurate when the thermal damping is sufficiently weak (0.1 day−1 or less) that an equatorial Kelvin wave can propagate around the globe without substantial loss of amplitude. Free Rossby waves are not equatorially trapped under WTG, and this increases the magnitude of the response far from the equator.

On turbulence and normal modes in a basin

The problem of forced, geostrophic turbulence in a basin is revisited. The primary focus is the time dependent field, which is shown to be approximately isotropic (in contrast to the strongly zonally anisotropic fields seen in periodic domains). It is also approximately homogeneous, away from the boundaries. Phenomenological arguments suggest the isotropy occurs because the inverse cascade of energy is arrested by basin normal modes rather than by free Rossby waves. Peaks in the velocity spectra at modal frequencies are consistent with basin modes, as has been noted previously. We discuss which modes would be excited and whether dissipation or the mean flow would be expected to alter the modes and their frequencies. A relatively novel feature is the use of Eulerian velocity statistics to quantify the wave and turbulence characteristics. These measures are more suitable to this environment than measures like wavenumber spectra, given the inhomogeneities associated with the boundaries. With regards to the mean, we observe a linear - relation in the region of the mean gyres (at the northern and southern boundaries), consistent with previous theories. This is of interest because our numerica. advection scheme has implicit rather than explicit small scale dissipation, and requires no boundary conditions on the vorticity. The gyre structure is however somewhat different than in an (inviscid) Fofonoff-type solution, suggesting dissipation cannot be neglected.

Annual variability of sea surface height and upper layer thickness in the Pacific Ocean

The annual variabilities of the sea surface height in the Pacific Ocean were investigated by analyzing the TOPEX/POSEIDON satellite data and by solving a reduced gravity model. We discuss how adequately the simple model can capture the variabilities of the sea surface height, and what the cause of the variabilities is. Three large amplitude peaks in the satellite data are found along the 12°N longitude line. Two elongated zones with a large amplitude are also found: one extends east-west along 6°N and the other extends northwestward from South America around 25°S. These features are adequately reproduced in the numerical simulation of the reduced gravity model. The propagation of the Rossby wave is analyzed by the use of the extended Eliassen-Palm flux to investigate the mechanism of these annual variabilities. The two east peaks around 12°N can be explained in terms of the interference between the local Ekman pumping and the free wave emitted near the western coast of North America, and the most western peak is affected by the Rossby wave formed by the local wind stress. The elongated zonal area around 6°N is mainly due to the local Ekman pumping. Another area around 25°S results from the convergence of the free Rossby wave emitted from the eastern boundary and the area with the strong wind stress curl off South America. A discrepancy between the satellite data and the model results suggests that the eastern equatorial Pacific Ocean is relatively calm in the model but not in the satellite data.