Mode Rossby Waves Research Articles

Baroclinic Rossby Waves With Phase Lag Cause Seasonal Upward‐Propagating Signals in the Mid‐Depth Equatorial Pacific Ocean

AbstractBased on OFES outputs verified by mooring observations, the seasonal characteristics in the middepth (1,000–3,000 m) equatorial Pacific Ocean are investigated in detail. The seasonal upward‐propagating signals, consisting of one positive and one negative anomaly, are identified at the equator. The harmonic analyses indicate that the seasonal variations in the middepth equatorial Pacific Ocean originate from the downward‐propagating energy dominated by the first meridional modes of Rossby waves. The superposition of first and second baroclinic modes of Rossby waves could reproduce the seasonal variations. Furthermore, a series of superposition experiments show that the phase lag between the two modes needs to be in the range of 0 to π to cause upward phase propagation. It implies that the baroclinic modes in the seasonal variations may not be generated simultaneously so that the Rossby waves with specific phase lag can cause upward‐propagating signals in the middepth equatorial Pacific Ocean. This new finding will enhance the understanding of seasonal variations in the middepth equatorial Pacific Ocean.

How Mesoscale Eddies Masquerade as Rossby Waves in Merged Altimetric Products

AbstractWave‐like signals formed by mesoscale‐eddy propagation, in particular, overlap with actual waves, resulting in Rossby waves being misidentified or overestimated. This study revisited the puzzle of wave‐eddy aliasing in state‐of‐the‐art altimetric products, with up to six altimetry satellites operating simultaneously after 2016. Spatiotemporal scales and westward‐propagating speeds are the primary factors in diagnosing a low‐latitude Rossby wave regime from a high‐latitude geostrophic turbulence regime, confirming the coexistence of Rossby waves and eddies in wave‐like components. Long‐lived westward‐propagating eddies (prevailing in oceans at latitudes 10°–40°) with weaker meridional deflection are good candidates for masquerading as Rossby waves. The focus here is therefore on the long, first baroclinic mode Rossby waves, which are quantified in several periodic bands by removing eddy signals. From 2016 to 2020, energetic biannual Rossby waves can explain more than 10% of observed sea level anomalies at latitudes equatorward of ±25°, ±20°, and ±15° in the Pacific, Indian, and Atlantic Oceans, respectively. Numerical modeling results support similar assessments, indicating an intrinsic property of eddies masquerading as Rossby waves. This study provides a more accurate assessment of oceanic Rossby waves, which can deepen insight into the energy cascade of the geostrophic features and their dynamic effects on biogeochemical cycles.

Modes of summer temperature intraseasonal oscillations and heatwaves over the Indian region

Over the Indian region, the pre-monsoon (i.e. April–May) is a dry summer season. The heatwaves, as well as local temperature variations during this season, are not associated with significant large-scale convective heating like the monsoonal modes, and several studies identified several drivers of heatwaves. Heatwaves are extreme events. Are these extremes arising from low-frequency intraseasonal modes, in the same way, extreme rainfall occurs on a synoptic or intraseasonal mode during monsoon? Studies do not explicitly point out the existence of temperature intraseasonal modes during April–May over the Indian region, and it is not clear if some of the drivers of heatwaves can also explain the April–May temperature variations as derivative of some modes. This study identifies the dominant pair of the intrinsic mode of temperature intraseasonal oscillations, which can also explain the heatwave spikes. The empirical orthogonal function based modes are isolated in the detrended surface temperature data to remove the global warming mode. It was found that the subtropical jet acting as a Rossby wave guide drives the first mode with pan India spatial modal signature, while the second mode is driven by the extratropical Rossby wave modes originating from the latitudes of the eddy-driven jet. Another important result is that the first (second) mode principal component shows a significant decreasing (increasing) trend from 1981–2020 period. The observed spatial heterogeneity in warming and the trend in the spatial distribution of extreme temperature events in India could also be explained by the trend in the two modes of oscillation.

Second Baroclinic Mode Rossby Waves in the South Indian Ocean

Abstract Many previous studies of midlatitude Rossby waves have examined satellite altimetry data, which reflect variability near the surface above the pycnocline. Argo float observations provide hydrographic data in the upper 2000 m, which likely monitor subsurface variability below the pycnocline. This study examines the variability in meridional velocity at midlatitudes and investigates Rossby waves in the southern Indian Ocean using an ocean reanalysis generated by a 4DVAR method. The results show two modes of variability. One is trapped near the surface and propagates to the west at a phase speed close to that of first baroclinic mode Rossby waves. This mode is representative of variability detected by satellite altimetry. The other mode has a local peak in amplitude at ∼600-m depth and propagates to the west at a phase speed 3 times slower than the first baroclinic mode. Such slowly propagating signals are observed globally, but they are largest in amplitude in the southern Indian Ocean and consistent in phase speed with the second baroclinic mode. Results from numerical experiments using an OGCM show that zonal winds in the tropical Pacific Ocean related to ENSO are the primary driver of slowly propagating signals in the southern Indian Ocean. Wind forcing in the tropical Pacific Ocean drives a surface trapped jet that propagates via the Indonesian Archipelago and excites subsurface variability in meridional velocity in the southern Indian Ocean. In addition, surface heat flux and meridional winds near the west coast of Australia can drive subsurface variability. Significance Statement Many previous studies of midlatitude Rossby waves have used satellite altimetry measurements, which reflect variability in the upper few hundred meters of the ocean. Argo float observations have provided in situ hydrographic observations in the upper 2000 m, and these enable us to examine subsurface variability with high reliability. In this study, we used output from an ocean reanalysis, which assimilates in situ observations, and found that the meridional velocity below the surface (∼600-m depth) of the southern Indian Ocean propagates at a phase speed 3 times slower than that of surface variability. These slowly propagating signals can be of climatic importance because of their possible impact on meridional heat transport. We also discuss the driving force of these slowly propagating signals.

Morlet Cross-Wavelet Analysis of Climatic State Variables Expressed as a Function of Latitude, Longitude, and Time: New Light on Extreme Events

This study aims to advance our knowledge in the genesis of extreme climatic events with the dual aim of improving forecasting methods while clarifying the role played by anthropogenic warming. Wavelet analysis is used to highlight the role of coherent Sea Surface Temperature (SST) anomalies produced from short-period oceanic Rossby waves resonantly forced, with two case studies: a Marine Heatwave (MHW) that occurred in the northwestern Pacific with a strong climatic impact in Japan, and an extreme flood event that occurred in Germany. Ocean–atmosphere interactions are evidenced by decomposing state variables into period bands within the cross-wavelet power spectra, namely SST, Sea Surface Height (SSH), and the zonal and meridional modulated geostrophic currents as well as precipitation height, i.e., the thickness of the layer of water produced during a day, with regard to subtropical cyclones. The bands are chosen according to the different harmonic modes of the oceanic Rossby waves. In each period band, the joint analysis of the amplitude and the phase of the state variables allow the estimation of the regionalized intensity of anomalies versus their time lag in relation to the date of occurrence of the extreme event. Regarding MHWs in the northwestern Pacific, it is shown how a warm SST anomaly associated with the northward component of the wind resulting from the low-pression system induces an SST response to latent and sensible heat transfer where the latitudinal SST gradient is steep. The SST anomaly is then shifted to the north as the phase becomes homogenized. As for subtropical cyclones, extreme events are the culmination of exceptional circumstances, some of which are foreseeable due to their relatively long maturation time. This is particularly the case of ocean–atmosphere interactions leading to the homogenization of the phase of SST anomalies that can potentially contribute to the supply of low-pressure systems. The same goes for the coalescence of distinct low-pressure systems during cyclogenesis. Some avenues are developed with the aim of better understanding how anthropogenic warming can modify certain key mechanisms in the evolution of those dynamic systems leading to extreme events.

Atlantic equatorial deep jets in Argo float data

Abstract Equatorial deep jets (EDJ) are zonal currents along the equator in all three ocean basins that alternate in direction with depth and time. In the Atlantic below the thermocline, they are the dominant variability on interannual timescales. Observations of equatorial deep jets are available but scarce, given the EDJs’ location at depth, their small vertical scale and their long periodicity of several years. In the last few years, Argo floats have added a significant amount of measurements at intermediate depth. In this study we therefore revise estimates of the EDJ scales based on Argo float data. Mostly, we use velocity data at 1000 m depth calculated from float displacement, which yield robust estimates of the Atlantic EDJ period (4.6 years), amplitude distribution, phase distribution, zonal wavelength (146.7°), and meridional structure. We also show that the equatorial amplitude of the EDJs’ first meridional mode Rossby wave component (9.8 cm s−1) is larger than that of their Kelvin wave component (2.8 cm s−1). Additionally, we present a new estimation of the EDJs’ vertical structure throughout the Atlantic basin, based on an equatorial geostrophic velocity reconstruction from hydrographic Argo float measurements from depths between 400 and 2000 m. Our new estimates from Argo float data provide the first basin-wide assessment of the Atlantic EDJ scales, as well as having smaller uncertainties than estimates from earlier studies.

Roles of vertical distributions of atmospheric transient eddy dynamical forcing and diabatic heating in midlatitude unstable air\u2013sea interaction

Atmospheric transient eddy dynamical forcing (TEDF)-driven midlatitude unstable air–sea interaction has recently been recognized as a crucial positive feedback for the maintenance of the extratropical decadal variabilities. Our recent theoretical work (Chen et al., Clim Dyn https://doi.org/10.1007/s00382-020-05405-0, 2020) has characterized such an interaction through building an analytical midlatitude barotropic atmospheric model coupled to a simplified upper oceanic model. This study extends the analytical model to including a two-layer quasi-geostrophic baroclinic atmospheric model and then identifies the roles of vertical distributions of atmospheric TEDF and diabatic heating in midlatitude unstable air–sea interaction. It is found that midlatitude air–sea coupling with more realistic vertical profiles of atmospheric TEDF and diabatic heating destabilizes oceanic Rossby wave modes over the entire range of zonal wavelengths, in which the most unstable coupled mode features an equivalent barotropic atmospheric low (high) pressure over a cold (warm) oceanic surface. Spatial structure and period of the most unstable mode are more consistent with the observation than those from in previous model. Although either TEDF or diabatic heating alone can lead to a destabilized coupled mode, the former makes a dominant contribution to the instability. The increase of low-layer TEDF stimulates the instability more effectively if the TEDF in upper layer is larger than in lower layer, while the TEDF in either high or low layers can individually cause the instability. The surface heating always destabilizes the air–sea interaction, while the mid-level heating always decays the coupled mode. The results of this study further confirm the TEDF-driven positive feedback mechanism in midlatitude air–sea interaction proposed by recent observational and numerical experiment studies.

Glaciers and Paleorecords Tell Us How Atmospheric Circulation Changes and Successive Cooling Periods Occurred in the Fennoscandia during the Holocene

Two major climatic phenomena that occurred during the Holocene are interpreted from the resonance in subharmonic modes of long-period Rossby waves winding around the North Atlantic gyre, the so-called gyral Rossby waves (GRWs). These are, on the one hand, the change in atmospheric circulation that occurred in the North Atlantic in the middle Holocene, and, on the other hand, the occurrence of abrupt cooling events more frequently than what is generally accepted. The amplitude of GRWs is deduced by filtering, within bands characteristic of various subharmonic modes, climate records from the Greenland ice sheet, pollen, and tree rings in northern Fennoscandia, and from two Norwegian glaciers in northern Folgefonna and on the Lyngen peninsula. While the subharmonic modes reflect the acceleration/deceleration phases of the western boundary current, an anharmonic mode is evidenced in the 400–450 year band. Abrupt cooling events of the climate are paced by this anharmonic mode while the western boundary current is decelerating, and the northward heat advection of air favors the melting of the pack ice. Then, the current of the northernmost part of the North Atlantic gyre cools before branching off to the north, which alters its buoyancy. On the other hand, according to high subharmonic modes, high-pressure systems prevailed over the North Atlantic in the first half of the Holocene while low-pressure systems resulted from baroclinic instabilities of the atmosphere dominate during the second half, favoring the growth of glaciers in Scandinavia by a better snowfall in winter and cooler summers.

Four Types of Baroclinic Instability Waves in the Global Oceans and the Implications for the Vertical Structure of Mesoscale Eddies

AbstractLinear stability analysis is re‐conducted to fully understand the geostrophic distribution of the different types of baroclinic instability (BCI) in the global oceans, their correspondence to the different vertical structures of the observed mesoscale eddies, and the properties and formation mechanisms of the instability waves. Four principal vertical types of BCI are identified, which are found to exhibit large‐scale patterns in the global ocean. The surface‐ and bottom‐intensified type (called the Eady type hereafter) is mainly located in the Antarctic Circumpolar Current (ACC) region, locations of the bottom‐intensified type (Charney_b type) are scattered around the Eady type, the surface‐intensified type (Charney_s type) primarily occurs in the subtropics (10°–35°), and the interior‐intensified type (Phillips type) occurs primarily between 5° and 20° in both hemispheres. More specifically, both geostrophic locations and the depths of the maximum perturbation velocities of the Phillips type BCIs match those of observed subsurface eddies. Moreover, the BCI waves show regions of uniform propagation properties: eastward in the ACC and the mid‐latitudes (25°–45°), and westward in the low latitudes (30°S–30°N) of both hemispheres and in the high latitudes of the Northern Hemisphere (>50°N). These waves resemble normal mode Rossby waves in structure (i.e., first baroclinic, second baroclinic, and topographic Rossby waves), but their propagation speeds are found to be Doppler shifted by the mean flows relevant for the corresponding BCI type. Propagating signals with the same dispersion relationships as the BCI waves are captured with numerical ocean general circulation models.

Baroclinic Characteristics and Energetics of Annual Rossby Waves in the Southern Tropical Indian Ocean

AbstractThe first baroclinic mode Rossby wave is known to be of critical importance to the annual sea level variability in the southern tropical Indian Ocean (STIO; 0°–20°S, 50°–115°E). In this study, an analysis of continuously stratified linear ocean model reveals that the second baroclinic mode also has significant contribution to the annual sea level variability (as high as 81% of the first baroclinic mode). The contributions of residual high-order modes (3 ≤ n ≤ 25) are much less. The superposition of low-order (first and second) baroclinic Rossby waves (BRWs) primarily contribute to the high energy center of sea level variability at ~10°S in the STIO and the vertical energy penetration below the seasonal thermocline. We have found that 1) the low-order BRWs, having longer zonal wavelengths and weaker damping, can couple more efficiently to the local large-scale wind forcing than the high-order modes and 2) the zonal coherency of the Ekman pumping results in the latitudinal energy maximum of low-order BRWs. Overall, this study extends the traditional analysis to suggest the characteristics of the second baroclinic mode need to be taken into account in interpreting the annual variability in the STIO.

Numerical study on interaction between eddies and the Kuroshio Current east of Taiwan, China

We investigated the interaction between mesoscale eddies and the Kuroshio Current east of Taiwan, China, using a fine-resolution regional general circulation model. Mesoscale eddies are injected into a region east of Taiwan, China, according to the quasi-geostrophic theory of stratified fluids. Modeled eddies propagated westward at the velocity of the first baroclinic mode Rossby wave. When eddies collide with the Kuroshio Current east of Taiwan, China, the spatial structure and volume transport of the Kuroshio Current shows a significant variation. The upper 600 m of the anticyclonic eddy cannot cross the Kuroshio Current to reach the region west of the Kuroshio Current; rather, these waters flow northward along the eastern side of the Kuroshio Current. The upper water carried by the anticyclonic eddies cannot reach the shelf of the East China Sea (ECS). In contrast, the waters in the upper layer of the cyclonic eddy reach the western side of the Kuroshio Current and then flow northward. The dynamic mechanism analysis shows that the interaction between the Kuroshio Current and the cyclonic (anticyclonic) eddy decrease (increase) the horizontal potential vorticity (PV) gradient, or PV barrier, whereby the cyclonic (anticyclonic) eddy can (cannot) cross the Kuroshio Current. This study implies that the continental shelf could potentially be influenced by cyclonic eddies in the open ocean, which can transport heat and material from the upper open ocean across the Kuroshio Current to the shelf waters.

Intermediate Intraseasonal Variability in the Western Tropical Pacific Ocean: Meridional Distribution of Equatorial Rossby Waves Influenced by a Tilted Boundary

AbstractIntermediate-depth intraseasonal variability (ISV) at a 20–90-day period, as detected in velocity measurements from seven subsurface moorings in the tropical western Pacific, is interpreted in terms of equatorial Rossby waves. The moorings were deployed between 0° and 7.5°N along 142°E from September 2014 to October 2015. The strongest ISV energy at 1200 m occurs at 4.5°N. Peak energy at 4.5°N is also seen in an eddy-resolving global circulation model. An analysis of the model output identifies the source of the ISV as short equatorial Rossby waves with westward phase speed but southeastward and downward group velocity. Additionally, it is shown that a superposition of first three baroclinic modes is required to represent the ISV energy propagation. Further analysis using a 1.5-layer shallow water model suggests that the first meridional mode Rossby wave accounts for the specific meridional distribution of ISV in the western Pacific. The same model suggests that the tilted coastlines of Irian Jaya and Papua New Guinea, which lie to the south of the moorings, shift the location of the northern peak of meridional velocity oscillation from 3°N to near 4.5°N. The tilt of this boundary with respect to a purely zonal alignment therefore needs to be taken into account to explain this meridional shift of the peak. Calculation of the barotropic conversion rate indicates that the intraseasonal kinetic energy below 1000 m can be transferred into the mean flows, suggesting a possible forcing mechanism for intermediate-depth zonal jets.

The Structure of Baroclinic Modes in the Presence of Baroclinic Mean Flow

AbstractThis contribution seeks to understand the vertical structure of linearized quasigeostrophic baroclinic modes when they are modified by the presence of a baroclinic mean flow and associated potential vorticity gradients. It is found that even modest, O(0.05 m s−1), mean flows can give rise to very substantial changes in modal structures, often in the sense of increased surface intensification. The extent to which stable modes are modified depends strongly on the direction of Rossby wave propagation. Further, baroclinically unstable solutions can appear, and a meaningful inviscid critical-layer solution can occur at the transition to instability when the horizontal gradient of potential vorticity changes sign at some depth within the water column. In addition, the gravest, n = 0, vertical stable mode is no longer strictly barotropic, but rather it can carry density variability at frequencies much higher than those possible for baroclinic (higher) Rossby wave modes. This finding appears to be consistent with oceanic current-meter observations that suggest temperature variability propagation even when the frequency is too high for traditional baroclinic Rossby waves to exist.

Large‐Amplitude Quasi‐10‐Day Waves in the Middle Atmosphere During Final Warmings

AbstractGeopotential height measurements from the Aura Microwave Limb Sounder between 9‐ and 97‐km altitudes during 2004–2018 are used to examine long‐period (3–20 days) wave activity during the Northern Hemisphere winter and spring, with the primary focus on the response of normal mode Rossby waves in the middle atmosphere to sudden stratospheric warmings (SSWs). Unusually large westward propagating waves with Zonal Wave Number 1 and period ∼10 days are observed at 55° latitude at the stratopause height (∼48 km) and above following final warmings of 2016, 2015, and 2005. In each case, large‐amplitude waves are observed for the duration of two to three wave cycles. Characteristics of the waves are in conformity with the second antisymmetric Rossby normal mode of Zonal Wave Number 1, or the quasi‐10‐day wave. The growth rate of the waves is significantly greater than the classical normal mode in the upper stratosphere (approximately 30–50 km) where instability conditions are met, indicating the amplification or excitation of the waves in that region. The response of the quasi‐10‐day wave during midwinter SSWs, and also during the spring transition without an SSW, is not as obvious as the wave response during final warmings. The results suggest that not only the occurrence of SSW but also the seasonal timing of SSW is an important factor for the transient variability of the quasi‐10‐day wave in the middle atmosphere.

Wind-driven decadal sea surface height and main pycnocline depth changes in the western subarctic North Pacific

The northward shrinkage of the North Pacific western subarctic gyre (WSAG) in the early 2000s is associated with a sea surface height (SSH) elevation and is correlated to sea surface wind stress change. By using a Rossby wave model forced by wind stress, which computes the component variations due to the barotropic and first to fourth baroclinic modes, we estimated decadal changes in SSH and main pycnocline depth in the subpolar region. Realistic decadal SSH elevation and deepening of the main pycnocline depth associated with the northward shrinkage of the western subarctic gyre from the late 1990s to the mid-2000s were reproduced by the model. The sea surface elevation was caused primarily by the barotropic Rossby wave response to the relaxation of the Ekman suction due to the attenuation of the Aleutian Low by frequent La Niña occurrences after the late 1990s in addition to the long-term weakening of the westerly wind. The northward shrinkage of the WSAG was found to be associated with the intensification of an anticyclonic circulation centered around 43–44 ∘ N, 170–175 ∘ E. The westerly wind weakening deepened the main pycnocline in the western subarctic region through the baroclinic Rossby wave mode response to the wind stress change, which mostly accounts the equivalent halocline deepening at station K2 (47 ∘ N, 160 ∘ E). While the first baroclinic mode variation of the water density significantly attenuates during propagation, the higher mode variations, particularly the second and third mode variations, are locally excited through a quasi-resonant amplification mechanism and have profound impacts on the depth of the upper main pycnocline.

Investigating an Unusually Large 28‐Day Oscillation in Mesospheric Temperature Over Antarctica Using Ground‐Based and Satellite Measurements

AbstractThe Utah State University Advanced Mesospheric Temperature Mapper was deployed at the Amundsen‐Scott South Pole Station in 2010 to measure OH temperature at ~87 km as part of an international network to study the mesospheric dynamics over Antarctica. During the austral winter of 2014, an unusually large amplitude ~28‐day oscillation in mesospheric temperature was observed for ~100 days from the South Pole Station. This study investigates the characteristics and global structure of this exceptional planetary‐scale wave event utilizing ground‐based mesospheric OH temperature measurements from two Antarctic stations (South Pole and Rothera) together with satellite temperature measurements from the Microwave Limb Sounder on the Aura satellite and the Solar Occultation For Ice Experiment on the Aeronomy of Ice in the Mesosphere satellite. Our analyses have revealed that this large oscillation is a wintertime, high‐latitude phenomenon, exhibiting a coherent zonal wave #1 structure below 80‐km altitude. At higher altitudes, the wave was confined in longitude between 180°E and 360°E. The amplitude of this oscillation reached ~15 K at 85 km, and it was observed to grow with altitude as it extended from the stratosphere into the lower thermosphere in the Southern Hemisphere. The satellite data further established the existence of this oscillation in the Northern Hemisphere during the boreal wintertime. The main characteristics and global structure of this event as observed in temperature are consistent with the predicted 28‐day Rossby Wave (1,4) mode.

Mixed Rossby–Gravity Wave–Wave Interactions

AbstractMixed triad wave–wave interactions between Rossby and gravity waves are analytically derived using the kinetic equation for models of different complexity. Two examples are considered: initially vanishing linear gravity wave energy in the presence of a fully developed Rossby wave field and the reversed case of initially vanishing linear Rossby wave energy in the presence of a realistic gravity wave field. The kinetic equation in both cases is numerically evaluated, for which energy is conserved within numerical precision. The results are validated by a corresponding ensemble of numerical model simulations supporting the validity of the weak-interaction assumption necessary to derive the kinetic equation. Since they are generated by nonresonant interactions only, the energy transfers toward the respective linear wave mode with vanishing energy are small in both cases. The total generation of energy of the linear gravity wave mode in the first case scales to leading order as the square of the Rossby number in agreement with independent estimates from laboratory experiments, although a part of the linear gravity wave mode is slaved to the Rossby wave mode without wavelike temporal behavior.

Impact of Rossby waves on chlorophyll variability in the southeastern Arabian Sea

ABSTRACTWe use remotely sensed ocean colour data to show that Rossby waves are associated with the westward migration of chlorophyll distribution patterns in the southeastern Arabian Sea (SEAS). During the winter monsoon (November–February), the high chlorophyll concentrations observed along the west coast of India and Sri Lanka drifts westwards along with the downwelling Rossby waves. The speed of these chlorophyll signatures is in rough agreement with the expected second baroclinic mode Rossby wave speed. Observations from Ocean Surface Currents Analyses Real-time (OSCAR) suggest that it is the geostrophic currents associated with the Rossby wave propagation that influences the surface chlorophyll concentrations in the SEAS. The westward migration of chlorophyll is weaker during the summer monsoon (June–September) when the upwelling Rossby wave is observed in the sea-level data.

Equatorial Stokes drift and Rossby rip currents

AbstractThe Stokes drift in long baroclinic equatorial Rossby waves is investigated theoretically by using eigenfunction expansions in the vertical. These waves are nondispersive and propagate westward along the equator. Particular attention is paid to the first baroclinic, first meridional Rossby wave mode which has been observed in the equatorial Pacific. It is demonstrated that the Stokes drift depends very much on the depth‐variation of the Brunt‐Väisälä frequency. Even more importantly, it is found that, for arbitrary stable stratification, the total zonal Stokes volume transport induced by the Rossby wave mode (1,1) is identically zero. The eastward drift due reflected wave energy in the form of internal equatorial Kelvin waves is also addressed. Due to the very long period of the incident Rossby wave mode (1,1), the reflected equatorial Kelvin wave must at least be a 2. mode component in the vertical. The corresponding Stokes drift only induces a minor change near the surface of the total westward drift velocity at the equator. The implication for the existence of compensating Rossby rip currents along the equator is discussed.

Rotating magnetic shallow water waves and instabilities in a sphere

Waves in a thin layer on a rotating sphere are studied. The effect of a toroidal magnetic field is considered, using the shallow water ideal MHD equations. The work is motivated by suggestions that there is a stably stratified layer below the Earth’s core mantle boundary, and the existence of stable layers in stellar tachoclines. With an azimuthal background field known as the Malkus field, , being the co-latitude, a non-diffusive instability is found with azimuthal wavenumber . A necessary condition for instability is that the Alfvén speed exceeds where is the rotation rate and the sphere radius. Magneto-inertial gravity waves propagating westward and eastward occur, and become equatorially trapped when the field is strong. Magneto-Kelvin waves propagate eastward at low field strength, but a new westward propagating Kelvin wave is found when the field is strong. Fast magnetic Rossby waves travel westward, whilst the slow magnetic Rossby waves generally travel eastward, except for some modes at large field strength. An exceptional very slow westward magnetic Rossby wave mode occurs at all field strengths. The current-driven instability occurs for when the slow and fast magnetic Rossby waves interact. With strong field the magnetic Rossby waves become trapped at the pole. An asymptotic analysis giving the wave speed and wave form in terms of elementary functions is possible both in polar trapped and equatorially trapped cases.