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This study investigates the intensity change of binary tropical cyclones (TCs) in idealized cloud-resolving simulations. Four simulations of binary interaction between two initially identical mature TCs of about 70 m s−1 with initial separation distance varying from 480 to 840 km are conducted in a quiescent f-plane environment. Results show that two identical TCs finally merge if their initial separation distance is within 600 km. The binary TCs presents two weakening stages (stages 1 and 3) with a quasi-steady evolution (stage 2) in between. Such intensity change of one TC is correlated with the upper-layer vertical wind shear (VWS) associated with the upper-level anticyclone (ULA) of the other TC. The potential temperature budget shows that eddy radial advection of potential temperature induced by large upper-layer VWS contributes to the weakening of the upper-level warm core and thereby the weakening of binary TCs in stage 1. In stage 2, the upper-layer VWS first weakens and then restrengthens with relatively weak magnitude, leading to a quasi-steady intensity evolution. In stage 3, due to the increasing upper-layer VWS, the nonmerging binary TCs weaken again until their separation distance exceeds the local Rossby radius of deformation of the ULA (about 1600 km), which can serve as a dynamical critical distance within which direct interaction can occur between two TCs. In the merging cases, the binary TCs weaken prior to merging because highly asymmetric structure develops as a result of strong horizontal deformation of the inner core. However, the merged system intensifies shortly after merging.

Surface quasi-geostrophic (SQG) flows with a much larger horizontal scale than the Rossby radius of deformation are considered. A new version of the SQG model with two boundaries, which is reduced ...

In this study, we report results from a high-resolution measurement of submesoscale turbulence in a mesoscale eddy. The kinetic energy spectra in the mesoscale eddy are decomposed into mesoscale and submesoscale components using Helmholtz decomposition and wave-vortex decomposition methods. The length scale of transition from mesoscale to submesoscale is quantitatively determined, which is roughly consistent with the first baroclinic Rossby radius of deformation (44 km) and has a relatively weak dependence on depth. Two distinct spectral slopes for the mesoscale and submesoscale turbulence are identified: the kinetic energy spectrum at mesoscale has a vertical average − 2.6 slope, which agrees with the interior QG turbulence theory; at submesoscale, the average slope is −1.5 and weakly dependent on depth, which is consistent with the GM internal wave spectrum.

Hydraulic jumps at the interface of stratified rotating fluids are studied. The flow is de- fined with continuous density and velocity profiles, with the velocity in each layer changing (upstream shear). The study is conducted in jumps defined by an imposed velocity transition, and jumps developing over a topography. The numerical simulations conducted showed the qualitative structure of the flow changing in the cross-width direction, as well as the size and amount of turbulence of the jumps. Mixing in these jumps was shown to increase towards the side of the domain where the jumps were larger and more turbulent. The qualitative structure of the flow remained unchanged in the cases with topography. The amount of mixing was also shown to decrease as rotation values increase. In the simulations with topography, the size of the jumps and the amount of mixing were shown to depend on upstream shear developing over the topography.

In areas with rough bathymetry, the vertical structure of ocean eddies can be decomposed into “surface modes,” which are surface intensified, and exhibit a velocity of nearly zero at the bottom . Furthermore, ocean surface modes are ubiquitous. Atlases of the first surface mode (SM1) deformation radius were computed on a global $$0.25 \times 0.25^{^\circ }$$ grid using WOA2013 and the data from Generalized Digital Environment Model (GDEM). Monthly and seasonal changes were also analyzed. The annual average SM1 deformation radius was approximately 1.5 times larger than the Rossby radius of deformation; the main difference occurred in areas with rough bathymetry, including continental margins and mid-ocean ridges. The seasonal and monthly average SM1 deformation radius shows an evident annual cycle. The vertical structure of ocean eddies can be decomposed into “surface modes” with rough bathymetry. We used two sets of data to calculate the global distribution of deformation radius of the first surface mode (SM1) and its seasonal and monthly changes. The annual average SM1 deformation radius was approximately 1.5 times larger than the Rossby radius of deformation, and the main difference occurs in areas with rough bathymetry. The seasonal and monthly average SM1 deformation radius exhibits an annual cycle.

The weather layers of the gas giant planets, Jupiter and Saturn, comprise the shallow atmospheric layers that are influenced energetically by a combination of incoming solar radiation and localised latent heating of condensates, as well as by upwelling heat from their planetary interiors. They are also the most accessible regions of those planets to direct observations. Recent analyses in Oxford of cloud-tracked winds on Jupiter have demonstrated that kinetic energy is injected into the weather layer at scales comparable to the Rossby radius of deformation and cascades both upscale, mostly into the extra-tropical zonal jets, and downscale to the smallest resolvable scales in Cassini images. The large-scale flow on both Jupiter and Saturn appears to equilibrate towards a state which is close to marginal instability according to Arnol'd's 2nd stability theorem. This scenario is largely reproduced in a hierarchy of numerical models of giant planet weather layers, including relatively realistic models which seek to predict thermal and dynamical structures using a full set of parameterisations of radiative transfer, interior heat sources and even moist convection. Such models include the Jason GCM, developed in Oxford, which also represents the formation of (energetically passive) clouds of NH3, NH4SH and H2O condensates and the transport of condensable tracers. Recent results show some promise in comparison with observations from the Cassini and Juno missions, but some observed features (such as Jupiter's Great Red Spot and other compact ovals) are not yet captured spontaneously by any weather layer model. We review recent work in this vein and discuss a number of open questions for future study., 27 pages, including 7 figures. Submitted to Geoscience Letters as invited review from 2019 assembly of the Asia-Oceania Geosciences Society

How well do we know the particulate backscattering coefficient (bbp) in the global ocean? Satellite lidar bbp has never been validated globally and few studies have compared lidar bbp to bbp derived from reflectances (via ocean color) or in situ observations. Here, we validate lidar bbp with autonomous biogeochemical Argo floats using a decorrelation analysis to identify relevant spatiotemporal matchup scales inspired by geographical variability in the Rossby radius of deformation. We compare lidar, float, and ocean color bbp at the same locations and times to assess performance. Lidar bbp outperforms ocean color, with a median percent error of 18% compared to 24% in the best case and a relative bias of −11% compared to −21%, respectively. Phytoplankton carbon calculated from ocean color and lidar exhibits basin-scale differences that can reach ±50%., Plain Language Summary Backscattering of light by particles is an important input for many studies concerning ecology and the carbon cycle. There are two main types of satellite sensors that measure backscattering but they have not been validated worldwide. In order to use backscattering for global questions, we need to understand how well both satellite approaches perform. Passive ocean color sensors act like wide-view cameras capturing sunlight scattered by ocean constituents, whereas active sensors use a laser system that illuminates the ocean and measures the return pulses of light within a narrow spatial range. In this study, we compare backscatter data from both satellite sensor types to matchup backscattering data collected in situ by a global network of floats. We find that backscatter data from the active and passive satellite sensors disagree, particularly at low backscattering values. Overall, the active sensor performs best when compared to field data. We applied the lidar data to reassess global phytoplankton carbon and find regional differences from conventional estimates that can reach ±50%.

Convective mixing, mesoscale eddies and regenerated production sustain an above-average biological productivity in the North East Arabian Sea (NEAS) during the winter-spring transition period. Satellite-derived long-term data sets on Chlorophyll-a (Chl-a), Sea Surface Height Anomaly (SSHA), Sea Surface Temperature (SST) and Okubo-Weiss parameterization show existence of number of mesoscale eddies, propagating and non-propagating, that contribute to the regional production. The dominance of Eddy Kinetic Energy (EKE) over the Available Potential Energy (APE) in the core depth and the diameter (120 km) of the observed eddy being wider than the Rossby Radius of Deformation (RRD, 55 km), it is suggested that the baroclinic instability is a possible mechanism for the eddy formation. Spatial variation in APE and its influences on the regional dynamics, including chemical and biological response are explained. In the non-eddy areas, where convective mixing is active, diatoms (96.74%) dominated than dinoflagellates (3.14%), and the Chl-a in the Cold Core Eddy (CCE) were two to three folds higher to non-eddy regions. The abundance increased from core (58,152 cells L−1) to periphery (5.95 × 105 cells L−1) where the water column is less dynamic. Extensive blooms of the dinoflagellate green Noctiluca (N. scintillans) contribute to the very high cell density in the periphery of the CCE, where the currents were comparatively weak, and water column was more stable. Active mixing is associated with diatom dominance, followed by Noctiluca when the mixing slackens, making use of the available nutrients and supported by regenerated production. The bloom dynamics is explained for pre-bloom, bloom and post-bloom conditions with measurements on nutrients and plankton assemblages. The Noctiluca bloom (mid-March) is succeeded by Trichodesmium (April–May), in the stratified nutrient depleted, abundant light environment and propagated southwards. Observed increasing trends in the SSHA over the period indicate strengthening of stratification and hence altered production patterns in the NEAS.

Spectral nudging allows forcing a selected part of the spectrum of a model's solution with the equivalent part in a reference dataset, such as an analysis, reanalysis or another model. This constrains the evolution in certain scales, typically the synoptic ones, while allowing the others to evolve freely. In a limited area model (LAM) setting, spectral nudging is commonly used to impose the large-scale circulation in the interior of the domain, so that the high resolution features in the LAM's forecast are consistent with the global circulation patterns. In a previous study developed over a Mid-Latitude domain, we investigated two parameters of spectral nudging that are often overlooked despite having a significant impact on the model solution. First, the cut-off wave number, which is the parameter determining the scales that are nudged and has a critical impact on the spatial structure of the model solution. Second, the spin-up time, which is the time required to balance the nudging force with the model internal climate and roughly indicates the starting point from when the results of the simulation contain useful information. The question remains if our conclusions for Mid-Latitudes are applicable to other areas of the planet. Tropical Latitudes offer an interesting testbed as its atmospheric dynamics has unique characteristics with respect to that further North and yet it is the result of the same underlying physical principles. We study the impact of these two parameters in a domain centred in the Gulf of Mexico, with a particular aim to evaluate their performance related to hurricane modelling. We perform 4-day simulations along 6 monthly periods between 2010 and 2015, testing several spectral nudging configurations. Our results indicate that the optimal cut off wavenumber lies between 1000 Km and 1500 Km depending on the studied variable and that the spin-up time required is at least 72 h to 96 h, which is consistent with our previous work. We evaluate our findings in four hurricane cases, allowing for at least 96 h of spin-up time before the system becomes a tropical storm. Results confirm that the experiments with cut-off wavenumbers near the Rossby Radius of Deformation perform best. We also propose a novel approach in which a different cut-off wavenumber is used for each variable. Our tests in the hurricane cases show that the latter set up is able to outperform all of the other spectral nudging experiments when compared to observations.

International audience; This study is devoted to laboratory experiments on the coalescence of two lenticular anticyclones in a linearly stratified rotating fluid. These anticyclones are generated by injecting small volumes of fluid at the center of a rotating tank where a linearly stratified layer was previously prepared with salt. The characteristics of the interaction between the vortices are studied by visualization and Particle Image Velocimetry (PIV) as a function of the initial separation distance between the vortices, the Coriolis parameter of the rotating table and the Brünt-Väisälä frequency of the density stratification. Our results show that the merging critical distance depends drastically on the Rossby radius of deformation of the vortices and are in complete agreement with previous numerical modeling of vortex coalescence. We have also observed that mergers involve three-dimensional processes as the vortices intertwine together possibly because of the presence of an elliptic instability that tilts the vortex cores. They are also accompanied by the emission of vorticity filaments and internal gravity waves radiation although we cannot prove that in our experiments these waves are solely due to the merging process.

International audience; Ocean circulation is dominated by turbulent geostrophic eddy fields with typical scales ranging from 10 to 300 km. At mesoscales (>50 km), the size of eddy structures varies regionally following the Rossby radius of deformation. The variability of the scale of smaller eddies is not well known due to the limitations in existing numerical simulations and satellite capability. Nevertheless, it is well established that oceanic flows (

The barotropic vorticity equation is a classical model in atmospheric sciences. In this paper, we study the symmetry invariance properties of multipliers (integrating factors) admitted by this equation. The results are classified according to the ratio of the characteristic length scale to the Rossby radius of deformation and the variation of earth’s angular rotation. A plethora of conservation laws can be obtained by studying the interaction between Lie point symmetry generators and multipliers.

As climate models move towards higher resolution, their ocean components are now able to explicitly resolve mesoscale eddies. High resolution for ocean models is roughly classified into eddy-present (EP, ∼ 1/4°) and eddy-rich (ER, ∼ 1/12°) resolution. The cost–benefit of ER resolution over EP resolution remains debated. To inform this discussion, we quantify and compare the surface properties of coherent mesoscale eddies in high-resolution versions of the HadGEM3-GC3.1 coupled climate model, using an eddy tracking algorithm. The modelled properties are compared to altimeter observations. Relative to EP, ER resolution simulates more (+60%) and longer-lasting (+23%) eddies, in better agreement with observations. The representation of eddies in Western Boundary Currents (WBCs) and the Southern Ocean compares well with observations at both resolutions. However a common deficiency in the models is the low eddy population in subtropical gyre interiors, which reflects model biases at the Eastern Boundary Upwelling Systems and at the Indonesian outflow, where most of these eddies are generated in observations. Despite a grid spacing larger than the Rossby radius of deformation at high-latitudes, EP resolution does allow for eddy growth in these regions, although at a lower rate than seen in observations and ER resolution. A key finding of our analysis is the large differences in eddy size across the two resolutions and observations: the median speed-based radius increases from 14 km at ER resolution to 32 km at EP resolution, compared with 48 km in observations. It is likely that observed radii are biased high by the effective resolution of the gridded altimeter dataset due to post-processing. Our results highlight the limitations of the altimeter products and the required caution when employed for understanding eddy dynamics and developing eddy parameterizations.

This study aims to determine the spatial–temporal scales where the SST forcing of the near-surface winds takes places, and its relationship with the action of coherent ocean eddies. Here, cross-spectral statistics are used to examine the relationship between satellite-based SST and 10-m wind speed (w) fields at scales between 10 $$^2$$ –10 $$^4$$ km and 10 $$^1$$ –10 $$^3$$ days. It is shown that the transition from negative SST/w correlations at large-scales to positive at oceanic mesoscales occurs at wavelengths coinciding with the atmospheric first baroclinic Rossby radius of deformation; and that the dispersion of positively-correlated signals resembles tropical instability waves near the equator, and Rossby waves in the extratropics. Transfer functions are used to estimate the SST-driven w response in physical space ( $$w_c$$ ), a signal that explains 5–40% of the mesoscale w variance in the equatorial cold tongues, and 2–15% at extratropical SST fronts. The signature of ocean eddies is clearly visible in $$w_c$$ , accounting for 20–60% of its variability in eddy-rich regions. To provide further insight on the role of ocean eddies in the SST-driven coupling, the analysis is repeated for two climate model (CCSM) simulations using ocean grid resolutions of $$1^\circ$$ (eddy-parameterized, LR) and $$0.1^\circ$$ (eddy-resolving, HR). The lack of resolved eddies in LR leads to a significantly underestimated mesoscale w variance relative to HR. Conversely, the $$w_c$$ variability in HR can exceed the satellite estimates by a factor of two at extratropical SST fronts and underestimate it by a factor of almost six near the equator, reflecting shortcomings of the CCSM to be addressed in its future developments.

Based on an eddy-permitting numerical model, the mesoscale variability in the East-Sakhalin Current is investigated during the winter-spring period. Analysis of necessary conditions for the development of baroclinic instability showed that the nearshore component of the East-Sakhalin Current is potentially baroclinic unstable in the first half-year. The simulated circulation uncovered a generation of anticyclonic eddies on the eastern Sakhalin shelf. It was established that a spatial scale of these eddies and the first baroclinic Rossby radius of deformation are values of the same order; a lifetime of these eddies varies from 4 to 6 weeks, given the Rossby number varies from 0.05 to 0.2. Analysis of the rate of eddy energy conversion on the eastern Sakhalin shelf showed that the generation of the revealed mesoscale eddies results from, mainly, baroclinic instability, whereas barotropic instability can be both favoring and preventing to the generation of these eddies.

We consider quasi-geostrophic (Q-G) models in two- and three-layers that are useful in theoretical studies of planetary atmospheres and oceans. In these models, the streamfunctions are given by (1+2) partial differen- tial systems of evolution equations. A two-layer Q-G model, in a simpli- fied version, is dependent exclusively on the Rossby radius of deformation. However, the f-plane Q-G point vortex model contains factors such as the density, thickness of each layer, the Coriolis parameter, and the constant of gravitational acceleration, and this two-layered model admits a lesser number of Lie point symmetries, as compared to the simplified model. Finally, we study a three-layer oceanography Q-G model of special inter- est, which includes asymmetric wind curl forcing or Ekman pumping, that drives double-gyre ocean circulation. In three-layers, we obtain solutions pertaining to the wind-driven double-gyre ocean flow for a range of physi- cally relevant features, such as lateral friction and the analogue parameters of the f-plane Q-G model. Zero-order invariants are used to reduce the partial differential systems to ordinary differential systems. We determine conservation laws for these Q-G systems via multiplier methods., 14 pages, 6 figures, 1 table

We discuss the performance of the Finite Element Ocean Model (FESOM) on locally eddy-resolving global unstructured meshes. In particular, the utility of the mesh design approach whereby mesh horizontal resolution is varied as half the Rossby radius in most of the model domain is explored. Model simulations on such a mesh (FESOM-XR) are compared with FESOM simulations on a smaller-size mesh, where refinement depends only on the pattern of observed variability (FESOM-HR). We also compare FESOM results to a simulation of the ocean model of the Max Planck Institute for Meteorology (MPIOM) on a tripolar regular grid with refinement toward the poles, which uses a number of degrees of freedom similar to FESOM-XR. The mesh design strategy, which relies on the Rossby radius and/or the observed variability pattern, tends to coarsen the resolution in tropical and partly subtropical latitudes compared to the regular MPIOM grid. Excessive variations of mesh resolution are found to affect the performance in other nearby areas, presumably through dissipation that increases if resolution is coarsened. The largest improvement shown by FESOM-XR is a reduction of the surface temperature bias in the so-called North-West corner of the North Atlantic Ocean where horizontal resolution was increased dramatically. However, other biases in FESOM-XR remain largely unchanged compared to FESOM-HR. We conclude that resolving the Rossby radius alone (with two points per Rossby radius) is insufficient, and that careful use of a priori information on eddy dynamics is required to exploit the full potential of ocean models on unstructured meshes.

We have studied rotating magnetohydrodynamic flows of a thin layer of astrophysical plasma with a free boundary in the β-plane. Nonlinear interactions of the Rossby waves have been analyzed in the shallow-water approximation based on the averaging of the initial equations of the magnetic fluid dynamics of the plasma over the depth. The shallow-water magnetohydrodynamic equations have been generalized to the case of a plasma layer in an external vertical magnetic field. We have considered two types of the flow, viz., the flow in an external vertical magnetic field and the flow in the presence of a horizontal magnetic field. Qualitative analysis of the dispersion curves shows the presence of three-wave nonlinear interactions of the magnetic Rossby waves in both cases. In the particular case of zero external magnetic field, the wave dynamics in the layer of a plasma is analogous to the wave dynamics in a neutral fluid. The asymptotic method of multiscale expansions has been used for deriving the nonlinear equations of interaction in an external vertical magnetic field for slowly varying amplitudes, which describe three-wave interactions in a vertical external magnetic field as well as three-wave interactions of waves in a horizontal magnetic field. It is shown that decay instabilities and parametric wave amplification mechanisms exist in each case under investigation. The instability increments and the parametric gain coefficients have been determined for the relevant processes.

A climatological characterization of Rossby wave generation events in the middle atmosphere of the Southern Hemisphere is conducted using 20 years of Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalysis. An automatic detection technique of wave generation events is developed and applied to MERRA reanalysis. The Rossby wave generation events with wave period of 1.25 to 5.5 days and zonal wave number from one to three dominate the Eliassen-Palm flux divergence around the stratopause at high latitudes in the examined 20 year period. These produce an eastward forcing of the general circulation between May and mid-August in that region. Afterward from mid-August to the final warming date, Rossby wave generation events are still present but the Eliassen-Palm flux divergence in the polar stratopause is dominated by low-frequency Rossby waves that propagate from the troposphere. The Rossby wave generation events are associated with potential vorticity gradient inversion, and so they are a manifestation of the dominant barotropic/baroclinic unstable modes that grow at the cost of smearing the negative meridional gradient of potential vorticity. The most likely region of wave generation is found between 60° and 80°S and at a height of 0.7 hPa, but events were detected from 40 hPa to 0.3 hPa (which is the top of the examined region). The mean number of events per year is 24, and its mean duration is 3.35 days. The event duration follows an exponential distribution. Fil: Rodas, Claudio José Francisco. Universidad Nacional del Nordeste; Argentina Fil: Pulido, Manuel Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; Argentina

It has been suggested that upper-tropospheric Rossby wave packets propagating along the midlatitude waveguide may play a role for triggering severe weather. This motivates the search for robust methods to detect and track Rossby wave packets and to diagnose their properties. In the framework of several observed cases, this paper compares different methods that have been proposed for these tasks, with an emphasis on horizontal propagation and on a particular formulation of a wave activity flux previously suggested by Takaya and Nakamura. The utility of this flux is compromised by the semigeostrophic nature of upper-tropospheric Rossby waves, but this problem can partly be overcome by a semigeostrophic coordinate transformation. The wave activity flux allows one to obtain information from a single snapshot about the meridional propagation, in particular propagation from or into polar and subtropical latitudes, as well as about the onset of wave breaking. This helps to clarify the dynamics of individual wave packets in cases where other, more conventional methods provide ambiguous or even misleading information. In some cases, the “true dynamics” of the Rossby wave packet turns out to be more complex than apparent from the more conventional diagnostics, and this may have important implications for the predictability of the wave packet.

An array of six oceanographic moorings with acoustic and environmental sensors was deployed in the central Philippine Sea from April 2010 to April 2011. The location spanned 18−23°N, 124 – 130°E in the Subtropical Countercurrent (STCC). The most prominent feature of the data set was a densely-packed eddy field with about equal numbers of cyclones and anticyclones moving westward at 6–12 km d−1. Eddies of either sign displaced the thermocline about ±50 m and had surface velocities exceeding 110 cm s−1. While warm eddies were slightly larger than cold eddies, the distance to maximum radial velocity was similar for both at about 65 km, close to the local Rossby radius of deformation. The steepness parameter U/c in the eddies ranged from 3 to 10, accompanied by relative vorticity of order 0.1–0.3 f, suggesting nonlinear, quasigeostrophic features with trapped cores rather than linear waves. This was borne out by the water mass analysis which showed high salinity, high spice North Pacific Tropical Water (NPTW) being transported westward in the warm eddy cores. The total KE and APE in eddies of both signs was about 1×1015 J with 85% of the APE and 74% of the KE located above 250 m depth. This equipartitioning of energy suggests mature eddies near equilibrium, that had been evolving for some time as they propagated into the area from the east.

Motivated by recent studies on the significant summertime weather patterns in the Australian region, the life cycle of summertime transient Rossby wave packets in the Southern Hemisphere is investigated. The strength of the interaction between the wave packets and the jet I is defined by the advection of potential vorticity by the divergent part of the wind on the 350 K isentropic surface. The magnitude of I is used as the basis for time-lagged composites in distinct regions: SW Chile, SW Africa, over the Indian Ocean, SW Australia, and over the W Pacific. The interaction is strongest on the stratospheric side of the jet core. Although in each case cyclogenesis from a pre-existing disturbance in the upper troposphere precedes the generation of the Rossby wave packets, there are two types of interaction with the jet. In the SW Chile, SW Africa and Indian Ocean cases extratropical cyclogenesis and the associated convection lies on the poleward side of the jet, and hence I is positive. In the SW Australia and W Pacific cases, extratropical cyclogenesis occurs 3 days earlier than the others, and I is negative as it describes the interaction of a downstream propagating Rossby wave packet with the subtropical jet. In all cases, as the cyclones develop, the wave activity propagates from low levels to the upper levels of the troposphere, and then downstream and equatorwards towards higher values of refractive index. The equatorward refraction of the SW Australia and W Pacific wave packets is accompanied by enhanced tropical convection in the warm conveyor belt of the advancing front.

Convective variations over the tropical Indian Ocean associated with ENSO and the Indian Ocean Dipole force a Rossby wave train that appears to emanate poleward and eastward to the south of Australia and which causes climate variations across southern Australia and more generally throughout the Southern Hemisphere extratropics. However, during austral winter, the subtropical jet that extends from the eastern Indian Ocean into the western Pacific at Australian latitudes should effectively prohibit continuous propagation of a stationary Rossby wave from the tropics into the extratropics because the meridional gradient of mean absolute vorticity goes to zero on its poleward flank. The observed wave train indeed exhibits strong convergence of wave activity flux upon encountering this region of vanishing vorticity gradient and with some indication of reflection back into the tropics, indicating the continuous propagation of the stationary Rossby wave train from low to high latitudes is inhibited across the south of Australia. However, another Rossby wave train appears to emanate upstream of Australia on the poleward side of the subtropical jet and propagates eastward along the waveguide of the eddy-driven (sub-polar) jet into the Pacific sector of the Southern Ocean. This combination of evanescent wave train from the tropics and eastward propagating wave train emanating from higher latitudes upstream of Australia gives the appearance of a continuous Rossby wave train propagating from the tropical Indian Ocean into higher southern latitudes. The extratropical Rossby wave source on the poleward side of the subtropical jet stems from induced changes in transient eddy activity in the main storm track of the Southern Hemisphere. During austral spring, when the subtropical jet weakens, the Rossby wave train emanating from Indian Ocean convection is explained more traditionally by direct dispersion from divergence forcing at low latitudes.

The Stokes drift in long baroclinic equatorial Rossby waves is investigated theoretically by using eigenfunction expansions in the vertical. These waves are non-dispersive 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-Vaisala 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.

The adiabatic and diabatic processes inherent to midlatitude deep convective storms are well known to modify the atmospheric temperature, moisture, and winds especially within horizontal scales equivalent to a Rossby radius of deformation. Such modifications, or “feedbacks,” induced by supercell thunderstorms were a particular focus of the Mesoscale Predictability Experiment (MPEX), owing to the unique supercell dynamics and associated supercell intensity and longevity. During the MPEX field phase, which was conducted 15 May–15 June 2013 within the Great Plains region of the United States, radiosonde observations collected in immediate supercell wakes exhibited temperature lapse rates that were qualitatively and quantitatively similar to preconvective lapse rates above the boundary layer. Complementary idealized model simulations were used to confirm that there was little residual effect of the supercell in the wake of the moving storm except within the area occupied by the surface cold pool, and where stabilizations were induced adiabatically by transient gravity wave disturbances. The persistency of the (i) cold pool, and its inhibition to surface-based convection, depended on the evolving cold pool strength and environmental winds; and (ii) gravity wave effects depended on the Doppler-shifted phase speed relative to the moving storm. Otherwise, recovery of the wake environment to its preconvective state occurred approximately over a time scale defined by the updraft length scale and horizontal advective velocity scale.

Numerous studies have been presented describing the benefits of using Nudging to constrain the evolution of a numerical model. Recently, a variation of this approach called Spectral Nudging, has gained popularity for its ability to maintain the higher temporal and spatial variability of the model results, while forcing the large scales in the solution with a coarser resolution field. Here, we focus on a not much explored aspect of this technique: the impact of selecting different cut-off wave numbers and spin-up times. We perform four-day long simulations with the WRF model, daily for three different one-month periods including a free run and several Spectral Nudging experiments with cut-off wave numbers ranging from the smallest to the largest possible (Grid Nudging). Results show that Spectral Nudging is very effective at imposing the selected synoptic scales onto the solution, while allowing the limited area model to incorporate finer scale features. The model error diminishes rapidly as the nudging expands over broader parts of the spectrum, but this decreasing trend ceases sharply at cut-off wave numbers equivalent to a length scale of about 1000 km, and the error magnitude changes minimally thereafter. This scale corresponds to the Rossby Radius of deformation, separating synoptic from convective scales in the flow. When nudging is applied for scales larger than the Rossby Radius of deformation, a shifting of the synoptic patterns can occur in the solution, yielding large model corrections towards the analysis. However, when selecting smaller scales, the fine scale contribution of the model is damped, thus making 1000 km the appropriate scale threshold to nudge in order to balance both effects. Finally, we note that longer spin-up times are needed for model errors to stabilize when using Spectral Nudging than with Grid Nudging. Results suggest that this time is between 36 and 48 hours.

The study of the adjustment to equilibrium by a stratified fluid in a rotating reference frame is a classical problem in geophysical fluid dynamics. We consider the fully nonlinear, stratified adjustment problem from a numerical point of view. We present results of smoothed dam break simulations based on experiments in the published literature, with a focus on both the wave trains that propagate away from the nascent geostrophic state and the geostrophic state itself. We demonstrate that for Rossby numbers in excess of roughly 2 the wave train cannot be interpreted in terms of linear theory. This wave train consists of a leading solitary-like packet and a trailing tail of dispersive waves. However, it is found that the leading wave packet never completely separates from the trailing tail. Somewhat surprisingly, the inertial oscillations associated with the geostrophic state exhibit evidence of nonlinearity even when the Rossby number falls below 1. We vary the width of the initial disturbance and the rotation rate so as to keep the Rossby number fixed, and find that while the qualitative response remains consistent, the Froude number varies, and these variations are manifested in the form of the emanating wave train. For wider initial disturbances we find clear evidence of a wave train that initially propagates toward the near wall, reflects, and propagates away from the geostrophic state behind the leading wave train. We compare kinetic energy inside and outside of the geostrophic state, finding that for long times a Rossby number of around one-quarter yields an equal split between the two, with lower (higher) Rossby numbers yielding more energy in the geostrophic state (wave train). Finally we compare the energetics of the geostrophic state as the Rossby number varies, finding long-lived inertial oscillations in the majority of the cases and a general agreement with the past literature that employed either hydrostatic, shallow-water equation-based theory or stratified Navier–Stokes equations with a linear stratification.

A 2-km-resolution model of the eastern Bering Sea is developed to capture dynamical processes on the scale of the Rossby radius of deformation on tidal to seasonal time scales. The model spans the region from 178°E to the Alaskan coast and from roughly 50° to 66°N, including the Aleutian Islands in the south and the Bering Strait in the north. The high resolution throughout ensures that the mesoscale dynamics of significant subregions of the domain, such as the Aleutian Island passes, Bering Sea slope, and the shelf canyons, are captured simultaneously without the concern for loss of interconnectivity between regions. Simulations are performed for the ice-free season (June–October) of 2009, with tidal and atmospheric forcing. The model compares favorably with observations from AVHRR and Envisat satellites, Argo drifters, and Bering Sea shelf moorings. The mesoscale dynamics of the mixing and exchange flow through the eastern Aleutian Island passes, which exhibit strong diurnal and two-week variability, are well represented. The two-week oscillation in volume flux through the largest of these passes, Amukta Pass, is found to be out of phase with the transport through the neighboring passes (e.g., Seguam and Samalga passes). Mesoscale structure is also found to be ubiquitous along the mixing front of the cold pool. Structures at the scale of O(20 km) persist and play a role in determining the pattern of erosion of the water mass as the shelf warms and mixes. On the Bering Sea shelf, tidal motions are dominant, and variability on the horizontal scale of the first-mode internal tide develops (O(30 km)) from the shelf break to the onshore edge of the Bering shelf cold pool.

Using satellite altimetry measurement data for 1993–2013, we study the spectral characteristics of Rossby waves in the Northwestern Pacific (25°–50° N, 140°–180° E). For each latitude degree, we draw integral plots of spectral power density calculated with a two-dimensional Fourier transform (2D-FFT). We compare the dispersion equations of Rossby waves calculated from the WKB-approximation and an approximation of a two-layer ocean model with the empirical velocities determined by the slope of isopleths by the Radon method; also, we compare the dispersion equations with the spectral distributions of level variations. It is shown that the main energy of Rossby waves in the Northwestern Pacific corresponds to the first baroclinic mode. At almost all latitudes, there is good agreement between the empirical phase velocities calculated by isopleths by the Radon method and the theoretical values; also, the spectral peaks correspond to graphs of the dispersion equations for the first baroclinic mode Rossby waves, except for the Kuroshio region, where some peaks correspond to the second mode.

The baroclinic-to-barotropic pathway in ENSO teleconnections is examined from the viewpoint of a barotropic Rossby wave source that results from decomposition into barotropic and baroclinic components. Diagnoses using the NCEP–NCAR reanalysis are supplemented by analysis of the response of a tropical atmospheric model of intermediate complexity to the NCEP–NCAR barotropic Rossby wave source. Among the three barotropic Rossby wave source contributions (shear advection, vertical advection, and surface drag), the leading contribution is from shear advection and, more specifically, the mean baroclinic zonal wind advecting the anomalous baroclinic zonal wind. Vertical advection is the smallest term, while surface drag tends to cancel and reinforce the shear advection in different regions through damping on the baroclinic mode, which spins up a barotropic response. There are also nontrivial impacts of transients in the barotropic wind response to ENSO. Both tropical and subtropical baroclinic vorticity advection contribute to the barotropic component of the Pacific subtropical jet near the coast of North America, where the resulting barotropic wind contribution approximately doubles the zonal jet anomaly at upper levels, relative to the baroclinic anomalies alone. In this view, the barotropic Rossby wave source in the subtropics simply arises from the basic-state baroclinic flow acting on the well-known baroclinic ENSO flow pattern that spreads from the deep tropics into the subtropics over a scale of equatorial radius of deformation. This is inseparably connected to the leading deep tropical Rossby wave source that arises from eastern Pacific climatological baroclinic winds advecting the tropical portion of the same ENSO flow pattern.

The present study examined ENSO-related wind forcing contribution to off-equatorial Rossby wave formations in the eastern tropical regions of the North and South Pacific using satellite altimeter data and atmospheric reanalysis data during the period of 1993–2013. After mature phases of ENSO events, the sea surface height anomaly fields showed that off-equatorial Rossby waves propagated westward along 11°N and 8°S from the eastern Pacific. Starting longitudes of the westward propagation were distant from the eastern coast, especially for weak El Niño events in the 2000s, in contrast to the strong 1997/98 El Niño event in which the propagations started from the coast. Based on observational data, it was hypothesized that the Rossby waves could be formed by off-equatorial zonal belts of wind stress curl anomalies (WSCAs) in 135°–90°W rather than by wave emissions from the eastern coast. A numerical model forced only by WSCAs, that is, without wave emissions from the coast, successfully reproduced observed features of the Rossby waves in 180°–120°W, supporting the study’s hypothesis. During mature phases of El Niño events, equatorially symmetric negative sea level pressure anomalies (SLPAs) resulting from hydrostatic adjustment to the underlying warm sea surface temperature anomalies dominated over the eastern tropical Pacific. Anomalous surface easterlies blowing around the negative SLPA area as geostrophic winds were a major contributor in forming the anticyclonic WSCAs. The polarity of the anomalies is reversed during La Niña events. Therefore, spatial patterns of the SLPAs associated with the ENSO events are necessary to understand the Rossby wave formations.

Rossby waves are a principal form of atmospheric communication between disparate parts of the climate system. These planetary waves are typically excited by diabatic or orographic forcing and can be subject to considerable downstream modification. Because of differences in wave properties, including vertical structure, phase speed, and group velocity, Rossby waves exhibit a wide range of behaviors. This study demonstrates the combined effects of eastward-propagating stationary barotropic Rossby waves and westward-propagating very-low-zonal-wavenumber stationary barotropic Rossby waves on the atmospheric response to wintertime El Niño convective forcing over the tropical Pacific. Experiments are conducted using the Community Atmosphere Model, version 4.0, in which both diabatic forcing over the Pacific and localized relaxation outside the forcing region are applied. The localized relaxation is used to dampen Rossby wave propagation to either the west or east of the forcing region and isolate the alternate direction signal. The experiments reveal that El Niño forcing produces both eastward- and westward-propagating stationary waves in the upper troposphere. Over North Africa and Asia the aggregate undamped upper-tropospheric response is due to the superposition and interaction of these oppositely directed planetary waves that emanate from the forcing region and encircle the planet.

This study investigates tropical cyclone energy dispersion under horizontally sheared flows using a nonlinear barotropic model. In addition to common patterns, unusual features of Rossby wave trains are also found in flows with constant vorticity and vorticity gradients. In terms of the direction of the energy dispersion, the wave train can rotate clockwise and elongate southwestward under anticyclonic circulation (ASH), which contributes to the reenhancement of the tropical cyclone (TC). The wave train even splits into two obvious wavelike trains in flows with a southward vorticity gradient (WSH). Energy dispersed from TCs varies over time, and variations in the intensity of the wave train components typically occur in two stages. Wave-activity flux diagnosis and ray tracing calculations are extended to the frame that moves along with the TC to reveal the concrete progress of wave propagation. The direction of the wave-activity flux is primarily determined by the combination of the basic flow and the TC velocity. Along the flux, the distribution of pseudomomentum effectively illustrates the development of wave trains, particularly the rotation and split of wave propagation. Ray tracing involves the quantitative tracing of wave features along rays, which effectively coincide with the wave train regimes. Flows of a constant shear (parabolic meridional variation) produce linear (nonlinear) wave number variations. For the split wave trains, the real and complex wave number waves move along divergent trajectories and are responsible for different energy dispersion ducts.

The linear theory predicts that Rossby waves are the large scale mechanism of adjustment to perturbations of the geophysical fluid. Satellite measurements of sea level anomaly (SLA) provided sturdy evidence of the existence of these waves. Recent studies suggest that the variability in the altimeter records is mostly due to mesoscale nonlinear eddies and challenges the original interpretation of westward propagating features as Rossby waves. The objective of this work is to test whether a classic linear dynamic model is a reasonable explanation for the observed SLA. A linear-reduced gravity non-dispersive Rossby wave model is used to estimate the SLA forced by direct and remote wind stress. Correlations between model results and observations are up to 0.88. The best agreement is in the tropical region of all ocean basins. These correlations decrease towards insignificance in mid-latitudes. The relative contributions of eastern boundary (remote) forcing and local wind forcing in the generation of Rossby waves are also estimated and suggest that the main wave forming mechanism is the remote forcing. Results suggest that linear long baroclinic Rossby wave dynamics explain a significant part of the SLA annual variability at least in the tropical oceans.

Based on the Petviashvili equation, dynamics of Rossby dipole with effect of scalar nonlinearity is discussed. It is shown that the final dynamics of Rossby dipole depends on many factors such as interaction of scalar nonlinearity, vector nonlinearity and background flows. The Rossby blocking dipole is affected by the scalar nonlinearity more evidently. The seesaw phenomenon is also observed in the Rossby dipole evolution due to the two nonlinearities balance or its rotation structure.

Depth profiles of nitrous oxide (N2O) were measured during six cruises to the upwelling area and oxygen minimum zone (OMZ) off Peru in 2009 and 2012/2013, covering both the coastal shelf region and the adjacent open ocean. N2O profiles displayed a strong sensitivity towards oxygen concentrations. Open ocean profiles with distances to the shelf break larger than the first baroclinic Rossby radius of deformation showed a transition from a broad maximum close to the Equator to a double-peak structure south of 5° S where the oxygen minimum was more pronounced. Maximum N2O concentrations in the open ocean were about 80 nM. A linear relationship between ΔN2O and apparent oxygen utilization (AOU) could be found for measurements within the upper oxycline, with a slope similar to studies in other oceanic regions. In contrast, N2O profiles close to the shelf revealed a much higher variability, and N2O concentrations higher than 100 nM were often observed. The highest N2O concentration measured at the shelf was ∼ 850 nM. Due to the extremely sharp oxygen gradients at the shelf, N2O maxima occurred in very shallow water depths of less than 50 m. In the coastal area, a linear relationship between ΔN2O and AOU could not be observed as extremely high ΔN2O values were scattered over the full range of oxygen concentrations. The data points that showed the strongest deviation from a linear ΔN2O ∕ AOU relationship also showed signals of intense nitrogen loss. These results indicate that the coastal upwelling at the Peruvian coast and the subsequent strong remineralization in the water column causes conditions that lead to extreme N2O accumulation, most likely due to the interplay of intense mixing and high rates of remineralization which lead to a rapid switching of the OMZ waters between anoxic and oxic conditions. This, in turn, could trigger incomplete denitrification or pulses of increased nitrification with extreme N2O production.

Continental shelf baroclinic instability energized by fluctuating alongshore winds is treated using idealized primitive equation numerical model experiments. A spatially uniform alongshore wind, sinusoidal in time, alternately drives upwelling and downwelling and so creates highly variable, but slowly increasing, available potential energy. For all of the 30 model runs, conducted with a wide range of parameters (varying Coriolis parameter, initial stratification, bottom friction, forcing period, wind strength, and bottom slope), a baroclinic instability and subsequent eddy field develop. Model results and scalings show that the eddy kinetic energy increases with wind amplitude, forcing period, stratification, and bottom slope. The dominant alongshore length scale of the eddy field is essentially an internal Rossby radius of deformation. The resulting depth-averaged alongshore flow field is dominated by the large-scale, periodic wind forcing, while the cross-shelf flow field is dominated by the eddy variability. The result is that correlation length scales for alongshore flow are far greater than those for cross-shelf velocity. This scale discrepancy is qualitatively consistent with midshelf observations by Kundu and Allen, among others.

Annual Rossby waves in northern South China Sea had previously been studied using altimetry and model data; however, how they connect to subsurface temperature fluctuations has not been examined. This study analyzed a 22-month, surface to −500-m temperature time series at 18.3°N, 115.5°E, together with satellite and other data, to show the arrivals near z ≈ −300 m and deeper cool (warm) Rossby waves after their generation near the Luzon Strait in winter (summer). Temperature fluctuations with time scales of a few weeks, and with maximum anomalies near z ≈ −100 m, were also found embedded in the smooth Rossby waves and caused by propagating eddies. Eddy fluctuations and propagation past the mooring were of two types: southwestward from southwestern Taiwan, triggered by Kuroshio intrusion that produced anticyclone–cyclone pairs in late fall and winter, and eddies propagating westward from Luzon forced by annual anomalies of wind stress curl and Kuroshio path in the Luzon Strait

In epicontinental seas, as well as in oceans, amphidromic systems control tidal movement, acting on coastal dynamics and, therefore, influencing the depositional record. Inland seas were common in Pangea during the Permian. However, estimating the conditions that governed the tide in these seas is highly complex. Although Permian marine deposits are well documented on a regional scale, the tidal behavior in the epicontinental sea has not been analyzed yet. In this work, we present a theoretical perspective on the behavior of tides in the epicontinental sea of the Parana Basin during the Early Permian (Guata Sea), covering an area of ~1200,000 km2. Mathematical models were applied to test the existence of amphidromic points in the basin (determined from the Rossby radius of deformation) as well as to verify the possibility of resonance. Since paleodepth is unknown and the basin tectonism is still under discussion, an estimated bathymetry from 20 to 500 m was used to cover even some unlikely scenarios. We also tested, using mathematical models, the amplification of the tide inside two paleovalleys. The obtained results were compared to Hudson Bay, considered here to be a modern analog of the Guata Sea. According to the paleogeography, paleolatitude (Southern Hemisphere), and depositional records, the Guata Sea had clockwise-rotation amphidromic systems. However, resonant effects may also have affected circulation, especially at sea depth below 100 m. In the simulated scenarios, the tide amplification in both valleys was variable but concentrated between micro to mesotidal amplitudes. This study presents the first contribution to the understanding of the tidal behavior of the Early Permian epicontinental sea of the Parana Basin in the basinal context of the Gondwanan paleocontinent. Recognition of amphidromic circulation in an inland sea is important because it may help to explain the general behavior of tidal deposits recorded in the basin, which were built and reworked under the influence of this system.

In this paper we present a research of propagation characteristics of global Rossby wave and mesoscale eddies, and we preliminarily discussing the relationship between them from multiple datasets analysis. By filtering the MSLA-H data and by means of optimized SSH method we have extracted signals of the Rossby wave, and estimated the propagation speed (zonal phase speed) of the Rossby wave and eddies. Validation for the identification of the Rossby wave also has been completed with the Argo temperature and salinity data. The prime focus covers: propagation speed comparison between the Rossby wave and the eddies, propagation characteristics in different regions. Overlaying the signals of the Rossby wave with the signatures of the eddies indicates that the Rossby wave and the eddies propagates together (westward only) in the mid-latitude, but differences appear with increasing of latitude, especially in some areas affected by ocean current, for instance, the West Wind Drift(WWD) and the North Atlantic Drift(NAD). Actually we have found that the currents led the eddies, and the Rossby wave might play an accelerative or moderative role in the eddies propagation, as a result of the velocities of the eddies and the currents were matched well, but comparison between the Rossby wave and the eddies revealed disparity. The findings are useful for understanding the relationship between the Rossby wave and mesoscale eddies.

This study examines the link between upper-tropospheric planetary-scale Rossby waves and surface meteorological parameters based on the observations made in association with the Ganges Valley Aerosol Experiment (GVAX) campaign at an extratropical site at Aryabhatta Research Institute of Observational Sciences, Nainital (29.45° N, 79.5° E) during November–December 2011. The spectral analysis of the tropospheric wind field from radiosonde measurements indicates a predominance power of around 8 days in the upper troposphere during the observational period. An analysis of the 200 hPa meridional wind (v200 hPa) anomalies from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalysis shows distinct Rossby-wave-like structures over a high-altitude site in the central Himalayan region. Furthermore, the spectral analysis of global v200 hPa anomalies indicates the Rossby waves are characterized by zonal wave number 6. The amplification of the Rossby wave packets over the site leads to persistent subtropical jet stream (STJ) patterns, which further affects the surface weather conditions. The propagating Rossby waves in the upper troposphere along with the undulations in the STJ create convergence and divergence regions in the mid-troposphere. Therefore, the surface meteorological parameters such as the relative humidity, wind speeds, and temperature are synchronized with the phase of the propagating Rossby waves. Moreover, the present study finds important implications for medium-range forecasting through the upper-level Rossby waves over the study region.