Wave interaction for a generalized higher-dimensional Boussinesq equation describing the nonlinear Rossby waves

Based on an algebraically Rossby solitary waves evolution model,namely an extended(2+1)-dimensional Boussinesq equation,we firstly introduced a special transformation and utilized the Hirota method,which enable us to obtain multi-complexiton solutions and explore the interaction among the solutions.These wave functions are then employed to infer the influence of background flow on the propagation of Rossby waves,as well as the characteristics of propagation in multi-wave running processes.Additionally,we generated stereogram drawings and projection figures to visually represent these solutions.The dynamical behavior of these solutions is thoroughly examined through analytical and graphical analyses.Furthermore,we investigated the influence of the generalized beta effect and the Coriolis parameter on the evolution of Rossby waves.

Modified KdV equation for solitary Rossby waves with β effect in barotropic fluids

This paper uses the weakly nonlinear method and perturbation method to deal with the quasi-geostrophic vorticity equation,and the modified Korteweg-de Vries（mKdV） equations describing the evolution of the amplitude of solitary Rossby waves as the change of Rossby parameter β（у） with latitude у is obtained.

Long baroclinic Rossby waves with periods of about 500 d near 20°N in the northwest Pacific Ocean

On the basis of maps of sea level anomalies data set from October 1992 to January 2004, pronounced low frequency variations with periods of about 500 d are detected in the area near 20°N from 160°W to 130°E. A linear two-layer model is employed to explain the mechanism. It is found that the first-mode long baroclinic Rossby waves at 20°N in the northwest Pacific propagate westward in the form of free waves at a speed of about 10.3 cm/s. This confirms that the observed low frequency variabilities appear as baroclinic Rossby waves. It further shows that these low frequency variabilities around 20°N in the northwest Pacific can potentially be predicted with a lead up to 900 d.

Mesoscale Barotropic Instability of Vortex Rossby Waves in Tropical Cyclones

In this study, the barotropic stability of vortex Rossby waves （VRWs） in 2D inviscid tropical cyclone （TC）-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable conditions are discovered： （a） there must be at least one zero point of basic vorticity gradient in the radial scope; and （b） the relative propagation velocity of perturbations must be negative to the basic vorticity gradient, which reflects the restriction relationship of instable energy. The maximum growth rate of instable waves depends on the peak radial gradient of the mean vorticity and the tangential wavenumber （WN）. The vortex-semicircle theorem is also derived to provide bounds on the growth rates and phase speeds of VRWs. The typical basic states and different WN perturbations in a tropical cyclone （TC） are obtained from a high resolution simulation. It is shown that the first necessary condition for vortex barotropic instability can be easily met at the radius of maximum vorticity （RMV）. The wave energy tends to decay （grow） inside （outside） the RMV due mainly to the negative （positive） sign of the radial gradient of the mean absolute vorticity. This finding appears to help explain the developemnt of strong vortices in the eyewall of TCs.

Varying Rossby Wave Trains from the Developing to Decaying Period of the Upper Atmospheric Heat Source over the Tibetan Plateau in Boreal Summer

This study demonstrates the two different Rossby wave train（RWT） patterns related to the developing/decaying upper atmospheric heat source over the Tibetan Plateau（TPUHS） in boreal summer. The results show that the summer TPUHS is dominated by quasi-biweekly variability, particularly from late July to mid-August when the subtropical jet steadily stays to the north of the TP. During the developing period of TPUHS events, the intensifying TPUHS corresponds to an anomalous upper-tropospheric high over the TP, which acts as the main source of a RWT that extends northeastward, via North China, the central Pacific and Alaska, to the northeastern Pacific region. This RWT breaks up while the anomalous high is temporarily replaced by an anomalous low due to the further deepened convective heating around the TPUHS peak. However, this anomalous low, though existing for only three to four days due to the counteracting dynamical effects of the persisting upper/lower divergence/convergence over the TP, acts as a new wave source to connect to an anomalous dynamical high over the Baikal region. Whilst the anomalous low is diminishing rapidly, this Baikal high becomes the main source of a new RWT, which develops eastward over the North Pacific region till around eight days after the TPUHS peak. Nevertheless, the anomaly centers along this decaying-TPUHS-related RWT mostly appear much weaker than those along the previous RWT.Therefore, their impacts on circulation and weather differ considerably from the developing to the decaying period of TPUHS events.

Large Scale Perturbations in Extratropical Atmosphere-Part Ⅰ: On Rossby Waves

This study reexamines the propagation mechanism and geostrophic property of the classical two-dimensional Rossby waves in a non-divergent barotropic atmosphere. It will be found that propagation of large scale atmospheric waves depends crucially on horizontal divergence. A small Rossby number in Rossby waves is not sufficient for the waves to have a small ageostrophic component, because the two-dimensional classical Rossby waves do not manifest the geostrophic balance as good as observed in the atmosphere.

Equatorward shift of annual Rossby waves in the Equatorial Pacific Ocean

Annual Rossby wave is a key component of the ENSO phenomenon in the equatorial Pacific Ocean. Due to the paucity and seasonal bias in historical hydrographic data,previous studies on equatorial Rossby waves only gave qualitative description. The accumulation of Argo measurements in recent years has greatly alleviated the data problem. In this study,seasonal variation of the equatorial Pacific Ocean is examined with annual harmonic analysis of Argo gridded data. Results show that strong seasonal signal is present in the western equatorial Pacific and explains more than 50% of the thermal variance below 500 m. Lag-correlation tracing further shows that this sub-thermocline seasonal signal originates from the eastern equatorial Pacific via downward and southwestward propagation of annual Rossby waves. Possible mechanisms for the equatorward shift of Rossby wave path are also discussed.

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean,and are parts of a large-scale system in fluid.The theory and observation show that,they satisfy quasi-geostrophic and quasi-static equilibrium approximations.In this paper,solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied.In order to simplify the problem,the topography is taken as a linear function of latitude variable y,then employing a weakly nonlinear method and a perturbation method,a KdV(Korteweg-de Vries) equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived.The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow,and extend the classical geophysical theory of fluid dynamics.

Variations in Wave Energy and Amplitudes along the Energy Dispersion Paths of Nonstationary Barotropic Rossby Waves

The variations in the wave energy and the amplitude along the energy dispersion paths of the barotropic Rossby waves in zonally symmetric basic flow are studied by solving the wave energy equation,which expresses that the wave energy variability is determined by the divergence of the group velocity and the energy budget from the basic flow.The results suggest that both the wave energy and the amplitude of a leading wave increase significantly in the propagating region that is located south of the jet axis and enclosed by a southern critical line and a northern turning latitude.The leading wave gains the barotropic energy from the basic flow by eddy activities.The amplitude continuously climbs up a peak at the turning latitude due to increasing wave energy and enlarging horizontal scale(shrinking total wavenumber).Both the wave energy and the amplitude eventually decrease when the trailing wave continuously approaches southward to the critical line.The trailing wave decays and its energy is continuously absorbed by the basic flow.Furthermore,both the wave energy and the amplitude oscillate with a limited range in the propagating region that is located near the jet axis and enclosed by two turning latitudes.Both the leading and trailing waves neither develop nor decay significantly.The jet works as a waveguide to allow the waves to propagate a long distance.

THE EFFECTS OF THE PLATEAU'S TOPOGRAPHIC GRADIENT ON ROSSBY WAVES AND ITS NUMERICAL SIMULATION

By using barotropic model equations, this article analyzed the characteristics of Rossby waves, the propaga- tion features of wave energy and the influence of dynamic and thermal effects of the Tibetan Plateau on Rossby waves, and the focus is on discussing the plateau＇s topographic gradient effects on atmospheric Rossby waves. Then based on the WRF3.2 and the NCEP/NCAR FNL reanalysis data, we devised comparative tests of changing the plateau＇s topo- graphic gradient and simulated a process of persistent heavy rain that happened in May 2010 in South China. The re- sults are shown as follows. The Tibetan Platean＇s topography is conducive to the formation of atmospheric Rossby waves, while the platean＇s terrain, its friction and heating effects can all make the atmospheric Rossby waves develop into the planetary waves; The effects of platean＇s north and south slopes on the Rossby wave＇ phase velocity is opposite, and when the slope reached a certain value can the quasi-steady normal fluctuations be generated; Simultaneously, due to the plateau＇s topographic gradient, descending motion appears at the west side of the plateau while ascending motion appears at the east side, and the vertical movement increased with the amplification of topographic gradients. The plateau＇s topographic gradient also obviously amplified the precipitation in South China, and the rainfall area increased with the amplification of topographic gradients and gradually moved from south to north and from west to east, which is conducive to the occurrence and development of convective activities in the downstream areas of the Tibetan Plateau; Moreover, for the plateau＇s dynamic and thermal effects, the Rossby wave＇ propagation shows upstream effects of ener- gy dispersion, so the plateau can then affect the weather in downstream areas. Moreover, the wave group velocity in- creased with the degree of topographic slope.

Mean Flow–Storm Track Relationship and Rossby Wave Breaking in Two Types of El-Nino

The features of large-scale circulation, storm tracks and the dynamical relationship between them were examined by investigating Rossby wave breaking （RWB） processes associated with Eastern Pacific （EP） and Central Pacific （CP） E1-Nifio. During EP E1-Nino, the geopotential height anomaly at 500 hPa （Z500） exhibits a Pacific-North America （PNA） pattern. During CP EI-Nifio, the Z500 anomaly shows a north positive-south negative pattern over the North Pacific. The anomalous distributions of baroclinicity and storm track are consistent with those of upper-level zonal wind for both EP and CP EI-Nino, suggesting impacts of mean flow on storm track variability. Anticyclonic wave breaking （AWB） oczurs less frequently in EP EI-Nino years, while cyclonic wave breaking （CWB） occurs more frequently in CP EI-Nino years over the North Pacific sector. Outside the North Pacific, more CWB events occur over North America during EP Ei-NiNo. When AWB events occur less frequently over the North Pacific during EP EI-Nino, Z500 decreases locally and the zonal wind is strengthened （weakened） to the south （north）. This is because AWB events reflect a monopoie high anomaly at the centroid of breaking events. When CWB events occur more frequently over the North Pacific under CP EI-Nino conditions, and over North America under EP EI-Nino condition, Z500 increases （decreases） to the northeast （southwest）, since CWB events are related to a northeast-southwest dipole Z500 anomaly. The anomalous RWB events act to invigorate and reinforce the circulation anomalies over the North Pacific-North America region linked with the two types of EI-Nino.

Propagation and modulational instability of Rossby waves in stratified fluids

Perturbation analysis and scale expansion are used to derive the(2+1)-dimensional coupled nonlinear Schr¨odinger(CNLS)equations that can describe interactions of two Rossby waves propagating in stratified fluids.The(2+1)-dimensional equations can reflect and describe the wave propagation more intuitively and accurately.The properties of the two waves in the process of propagation can be analyzed by the solution obtained from the equations using the Hirota bilinear method,and the influence factors of modulational instability are analyzed.The results suggest that,when two Rossby waves with slightly different wave numbers propagate in the stratified fluids,the intensity of bright soliton decreases with the increases of dark soliton coefficients.In addition,the size of modulational instable area is related to the amplitude and wave number in y direction.

mKdV Equation for Solitary Rossby Waves with Linear Topography Effect in Barotropic Fluids

The modify Korteweg-de Vries(mKdV) equations,governing the evolution of the amplitude of solitary Rossby waves,are derived from quasi-geostrophic vorticity equation by using the perturbation method.The result manifests that the linear topography effect with the change of latitude can induce solitary Rossby wave.

On the contribution of Rossby waves driven by surface buoyancy fluxes to low-frequency North Atlantic steric sea surface height variations

Previous studies have shown that wind-forced baroclinic Rossby waves can capture a large portion of lowfrequency steric sea surface height(SSH)variations in the North Atlantic.In this paper,the classical wind-driven Rossby wave model derived in a 1.5-layer ocean is extended to include surface buoyancy forcing,and the new model is then used to assess the contribution from buoyancy-forced Rossby waves to low-frequency North Atlantic steric SSH variations.Buoyancy forcing is determined from surface heating as freshwater fluxes are negligible.It is found that buoyancy-forced Rossby waves are important in only a few regions belonging to the subtropicaltomidlatitude and eastern subpolar North Atlantic.In these regions,the new Rossby wave model accounts for 25%-70% of low-frequency steric SSH variations.Furthermore,as part of the analysis it is also shown that a simple static model driven by local surface heat fluxes captures 60%-75% of low-frequency steric SSH variations in the Labrador Sea,which is a region where Rossby waves are found to have no influence on the steric SSH.

Two-Dimensional Rossby Waves： Exact Solutions to Petviashvili Equation

The two-dimensional （2D） nonlinear Rossby waves described by the Petviashvili equation, which has been invoked as an ageostrophic extension of the barotropic quasi-geostrophic potential vorticity equation, can be investigated through the exact periodic-wave solutions for the Petviashvili equation, while the exact analytical periodic-wave solutions to the Petviashvili equation are obtained by using the Jacobi elliptic function expansion method. It is shown that periodicwave 2D Rossby solutions can be obtained by this method, and in the limit cases, the 213 Rossby soliton solutions are also obtained.

A Survey of Statistical Relationships between Tropical Cyclone Genesis and Convectively Coupled Equatorial Rossby Waves

Convectively coupled equatorial Rossby waves(ERW)modulate tropical cyclone activities over tropical oceans.This study presents a survey of the statistical relationship between intraseasonal ERWs and tropical cyclone genesis(TCG)over major global TC basins using four-decade-long outgoing longwave radiation(OLR)and TC best-track datasets.Intraseasonal ERWs are identified from the OLR anomalies using an empirical orthogonal function(EOF)analysis method without imposing equatorial symmetry.We find that westward-propagating ERWs are most significant in four tropical ocean basins over the summer hemisphere and that ERWs exhibit similar northeast-southwest(southeast-northwest)tilted phase lines in the northern(southern)hemisphere,with an appreciable poleward advance of wave energy in most TC basins.The EOF-based ERW indices quantitatively show that ERWs significantly modulate TC genesis.The convectively active(suppressed)phases of ERWs coincide with increased(reduced)TCG occurrences.The TCG modulation by ERWs achieves the maximum where the ERWs propagate through the climatological TCG hotspots.As a result,the total number of TCG occurrences in the TC basins varies significantly according to the ERW phase.The ERW-TCG relationship is significant over the northwestern Pacific Ocean,northeastern Pacific Ocean,and the northern Indian Ocean during the northern summer seasons.In the southern summer season,the ERW-TCG relationship is significant over the southern Indian Ocean,Indonesian-Australia basin,and the southwestern Pacific Ocean.However,ERW activities are weak in the main TC development region of the Atlantic Ocean;and the impact on Atlantic TCG appears to be insignificant.

Thermal Effects of the Tibetan Plateau on Rossby Waves from the Diabatic Quasi-Geostrophic Equations of Motion

From the diabatic quasi-geostrophic equations of motion, the authors analyze the characteristics of diabatic Rossby waves including the thermal effects of the Tibetan Plateau. When the basic zonal flow is barotropic, it is demonstrated that the cooling of the Tibetan Plateau in winter not only facilitates the meridional propagation of Rossby waves but is an important driving mechanism of the intraseasonal oscillations in middle and high latitudes. When the basic zonal flow is baroclinic, it is found that the cooling of the Tibetan Plateau in winter facilitates the instability of Rossby waves, while in summer there is a threshold for the influence of the heating of the Tibetan Plateau on the stability of Rossby waves.

Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model

Variations in wave energy and amplitude for Rossby waves are investigated by solving the wave energy equation for the quasigeostrophic barotropic potential vorticity model.The results suggest that compared with rays in the nondivergent barotropic model,rays in the divergent model can have enhanced meridional and zonal propagation,accompanied by a more dramatic variability in both wave energy and amplitude,which is caused by introducing the divergence effect of the free surface in the quasigeostrophic model.For rays propagating in a region enclosed by a turning latitude and a critical latitude,the wave energy approaches the maximum value inside the region,while the amplitude approaches the maximum at the turning latitude.Waves can develop when both the wave energy and amplitude increase.For rays propagating in a region enclosed by two turning latitudes,the wave energy approaches the minimum value at one turning latitude and the maximum value at the other latitude,while the total wavenumber approaches the maximum value inside the region.The resulting amplitude increases if the total wavenumber decreases or the wave energy increases more significantly and decreases if the total wavenumber increases or the wave energy decreases more significantly.The matched roles of the energy from the basic flow and the divergence of the group velocity contribute to the slightly oscillating wave energy,which causes a slightly oscillating amplitude as well as the slightly oscillating total wavenumber.

Effect of low-frequency Rossby wave on thermal structure of the upper southwestern tropical Indian Ocean

We investigate the influence of low-frequency Rossby waves on the thermal structure of the upper southwestern tropical Indian Ocean (SWTIO) using Argo profiles, satellite altimetric data, sea surface temperature, wind field data and the theory of linear vertical normal mode decomposition. Our results show that the SWTIO is generally dominated by the first baroclinic mode motion. As strong downwelling Rossby waves reach the SWTIO, the contribution of the second baroclinic mode motion in this region can be increased mainly because of the reduction in the vertical stratification of the upper layer above thermocline, and the enhancement in the vertical stratification of the lower layer under thermocline also contributes to it. The vertical displacement of each isothermal is enlarged and the thermal structure of the upper level is modulated, which is indicative of strong vertical mixing. However, the cold Rossby waves increase the vertical stratification of the upper level, restricting the variability related to the second baroclinic mode. On the other hand, during decaying phase of warm Rossby waves, Ekman upwelling and advection processes associated with the surface cyclonic wind circulation can restrain the downwelling processes, carrying the relatively colder water to the near-surface, which results in an out-of-phase phenomenon between sea surface temperature anomaly (SSTA) and sea surface height anomaly (SSHA) in the SWTIO.

The interaction between zonal flow and Rossby waves with scalar nonlinearity

The nonlinear interactions between zonal flow and Rossby waves are studied by numerical simulations with focus on the effects of scalar nonlinearity. The numerical results show that the scalar nonlinearity has an appreciable influence on the Rossby dipole evolution and can reduce the threshold of the disturbance energy increase.