Nonlinear Saturation of Baroclinic Instability in the Phillips Model: The Case of Energy

A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model—the case of energy—is studied within the context of Arnold’s second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd’s; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances Φ′ i at any time.

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL(Ⅱ)- THE LOWER BOUND ON THE DISTURBANCE ENERGY AND POTENTIAL ENSTROPHY TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigatedThe lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL (Ⅰ) -THE UPPER BOUND ON THE EVOLUTION OF DISTURBANCE TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol's second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance.

Improving energetics in an ideal baroclinic instability case with a Physical Conserving Fidelity model

To improve the energetics in the life cycle of an ideal baroclinic instability case, we develop a Physical Conserving Fidelity model （F-model）, and we compare the simulations from the F-model to those of the traditional global spectral semi-implicit model （control model）. The results for spectral kinetic energy and its budget indicate different performances at smaller scales in the two models. A two-way energy flow emerges in the generation and rapid growth stage of the baroclinic disturbance in the F-model. However, only a downscale mechanism dominates in the control model. In the F-model, the meso- and smaller scales are energized initially, and then an active upscale nonlinear cascade occurs. Thus, disturbances at prior scales are forced by both downscale and upscale energy cascades and by conversion from potential energy. An analysis of the eddy kinetic energy budget also shows remarkable enhancement of the energy conversion rate in the F-model. As a result, characteristics of the ideal baroclinic wave are greatly improved in the F-model, in terms of both intensity and time of formation.

Seasonal variation of mesoscale eddy intensity in the global ocean

Mesoscale eddies are a prominent oceanic phenomenon that plays an important role in oceanic mass transport and energy conversion.Characterizing by rotational speed,the eddy intensity is one of the most fundamental properties of an eddy.However,the seasonal spatiotemporal variation in eddy intensity has not been examined from a global ocean perspective.In this study,we unveil the seasonal spatiotemporal characteristics of eddy intensity in the global ocean by using the latest satellite-altimetry-derived eddy trajectory data set.The results suggest that the eddy intensity has a distinct seasonal variation,reaching a peak in spring while attaining a minimum in autumn in the Northern Hemisphere and the opposite in the Southern Hemisphere.The seasonal variation of eddy intensity is more intense in the tropical-subtropical transition zones within latitudinal bands between 15°and 30°in the western Pacific Ocean,the northwestern Atlantic Ocean,and the eastern Indian Ocean because baroclinic instability in these areas changes sharply.Further analysis found that the seasonal variation of baroclinic instability precedes the eddy intensity by a phase of 2–3 months due to the initial perturbations needing time to grow into mesoscale eddies.

A Further Investigation of the Decadal Variation of ENSO Characteristics with Instability Analysis

Based on instability theory and some former studies, the Simple Ocean Data Assimilation （SODA） data are analyzed to further study the difference between the propagation of the ENSO-related oceanic anomaly in the off-equatorial North Pacific Ocean before and after 1976. The investigation shows that after 1976 in the off-equatorial North Pacific Ocean, there is a larger area where the necessary conditions for baroclinic and/or barotropic instability are satisfied, which may help oceanic anomaly signals propagating in the form of Rossby waves to absorb energy from the mean currents so that they can grow and intensify. The baroclinic energy conversion rate in the North Pacific after 1976 is much higher than before 1976, which indicates that the baroclinic instability has intensified since 1976. Prom another perspective, the instability analysis gives an explanation of the phenomena that the ENSO-related oceanic anomaly signal in the North Pacific has intensified since 1976.

Propagation of Envelope Solitons in Baroclinic Atmosphere

The propagation of finns amplitude baroclinic wave packets in the two-layer model is investigated by using the multiple-scale method.It is shown that the propagation of the wave packets can be described by the so-called unstable nonlinear Schrodinger equation which possesses envelope soliton solutions.The speeds of the solitons are independent of their amplitudes,while the width of the solitons is directly proportional to their speeds but inversely proportional to their amplitudes.

Flow Instability of Molten GaAs in the Czochralski Configuration

The flow and heat transfer of molten GaAs under the interaction of buoyancy, Marangoni and crystal rotation in the Czochralski configuration are numerically studied by using a time-dependent and three-dimensional turbulent flow model for the first time. The transition from axisymmetric flow to non-axisymmetric flow and then returning to axisymmetric flow again with increasing centrifugal and coriolis forces by increasing the crystal rotation rate was numerically observed. The origin of the transition to non-axisymmetric flow has been proved to be baroclinic instability. Several important characteristics of baroclinic instability in the CZ GaAs melt have been predicted. These characteristics are found to be in agreement with experimental observations.

Seasonal variation of eddy kinetic energy in the South China Sea

Mesoscale eddy activity and its modulation mechanism in the South China Sea （SCS） are inves- tigated with newly reprocessed satellite altimetry observations and hydrographic data. The eddy kinetic energy （EKE） level of basin-wide averages show a distinct seasonal cycle with the maximum in August-December and the minimum in February-May. Furthermore, the seasonal pattern of EKE in the basin is dominated by region offshore of central Vietnam （OCV）, southwest of Taiwan Island （SWT）, and southwest of Luzon （SWL）, which are also the breeding grounds of mesoscale eddies in the SCS. Instability theory analysis suggests that the seasonal cycle of EKE is modulated by the baroclinic instability of the mean flow. High eddy growth rate （EGR） is found in the active eddy regions. Vertical velocity shear in the upper 50-500 m is crucial for the growth of baroclinic instability, leading to seasonal EKE evolution in the SCS.

Research on the Interannual Variability of the Great Whirl and the Related Mechanisms

Based on AVISO （archiving, validation and interpretation of satellite data in oceanography） data from 1993 to 2010, QuikSCAT （Quick Scatterometer） data from 2000 to 2008, and Argo data from 2003 to 2008, the interannual variability of the Great Whirl （GW） and related mechanisms are studied. It shows that the origin and termination times of the GW, as well as its location and intensity, have significant interarmual variability. The GW appeared earliest （latest） in 2004 （2008） and vanished ear- liest （latest） in 2006 （2001）, with the shortest （longest） duration in 2008 （2001）. Its center was most southward （northward） in 2007 （1995）, while the minimum （maximum） amplitude and area occurred in 2003 and 2002 （1997 and 2007）, respectively. The GW was weaker and disappeared earlier with its location tending to be in the southwest in 2003, while in 2005 it was stronger, van- ished later and tended to be in northeast. The abnormal years were often not the same among different characters of the GW, and were not all coincident with ENSO （El Nifio-Southern Oscillation） or IOD （Indian Ocean Dipole） events, indicating the very com- plex nature of GW variations. Mechanism investigations shows that the interannual variability of intraseasonal wind stress curl in GW region results in that of the GW. The generation of the GW is coincident with the arrival of Rossby waves at the Somali coast in spring; the intensity of the GW is also influenced by Rossby waves. The termination of the GW corresponds well to the second one of the top two peaks in the baroclinic energy conversion rate in GW region, and the intensity and the position of the GW are also closely related to the top two baroclinic energy conversion rates.

Snowstorm over the Southwestern Coast of the Korean Peninsula Associated with the Development of Mesocyclone over the Yellow Sea

This study investigates the characteristics of a heavy snowfall event over the southwestern part of the Korean Peninsula on 4 December 2005. The snowstorm was a type of mesoscale maritime cyclone which resulted from barotropic instability, and diabatic heating from the warm ocean in continental polar air masses. Based on surface observations, radiosonde soundings, MTSAT-1R satellite data and the 10-km grid RDAPS （Regional Assimilation and Prediction System based on the PSU/NCAR MM5） data, the evolution of the mesocyclone is explained by the following dynamics; （1） In the initial stage, the primary role in the cyclogenesis process of the mesocyclone is a barotropic instability in the horizontal shear zone. （2） In the developing stage, the mesocyclone moves and deepens into a baroclinic zone corresponding to the surface heating and moistening. （3） In the mature stage, it is found that the mesocyclone is intensified by the destabilization caused by enhanced low-level heating and condensation, the moisture flux convergence, and the interaction between upper and lower-level potential vorticity anomalies. We suggest that a checklist with stepwise indicators responsible for development be prepared for the forecasting of heavy snowfall over the southwestern part of the Korean Peninsula.

Meso-scale available gravitational potential energy in the world oceans

The pitfalls of applying the commonly used definition of available gravitational potential energy （AGPE） to the world oceans are re-examined. It is proposed that such definition should apply to the meso-scale problems in the oceans, not the global scale. Based on WOA98 climatological data, the meso-scale AGPE in the world oceans is estimated. Unlike previous results by Oort et al. , the meso-scale AGPE is large wherever there is a strong horizontal density gradient. The distribution of meso-scale AGPE reveals the close connection between the baroclinic instability and the release of gravitational potential energy stored within the scale of Rossby deformation radius.

The decadally modulating eddy field in the upstream Kuroshio Extension and its related mechanisms

Both the level of the high-frequency eddy kinetic energy（HF-EKE） and the energy-containing scale in the upstream Kuroshio Extension（KE） undergo a well-defined decadal modulation, which correlates well with the decadal KE path variability. The HF-EKE level and the energy-containing scales will increase with unstable KE path and decrease with stable KE path. Also the mesoscale eddies are a little meridionally elongated in the stable state, while they are much zonally elongated in the unstable state. The local baroclinic instability and the barotropic instability associated with the decadal modulation of HF-EKE have been investigated. The results show that the baroclinic instability is stronger in the stable state than that in the unstable state, with a shorter characteristic temporal scale and a larger characteristic spatial scale. Meanwhile, the regional-averaged barotropic conversion rate is larger in the unstable state than that in the stable state. The results also demonstrate that the baroclinic instability is not the dominant mechanism influencing the decadal modulation of the mesoscale eddy field, while the barotropic instability makes a positive contribution to the decadal modulation.

Flow transitions in model Czochralski GaAs melt

The flow and heat transfer of molten GaAs during Czochralski growth are studied with a time-dependent and three- dimensional turbulent flow model. A transition from axisymmetric flow to nonoaxisymmetric flow and then back to axisymmetric flow again with increasing the crucible rotation rate is predicted. In the non-axisymmetric regime, the thermal wave induced by the combination of coriolis force, buoyancy and viscous force in the GaAs melt is predicted for the first time. The thermal wave is confirmed to be baroclinic thermal wave. The origin of the transition to non-axisymmetric flow is baroclinic instability. The critical parameters for the, transitions are presented, which are quantitatively in agreement with Fein and Preffer＇s experimental results, The calculated results can be taken as a reference for the growth of GaAs single-crystal of high quality,

Infl uence of sequential tropical cyclones on phytoplankton blooms in the northwestern South China Sea

Upper ocean responses to the passage of sequential tropical cyclones over the northwestern South China Sea(SCS)in 2011 were investigated using satellite remote sensing data,Argo reanalysis data,and an array of mooring data.We found that the sea surface low temperature region lasted for more than 38 days and two phytoplankton blooms occurred after the passage of sequential tropical cyclones.The upper ocean cooling reached 2–5°C with a right-side bias was observed along the typhoon track to about 200 km.The maintenance of low temperature region and the two phytoplankton blooms were mainly driven by upwelling and near-inertial turbulence mixing induced by the sequential tropical cyclones.The fi rst phytoplankton bloom appeared on the 7 th day after the passage of the three tropical cyclones,and the chlorophyll-a(chl-a)concentration increased by 226%,which may be mainly driven by typhoons induced upwelling.The second phytoplankton bloom occurred on the 30 th day,the chl-a concentration increased by 290%.Further analysis suggested that only the typhoons with similar characteristics as Nesat and Nalgae can induce strong near-inertial oscillation(NIO).Strong turbulent mixing associated with the near-inertial baroclinic shear instability lasted for 26 days.The measured mean eddy diff usivity in the upper ocean was above 10-4 m 2/s after typhoon Nesat.Enhancement of the turbulent mixing in the upper ocean helped to transport nutrient-rich cold waters from the deep layer to the euphotic layer,and is a major mechanism for the long-term maintenance of low temperature region as well as the second phytoplankton bloom.

EFFECTS OF BOUNDARY LAYER FRICTION AND TOPOGRAPHY ON THE INSTABILITY OF BAROCLINIC WAVES

In this paper,the simultaneous effects of boundary layer and topography on the instability of Eady wave are investigated by using a new parameterization of the vertical velocity at the top of PBL and the influences of the stratification of the PBL,roughness and the slope of terrain are shown.Furthermore,the effects of the boundary layer friction and topography on generalized Eady wave are also investigated.

INSTABILITY PROPERTIES OF ATMOSPHERIC DISTURBANCES

There are some basic problems in previous theoretical studies of baroclinic instability.The derived critical baroclinity was considerably lower than the time averaged mean meridional temperature gradient,especially in the lower troposphere.Also,the linear mechanism of baroclinic disturbance development which is noted restricted by the critical baroclinity was not studied sufficiently.The realistic critical baroclinity and disturbance development are discussed in this study.It will be shown that the critical condition of instability and typical time and space scales of disturbances de- pend on three-dimensional structures of atmosphere and sphericity of the earth,other than the horizontal temperature gradient alone.The variant behaviour of atmospheric disturbances depends highly on their specific scales that may be described by the same theoretical model.Thus,there would be no substantial differences in the basic instability mecha- nism of many disturbances including the polar lows and explosive cyclones.

THE ANALYSIS OF INTRASEASONAL LONG ROSSBY WAVE SPEED IN THE SUBTROPICAL PACIFIC OCEAN

The analysis of the satellite altimeter data suggests that the propagating speed of intraseasonal long Rossby wave amplified in the subtropical Pacific Ocean is faster than that of first mode baroclinic free Rossby wave predicted by the liner theory and the propagating speed of intrascasonal long Rossby wave reflected in the eastern boundary of Pacific Ocean agrees basically with the liner theory speed of first mode baroelinic free P, ossby wave. If we do not distinguish the two kinds of hmg Rossby waves and estimate the Rossby wave speed in the whole basin, the phase speed is merely 25% higher than the linear theory long Rossby wave speed. The acceleration of the propagating speed of intraseasonal long Rossby wave amplified in the subtropical Pacific Ocean is due to the existence of westward thermolcline mean flow.

Drastic change in dynamics as Typhoon Lekima experiences an eyewall replacement cycle

Why does the 1909 typhoon,Lekima,become so destructive after making landfall in China?Using a newly developed mathematical apparatus,the multiscale window transform(MWT),and the MWT-based localized mutliscale energetics analysis and theory of canonical transfer,this study is intended to give a partial answer from a dynamical point of view.The ECMWF reanalysis fields are first reconstructed onto the background window,the TC-scale window,and the convection-scale window.A localized energetics analysis is then performed,which reveals to us distinctly different scenarios before and after August 8–9,2019,when an eyewall replacement cycle takes place.Before that,the energy supply in the upper layer is mainly via a strong upper layer-limited baroclinic instability;the available potential energy thus-gained is then converted into the TC-scale kinetic energy,with a portion to fuel Lekima’s upper part,another portion carried downward via pressure work flux to maintain the cyclone’s lower part.After the eyewall replacement cycle,a drastic change in dynamics occurs.First,the pressure work is greatly increased in magnitude.A positive baroclinic transfer almost spreads throughout the troposphere,and so does barotropic transfer;in other words,the whole air column is now both barotropically and baroclinically unstable.These newly occurred instabilities help compensate the increasing consumption of the TC-scale kinetic energy,and hence help counteract the dissipation of Lekima after making landfalls.