Linear Momentum Approximation and Frontogenesis Caused by Baroclinic Ekman Momentum Flow

A method of linear momentum approximation is proposed that deals with weak nonlinear problems in an approximate manner. A motion of nonlinear nature is obtained in the system by assuming the motion to be in the form of linear momentum flow in the corresponding space introduced, followed by the transformation from the specified into a physical space. Significant results have been thereby derived in examining the effects of baroclinic Ekman momentum flow upon Eady-type baroclinic waves and frontogenesis. Also, this technique can be applied to investigate the dynamic characteristics of the weak nonlinear boundary layer including topography, stratification and non-Ekmantype friction for gaining further insight into the influence on the boundary layer inner parameters of terrain, baroclinicity and inhomogeneous process so that the classic theory is revised.

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.

Influence of Bottom Inclination on the Flow Structure in a Rotating Convective Layer

The formation of convective flows in a rotating cylindrical layer with an inclined bottom and free surface is studied.Convection is driven by localized cooling at the center of the upper free surface and by rim heating at the bottom near the sidewall.The horizontal temperature difference in a rotating layer leads to the formation of a convective flow with a complex structure.The mean meridional circulation,consisting of three cells,provides a strongly non-uniform differential rotation.As a result of the instability of the main cyclonic zonal flow,the train of baroclinic waves appears in the upper layer.The baroclinic waves provide most of the heat transfer in the middle radii and are responsible for strong temperature and velocity fluctuations.It is shown that the inclination of the bottom is a crucial factor for the structure of the convective cells and the dynamics of the baroclinic waves.The increase in the inclination angle leads to a significant increase in the energy of the waves.The obtained results may be important for heat and mass transfer in various geophysical and industrial systems,including transport of various additives and impurities in rotating crucibles,and crystallization processes.

Conversion Characteristics between Barotropic and Baroclinic Circulations of the SAH in Its Seasonal Evolution

In the context of 1958–1997 NCEP/ NCAR re-analyses, the South Asia high (SAH) was divided into two components, barotropic and baroclinic, the former based on mass weighed vertical integration and the latter on the difference between the measured circulation and the barotropic component counterpart, whereupon the barotropic and baroclinic circulation conversion features were addressed of the research SAH during its seasonal variation. Evidence suggests that i) in summer (winter), the SAH is a thermal (dynamical) system, with dominant baroclinicity (barotropicity), either of the components accounting for approximately 70% of the total contribution; ii) as time progresses from winter to summer, accompanied by the barotropic SAH evolving into its baroclinic analog, the SAH is moving under the “ thermal guidance” of its baroclinic component circulation, suggesting that the component circulation precedes the system itself in variation; iii) the reversal happens when it goes from summer to winter, with the SAH displacement under the “ dynamic steering” of its barotropic component circulation. Key words SAH (South Asia high) - Barotropic circulation - Baroclinic circulation - Seasonal variation (1)This work is supported by the National Natural Sciences Foundation of China under Grant No.49735170.

A Study of Formation and Development of One Kind of Cyclone on the Mei-yu (Baiu) Front

The paper presents one diagnosis of baroclinity and the coupling of jets during the developing process of a cyclone that occurred on the mei-yu (Baiu) front around the end of the second stage of the mei-yu (Baiu) in 1998. Results have shown that (1) The advantageous changes of upper-level large-scale circulation μ caused the appearance and maintenance of the coupling between the upper-level jet (ULJ) and lower-level jet (LLJ) over the cyclone’s area. The coupling of jets in this case possesses some di?erent characteristics from previous cases. Moreover, the coupling between the ULJ and LLJ caused the intensi?cation of both lower-level convergence and upper-level divergence, which was favorable for the development of this cyclone. (2) From the analysis of the voricity budget, the role of lower-level convergence in the development of the cyclone was emphasized. Divergent wind in the lower troposphere was a direct contributor to the development of the cyclone. (3) During the development of the cyclone, cold air and warm air were active over the cyclone’s domain. Although this cyclone occurred at the mei-yu (Baiu) front, its development assumed baroclinity to a certain extent, which was just the main di?erence between this kind of cyclone and the ?rst kind of low which is usually barotropic (or quasi-barotropic). (4) In recent years, studies on mei-yu front lows have paid more attention to the lower troposphere. In this paper, the analysis of the energy budget further supports this point: the certain e?ect of baroclinity forcing in the upper troposphere on mei-yu front lows cannot be ignored.

Three Dimensional Baroclinic Numerical Model for Simulating Fresh and Salt Water Mixing in the Yangtze Estuary

For simulating fresh and salt water mixing in estuaries, a three dimensional nonlinear baroclinic numerical model is developed, in which the gradients of horizontal pressure contain die gradient of barotropic pressure arising from the gradient of tidal level and the gradient of baroclinic pressure due to the gradient of salinity. The Eulerian-Lagrangian method is employed to descretize both the momentum equations of tidal motion and the equation of salt water diffusion so as to improve the computational stability and accuracy. The methods to provide the boundary conditions and the initial conditions are proposed, and the criterion for computational stability of the salinity fields is presented. The present model is used for modeling fresh and salt water mixing in the Yangtze Estuary. Computations show that the salinity distribution has the characteristics of partial mixing pattern, and that the present model is suitable for simulation of fresh and salt water mixing in the Yangtze Estuary.

A survey of baroclinic tides in the Beibu Gulf in the South China Sea

The principal characteristics of the tides are investigated by a shipborne acoustic Doppler current Profiler at a fixed station located in the Beibu Gulf from 4 to 14 April 2003. Data analysis indicates that the diurnal tidal currents dominate local current variations at the observing site. Except the barotropic ME constituent, four principal tides comprise both back-and-forth barotropic and baroclinic tidal currents. The baroclinic tidal ellipse parameters vary with depth, showing complicate features, rather than monotonous features being figured. For baroclinic tidal constituents, vertical modes are different to each other. Similarly, the semi-major axes of the tidal constituents vary with depth. In the lower layer, a nonlinear regression approach is used to calculate and obtain the SEMA profiles of diurnal tidal constituents. Results show that in the thin bottom boundary layer, all of the parameters vary drastically with depth, totally distinguished from the vertical profiles above.

Study on Instability in Baroclinic Vortex Symmetric Disturbance under Effect of Nonuniform Environmental Parameters

With the aid of the baroclinicity parameter M2,inertial instability parameter F2 and the stratification instability paramter N2 as the slowly varying function both spatially and temporally,an energetic equation is derived of symmetric perturbation waves in baroclinic vortices in the framework of progressively changing wavetrain theory,or WKB,alongside the examination of effects of these parameters upon the vortex disturbance.

A 3-DIMENSIONAL BAROCLINIC CIRCULATION MODEL OF THE TROPICAL AND NORTHERN PACIFIC

A primitive equation 3-dimensional baroclinic ocean model without the rigid-lid approximation is described.The horizontal resolution is 2.5°×2°and the vertical variations of the velocity components are resolved by 6 layers. In order to increase the allowable integration time step which is constrained by stability requirements, the vertically integrated continuity equation is linearized and both the pressure gradient terms and the Coriolis terms in the momentum equations are finite-differenced semi-implicitly.The model is applied to simulate the circulation as well as the free surface elevation and temperature patterns in the tropical and northern Pacific Ocean in both summer and winter using the wind and temperature data at the 1000 mb pressure level as input to the .model. The computed results are in general consistent with observed patterns. In particular, it is shown that the positions of the meandering axis of the Kuroshio in summer and winter are markedly different.

Charney’s Model—the Renowned Prototype of Baroclinic Instability—Is Barotropically Unstable As Well

The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic;when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.

Energy Paths that Sustain the Warm-Sector Torrential Rainfall over South China and Their Contrasts to the Frontal Rainfall: A Case Study

Predicting warm-sector torrential rainfall over South China,which is famous for its destructive power,is one of the most challenging issues of the current numerical forecast field.Insufficient understanding of the key mechanisms underlying this type of event is the root cause.Since understanding the energetics is crucial to understanding the evolutions of various types of weather systems,a general methodology for investigating energetics of torrential rainfall is provided in this study.By applying this methodology to a persistent torrential rainfall event which had concurrent frontal and warm-sector precipitation,the first physical image on the energetics of the warm-sector torrential rainfall is established.This clarifies the energy sources for producing the warm-sector rainfall during this event.For the first time,fundamental similarities and differences between the warm-sector and frontal torrential rainfall are shown in terms of energetics.It is found that these two types of rainfall mainly differed from each other in the lower-tropospheric dynamical features,and their key differences lay in energy sources.Scale interactions(mainly through downscale energy cascade and transport)were a dominant factor for the warm-sector torrential rainfall during this event,whereas,for the frontal torrential rainfall,they were only of secondary importance.Three typical signals in the background environment are found to have supplied energy to the warm-sector torrential rainfall,with the quasi-biweekly oscillation having contributed the most.

Mesoscale Predictability of Moist Baroclinic Waves: Variable and Scale-dependent Error Growth

This study seeks to quantify the predictability of different forecast variables at various scales through spectral analysis of the difference between perturbed and unperturbed cloud-permitting simulations of idealized moist baroclinic waves amplify- ing in a conditionally unstable atmosphere. The error growth of a forecast variable is found to be strongly associated with its reference-state （unperturbed） power spectrum and slope, which differ significantly from variable to variable. The shallower the reference state spectrum, the more spectral energy resides at smaller scales, and thus the less predictable the variable since the error grows faster at smaller scales before it saturates. In general, the variables with more small-scale components （such as vertical velocity） are less predictable, and vice versa （such as pressure）. In higher-resolution simulations in which more rigorous small-scale instabilities become better resolved, the error grows faster at smaller scales and spreads to larger scales more quickly before the error saturates at those small scales during the first few hours of the forecast. Based on the reference power spectrum, an index on the degree of lack （or loss） of predictability （LPI） is further defined to quantify the predictive time scale of each forecast variable. Future studies are needed to investigate the scale- and variable-dependent predictability under different background reference flows, including real case studies through ensemble experiments.

Two Modes and Their Seasonal and Interannual Variation of the Baroclinic Waves/Storm Tracks over the Wintertime North Pacific

In this study,a newly developed method,termed moving empirical orthogonal function analysis（MEOF）,is applied to the study of midlatitude baroclinic waves over the wintertime North Pacific from 1979 to 2009.It is shown that when the daily,high-pass filtered（2–10 days） meridional wind at 250 h Pa is chosen as the variable of the MEOF analysis,typical features of baroclinic waves/storm tracks over the wintertime North Pacific can be well described by this method.It is found that the first two leading modes of the MEOF analysis,MEOF1 and MEOF2,assume quite different patterns.MEOF1 takes the form of a single wave train running in the east–west direction along 40°N,while MEOF2 is a double wave train pattern running in the east–west direction along 50°N and 30°N,respectively.The shift composites of various anomalous fields based on MEOF1 and MEOF2 assume typical baroclinic wave features.MEOF1 represents a primary storm track pulsing with an intrinsic time scale of two days.It shows significant ＂midwinter suppression＂ and apparent interannual variability.It is stronger after the mid-1990 s than before the mid-1990 s.MEOF2 represents a double-branch storm track,also with an intrinsic time scale of approximately two days,running along 50°N and 30°N,respectively.It shows no apparent seasonal variation,but its interannual and decadal variation is quite clear.It oscillates with larger amplitude and longer periods after the mid-1990 s than before the mid-1990 s,and is heavily modulated by El Ni n°o–Southern Oscillation（ENSO）.

Application of a self adaptive method to the simulation of the tidal front in the Huanghai Sea

A self adaptive three-dimensional baroclinic model is designed. A horizontal temperature gradient is used to control the grid size, which can improve computational precision in the fronts without inordinately increasing computation in the whole area. A simulation of the development and disappearance of the front in the Huanghai Sea is conducted with this model. Simulations of temperature distribution throughout the year are also conducted. The comoutational result agrees well with the observation.

The Role of the Halted Baroclinic Mode at the Central Equatorial Pacific in El Nifn Event

The role of halted ＂baroclinic modes＂ in the central equatorial Pacific is analyzed. It is found that dominant anomaly signals corresponding to ＂baroclinic modes＂ occur in the upper layer of the equatorial Pacific, in a two-and-a-half layer oceanic model, in assimilated results of a simple OGCM and in the ADCP observation of TAO. A second ＂baroclinic mode＂ is halted in the central equatorial Pacific corresponding to a positive SST anomaly while the first ＂baroclinic mode＂ propagates eastwards in the eastern equatorial Pacific. The role of the halted second ＂baroclinic mode＂ in the central equatorial Pacific is explained by a staged ocean-atmosphere interaction mechanism in the formation of El Nifio： the westerly bursts in boreal winter over the western equatorial Pacific generate the halted second ＂baroclinic mode＂ in the central equatorial Pacific, leading to the increase of heat content and temperature in the upper layer of the central Pacific which induces the shift of convection from over the western equatorial Pacific to the central equatorial Pacific; another wider, westerly anomaly burst is induced over the western region of convection above the central equatorial Pacific and the westerly anomaly burst generates the first ＂baroclinic mode＂ propagating to the eastern equatorial Pacific, resulting in a warm event in the eastern equatorial Pacific. The mechanism presented in this paper reveals that the central equatorial Pacific is a key region in detecting the possibility of ENSO and, by analyzing TAO observation data of ocean currents and temperature in the central equatorial Pacific, in predicting the coming of an El Nino several months ahead.

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.

Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation

This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-（3＋1）- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding （2＋1）-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given out.

AN EXACT SOLUTION OF SUB-INERTIAL FREQUENCY BAROCLINIC WAVES

By using a coordinate transformation, an exact solution of internal tides with sub-inertial frequency isobtained when the bottom slope is linear and the Vaisala frequency is constant. Accordingly thedispersion relations of free waves are presented. This solution is suitable for general coastal low-frequencybaroclinic waves with zero alongshore wavenumber.

A baroclinic typhoon model with a moving multi-nested grid and variational adjustment initialisationI. Numerical method

A baroclinic typhoon model with a moving multi--nested grid is applied in marine environmental forecasts. This paper describes the numerical methods of the model including governing equations, finite differencing, split scheme and time integration.

Vertical Structure of Baroclinic Currents over Northern South China Sea Continental Slope

The 28.6 d time series of ADCP currents at 27 depth levels, (11,15,…,115m) which are obtained from a mooring station at the northern South China Sea continental slope, have been decomposed into barotropic and baroclinic components. The emphasis in this paper is on the analysis of the time series of baroclinic currents by means of several methods,such as the tidal harmonic analysis, the power spectra and the kinetic energy estimation.The major results are as follows: (1) In respect of the baroclinic currents, the values of several parameters first decrease and then increase with depth. These parameters include the temporal mean value of the cross-shelf component, the standard deviations, the amplitudes of K1 constituents, the mean eddy kinetic energy, as well as the significant peaks of the power spectra of the cross-shelf components. (2) The diurnal period of the baroclinic currents is dominant. The diumal tidal current rotates clockwise and the major axis of current ellipse is located along the directions of NW-SE. The vertical distribution of the phases of the diurnal constituent varies with the different water layers. Around the 67m depth level, the phase changes very much.At those layers far away from the 67m depth level, the vertical distribution of the phase is relatively stable, but with opposite phases in the upper and lower water layers. For the upper layers between the surface and 67m,the phases are around 300°; for the lower layers between 67m and 115m, the phases are around 120° .(3) The mean eddy kinetic energy of the baroclinic current is quite large, accounting for 41% of the mean kinetic energy of the measured currents. The cross-shelf component is larger than the along-shelf one. The two baroclinic current components correspond to the major and minor axes of the current ellipse of the diurnal constituent respectively. (4) The power spectra of the baroclinic currents show a singnificant period of about 24h, with 23.6h at both 19m and 99m and 24.4h at 55m. The vertical distributions of the significant spectra-peak values of the power spectra of both the crossshelf and along-shelf components of both the baroclinic currents are different. The former increases with depth, then decreases and finally increases again while the latter decreases with depth.