The Early Mesozoic NE-SW Extensional Model and Exhumation Processes at the Southeastern Margin of the Central Asian Orogenic Belt:Insights from the Strain and Kinematic Vorticity Analysis of the Sonid Zuoqi Ductile Detachment Zone

The Sonid Zuoqi ductile detachment zone is located at the southeastern margin of the Central Asian orogenic belt(CAOB),striking EW and dipping to the S.The major rock type of the Sonid Zuoqi ductile detachment zone is mylonite derived from granite.The sequence of mylonite features is:(1)S and C foliations of mylonite,and(2)extensional crenulation cleavage(ecc)or C′and the kinematic vorticity(Wk)value changed from 0.70 to 0.95 and from 0.37 to 0.69,respectively;the strain type of the mylonites within the Sonid Zuoqi ductile detachment zone is compressional to planar strain.The strong deformation mylonite and Halatu plutons yielded a zircon U-Pb age of 244 Ma and a zircon(U-Th)/He age of 214 Ma,respectively.Based on the strain and kinematic vorticity analysis,together with the zircon U-Pb and zircon(U-Th)/He ages and the regional tectonic background,the study area experienced three stage evolution:tangential simpleshear(244 Ma),simple-shear-dominated general shear represented by upper crustal extension(224 Ma)and pure-shear-dominated general shear represented by the Halatu pluton doming(214 Ma),which constrained the early Mesozoic NE-SW crustal extension at the southeastern margin of the CAOB.This NE-SW extension probably originated from the postorogenic extensional collapse of the CAOB,subsequent exhumation being controlled by the far afield effects of the closure of the Mongol-Okhotsk belt.

Boundary Conditions for Momentum and Vorticity at an Interface between Two Fluids

Boundary conditions for momentum and vorticity have been precisely derived, paying attention to the physical meaning of each mathematical expression of terms rigorously obtained from the basic equations: Navier-Stokes equation and the equation of vorticity transport. It has been shown first that a contribution of fluid molecules crossing over a conceptual surface moving with fluid velocity due to their fluctuating motion is essentially important to understanding transport phenomena of momentum and vorticity. A notion of surface layers, which are thin layers at both sides of an interface, has been introduced next to elucidate the transporting mechanism of momentum and vorticity from one phase to the other at an interface through which no fluid molecules are crossing over. A fact that a size of δV, in which reliable values of density, momentum, and velocity of fluid are respectively defined as a volume-averaged mass of fluid molecules, a volume-averaged momentum of fluid molecules and a mass-averaged velocity of fluid molecules, is not infinitesimal but finite has been one of the key factors leading to the boundary conditions for vorticity at an interface between two fluids. The most distinguished characteristics of the boundary conditions derived here are the zero-value conditions for a normal component of momentum flux and tangential components of vorticity flux, at an interface.

Up-Sliding Slantwise Vorticity Development and the Complete Vorticity Equation with Mass Forcing

The moist potential vorticity (MPV) equation is derived from complete atmospheric equations including the effect of mass forcing, with which the theory of Up-sliding Slantwise Vorticity Development, (USVD) is proposed based on the theory of Slantwise Vorticity Development (SVD). When an air parcel slides up along a slantwise isentropic surface, its vertical component of relative vorticity will develop, and the steeper the isentropic surface is, the more violent the development will he. From the definition of MPV and the MPV equation produced here in, a complete vorticity equation is then put forward with mass forcing, which explicitly includes the effects of both internal forcings, such as variations of stability, baroclinicity, and vertical shear of horizontal wind, arid external forcings, such as diabatic heating, friction, and mass forcing. When isentropic surfaces are flat, the complete vorticity equation matches its traditional counterpart. The physical interpretations of some of the items which are included in the complete- vorticity equation but not in the traditional one are studied with a simplified model of the Changjiang-Huaihe Meiyu front. A 60-h simulation is then performed to reproduce a torrential rain event in the Changjiang-Huaihe region and the output of the model is studied qualitatively based on the theory of USVD. The result shows that the conditions of the theory of USVD are easily satisfied immediately in front of mesoscale rainstorms in the downwind direction, that is, the theory of USVD is important to the development and movement of these kinds of systems.

CFD Simulation of Flow Features and Vorticity Structures in Tuna-Like Swimming

The theoretical research on the propulsive principle of aquatic animal becomes more important and attracted more researchers to make efforts on it. In the present study, a computational fluid dynamic （CFD） simulation of a three-dimensional traveling-wave undulations body of tuna has been developed to investigate the fluid flow features and vorticity structures around this body when moving in a straight line. The undulation only takes place in the posterior half of the fish, and the tuna-tail is considered as a lunate fin oscillating with the mode combined swaying with yawing. A Reynolds-averaged Navier-Stokes （RANS） equation is developed, employing a control-volume method and a k-omega SST turbulent model; meanwhile an unstructured tetrahedral grid, which is generated for the three-dimensional geometry, is used based on the deformation of the hind parts of the body and corresponding movement of the tail. We calculated the hydrodynamic performance of tuna-like body when a tuna swims in a uniform velocity, and compared the input power coefficient, output power coefficient and propulsive efficiency of the oscillating tuna-tail with or without body vortex shedding. Additionally, the load distribution on the body, flow features and vorticity structures around the body were demonstrated. The effect of interaction between the body-generated vortices and the tail-generated vorticity on the hydrodynamic performance can be obtained.

Impacts of Cloud-Induced Mass Forcing on the Development of Moist Potential Vorticity Anomaly During Torrential Rains

The impacts of cloud-induced mass forcing on the development of the moist potential vorticity (MPV) anomaly associated with torrential rains are investigated by using NCEP/NCAR 1? × 1? data. The MPV tendency equation with the cloud-induced mass forcing is derived, and applied to the torrential rain event over the Changjiang River-Huaihe River Valleys during 26–30 June 1999. The result shows that positive anomalies are located mainly between 850 hPa and 500 hPa, while the maximum MPV, maximum positive tendency of the MPV, and maximum surface rainfall are nearly collocated. The cloud-induced mass forcing contributes to the positive tendency of the moist potential vorticity anomaly. The results indicate that the MPV may be used to track the propagation of rain systems for operational applications.

Study on Moist Potential Vorticity and Symmetric Instabilityduring a Heavy Rain Event Occurred inthe Jiang-Huai Valleys

In the light of the theory on moist potential vorticity (MPV) investigation was undertaken of the 700 hPa vertical (horizontal) component MP1 (MPV2) for the heavy rain event occurring in July 5–6, 1991. Results show that the distribution features of the two components were closely related to the development of a mesoscale cyclone as a rainstorm-causing weather system in the lower troposphere in such a way that the ambient atmosphere of which MPV1 > 0 and MPV2 < 0 with |MPV1| ≥ |MPV2| favored the genesis of conditional symmetric instability (CSI) and that, as indicated by calculations, a CSI sector was really existent in the lower troposphere during the heavy rain happening and contributed greatly to its development.

Potential Vorticity Structure and Inversion of the Cyclogenesis Over the Yangtze River and Huaihe River Valleys

In this paper, the potential vorticity structure and inversion of the cyclogenesis over the Yangtze River and Huaihe River valleys during 21 23 June 2003 are investigated with a potential vorticity （PV） framework. The cyclogenesis is manifested by a lower-tropospheric PV anomaly over the Yangtze River and Huaihe River valleys at early stages mainly due to latent heat release, which greatly affects the evolution of the associated lower-tropospheric geopotential height and wind fields as demonstrated by piecewise PV inversion. At later stages, an upper-tropospheric PV anomaly develops, resulting in the growth of ridges over the cyclone in both the upstream and downstream, which provide a favorable background field for the low-level cyclone development. But the effect of a surface thermal anomaly always impedes the development of the cyclone to different extents during this cyclogenesis. It is further demonstrated that the position and the strength of the PV anomaly are closely related to the low-level cyclone development, and the lower-tropospheric PV anomaly seems to constitute the most significant feature, for instance, contributing about 60% to the low-level jet （LLJ）.

Vorticity Budget Investigation of a Simulated Long-Lived Mesoscale Vortex in South China

A vorticity budget investigation is performed using the output data from a numerical simulation of a typical MCV (mesoscale convectively generated votex) case in South China. Results suggest that the divergence caused by convection in the low troposphere is the main producer of positive vorticity, while vertical vorticity transferred by the tilting term from the horizontal vorticity compensates the upward output of cyclonic vorticity. Scale analyses of the vorticity equation suggest that the advection of planetary vorticity can be neglected owing to the low latitude, which is di?erent from the larger scale systems in high latitude areas. In addition, the distribution of relative vorticity tendency on pressure level is not uniform. A vortex will move along the vector from the negative to the positive vorticity tendency region. The mechanism of the phenomenon—that nearly all of the convectively ascending region is located southward/southeastward of the vortex center—is also discussed. Convergence with regard to latent heat release would be in favor of the spin-up of meso-vortex, however, the horizontal vorticity caused by wind shear is tilted by vertical motion due to convection. Consequently, the negative and positive vorticity tendencies are located symmetrically about the convective center, which suggests that the vortex southward movement is dynamically driven by convection.

THE RELATIONSHIP BETWEEN HORIZONTAL VORTICITY INDUCED BY VERTICAL SHEAR AND VERTICAL MOTION DURING A SQUALL LINE PROCESS

The horizontal vorticity equation used in this study was obtained using the equations of motion in the pressure coordinate system without considering friction, to reveal its relationship with vertical shear. By diagnostically analyzing each term in the horizontal vorticity equation during a squall line process that occurred on 19 June 2010, we found that the non-thermal wind term had a negative contribution to the local change of upward movement in the low-level atmosphere, and that its impact changed gradually from negative to positive with altitude, which could influence upward movement in the mid-and upper-level atmosphere greatly. The contribution of upward vertical transport to vertical movement was the largest in the low-level atmosphere, but had negative contribution to the upper-level atmosphere. These features were most evident in the development stage of the squall line. Based on analysis of convection cells along a squall line, we found that in the process of cell development diabatic heating caused the subsidence of constant potential temperature surface and non-geostrophic motion, which then triggered strong convergence of horizontal acceleration in the mid-level atmosphere and divergence of horizontal acceleration in the upper-level atmosphere. These changes of horizontal wind field could cause a counterclockwise increment of the horizontal vorticity around the warm cell, which then generated an increase of upward movement. This was the main reason why the non-thermal wind term had the largest contribution to the strengthening of upward movement in the mid-and upper-level atmosphere. The vertical transport of large value of horizontal vorticity was the key to trigger convection in this squall line process.

Strain, Kinematic Vorticity and Ductile Thinning along the Detachment Zone of the Yunmeng Shan Metamorphic Core Complex, Beijing, China

The Yunmeng Shan metamorphic core complex （MCC） is composed of the lower plate, the upper plate and the detachment zone. The detachment zone consists of ductile shear zone （mylonite zone）, chloritized microbreccias zone and the brittle fault plane. The ductile shear zone contains mylonitic rocks, protomylonites, and mylonites. Finite strain measurements of feldspar porphyroclasts from those rocks using the Rf/φ method show that the strain intensities increase from mylonitic rocks （Es=0.66-0.72） to protomylonites （Es=0.66-0.83）, and to mylonites （Es=0.71-1.2）. The strain type is close to flatten strain. Kinematic vorticity estimated by Polar Mohr diagrams suggest that foliations and lineation of mylonite （0.47〈Wk〈0.85） record a bulk simple-dominated general shearing at the initial evolution stage of the Yunmeng Shan MCC＇s detachment zone; and the extensional crenulation cleavage（ecc） （0.34〈Wk〈0.77） recorded a bulk pure-dominated general shearing at the later stage of the evolution. Kinematic vorticity measurements also show that the Yunmeng Shan MCC detachment zone is a result of a combination of simple-dominated general shearing caused by crustal extension at the early stage and pure-dominated general shearing caused by MCC uplifting at the late stage. The ductile thinning estimated by finite strain measurements and estimation of Kinematic vorticity ranges from 52% to 82%, which is the minimum thining estimation. Our studies provide new evidence for mechanisms of the Yunmeng Shan MCC detachement zone.

Sensitivity of Cyclone Tracks to the Initial Moisture Distribution:A Moist Potential Vorticity Perspective

In this study, the characteristics of moist potential vorticity （MPV） in the vicinity of a surface cyclone center and their physical processes axe investigated. A prognostic equation of surface absolute vorticity is then used to examine the relationship between the cyclone tracks and negative MPV （NMPV） using numerical simulations of the life cycle of an extratropical cyclone. It is shown that the MPV approach developed herein, i.e., by tracing the peak NMPV, can be used to help trace surface cyclones during their development and mature stages. Sensitivity experiments are conducted to investigate the impact of different initial moisture fields on the effectiveness of the MPV approach. It is found that the lifetime of NMPV depends mainly on the initial moisture field, the magnitude of condensational heating, and the advection of NMPV. When NMPV moves into a saturated environment at or near a cyclone center, it can trace better the evolution of the surface cyclone due to the conservative property of MPV. It is also shown that the NMPV generation is closely associated with the coupling of large potential temperature and moisture gradients as a result of frontogenesis processes. Analyses indicate that condensation, confluence and tilting play important but different roles in determining the NMPV generation. NMPV is generated mainly through the changes in the strength of baroclinicity and in the direction of the moisture gradient due to moist and/or dry air mass intrusion into the baroclinic zone.

Interplay of surface geometry and vorticity dynamics in incompressible flows on curved surfaces

Incompressible viscous flows on curved surfaces are considered with respect to the interplay of surface geometry, curvature, and vorticity dynamics. Free flows and cylindrical wakes over a Gaussian bump are numerically solved using a surface vorticity- stream function formulation. Numerical simulations show that the Gaussian curvature can generate vorticity, and non-uniformity of the Gaussian curvature is the main cause. In the cylindrical wake, the bump dominated by the positive Gaussian curvature can significantly affect the vortex street by forming velocity depression and changing vorticity transport. The results may provide possibilities for manipulating surface flows through local change in the surface geometry.

A Diagnostic Study of Moist Potential Vorticity Generation in an Extratropical Cyclone

Moist potential vorticity (MPV) and its generation may be important in the development of mesoscale structures such as rainbands within cyclones. In an adiabatic and frictionless flow, MPV generation is possible if the flow is three-dimensional and the air is unsaturated. Moist potential vorticity can be generated through the combined effects of gradients in the potential temperature and moisture fields. The diagnosis of MPV generation in an extratropical cyclone was performed with the ECMWF objectively analyzed fields for a system that developed during February 1992. It was found that at various stages during the development of the cyclone, negative MPV was generated: at the north end of the cold front; along the occluded front and the cold front; and in the region of the warm core. This pattern of negative MPV generation is in excellent agreement with the predictions of previous theoretical and numerical studies. After the cyclone ceased to deepen, the region of negative MPV generated in the cyclone was horizontally advected into a saturated area. The area of negative MPV generated both along the occluded front in this case study and in the region of the bent-back warm front in a numerical simulation showed a mesoscale structure with a width of about 200-500 km. It was found that the intrusion of moist or dry air into baroclinic zones was important for MPV generation. In addition, baroclinicity increase (adjacent to the area of condensation) in the regions of high moisture gradients led to significant MPV production.

Idealized Numerical Simulation Study of the Potential Vorticity Banners over a Mesoscale Mountain: Dry Adiabatic Process

Topography-induced potential vorticity （PV） banners over a mesoscale topography （Dabie Mountain, hereafter DM） in eastern China, under an idealized dry adiabatic flow, are studied with a mesoscale numerical model, ARPS. PV banners generate over the leeside of the DM with a maximal intensity of ～1.5 PVU, and extend more than 100 km downstream, while the width varies from several to tens of kilometers, which contrasts with the half-width of the peaks along the ridge of the DM. Wave breaking occurs near the leeside surface of the DM, and leads to a strong PV generation. Combining with the PV generation, due to the friction and the flow splitting upstream, the PV is advected downstream, and then forms the PV banners over the DM. The PV banners are sensitive to the model resolution, Coriolis force, friction, subgrid turbulent mixing, stratification, the upstream wind speed and wind direction. The negative PV banners have a more compact connection with the low level turbulent kinetic energy. The PV banners are built up by the baroclinic and barotropic components. The barotropic-associated PV can identify the distribution of the PV banners, while the baroclinic one only has important contributions on the flanks and on the leeside near the topography. PV fluxes are diagnosed to investigate the influence of friction on the PV banners. Similar patterns are found between the total PV flux and the advective PV flux, except near the surface and inside the dipole of the PV banners, where the nonadvective PV flux associated with the friction has a net negative contribution.

RELATIONSHIP BETWEEN THE VARIATION IN HORIZONTAL VORTICITY AND HEAVY RAIN DURING THE PROCESS OF MCC TURNING INTO BANDED MCSS

Using real-time data and the WRF mesoscale model,a heavy rain event in the process of Mesoscale Convective Complex(MCC) turning into banded Mesoscale Convective Systems(MCSs) during 18-19 June 2010 is simulated and analyzed in this paper.The results indicated that the formation and maintenance of a southwest vortex and shear line at 850 h Pa was the mesoscale system that affected the production of this heavy rain.The low-vortex heavy rain mainly happened in the development stage of MCC,and the circular MCC turned into banded MCSs in the late stage with mainly shear line precipitation.In the vicinity of rainfall area,the intense horizontal vorticity due to the vertical shear of u and v caused the rotation,and in correspondence,the ascending branch of the vertical circulation triggered the formation of heavy rain.The different distributions of u and v in the vertical direction produced varying vertical circulations.The horizontal vorticity near the low-vortex and shear line had obvious differences which led to varying reasons for heavy rain formation.The low-vortex heavy rain was mainly caused by the vertical shear of v,and the shear line rainfall formed owing to the vertical shear of both u and v.In this process,the vertical shear of v constituted the EW-trending rain band along the shear line,and the latitudinal non-uniformity of the vertical shear in u caused the vertical motion,which was closely related to the generation and development of MCSs at the shear line and the formation of multiple rain clusters.There was also a similar difference in the positively-tilting term(conversion from horizontal vorticity to vertical positive vorticity) near the rainfall center between the low-vortex and the shear line.The conversion in the low vortex was mainly determined by бv/бp<0,while that of the shear line by бu/бp<0.The scale of the conversion from the horizontal vorticity to vertical vorticity was relatively small,and it was easily ignored in the averaged state.The twisting term was mainly conducive to the reinforcement of precipitation,whereas its contribution to the development of southwest vortex and shear line was relatively small.

Anomaly of the Moist Potential Vorticity Substance with Mass Forcing and Its Application in Diagnosing Mei-Yu Front Rainfall

The effects of precipitation on the moist potential vorticity substance(MPVS) are investigated by analyzing the MPVS with precipitation mass forcing and its impermeability in daily 1°× 1° data of the National Centers for Environmental Prediction/National Center for Atmospheric Research(NCEP/NCAR) over the Yangtze River Basin from 21 June to 2 July 1999. The results show that the positive MPVS anomalies appear mainly along the Mei-yu front, where the maximum MPVS collocates with the maximum surface rainfall. Rain case diagnoses indicate that the MPVS anomaly may be used as a dynamical signal to detect the location and shift of the rain band when its impermeability is considered.

Derivation of baroclinic Ertel–Rossby invariant-based thermally-coupled vorticity equation in moist flow

For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant （ERI）, is there a corresponding vorticity tendency equation？ Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors＇ influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.

Diagnosis of Moist Vorticity and Moist Divergence for a Heavy Precipitation Event in Southwestern China

A regional heavy precipitation event that occurred over Sichuan Province on 8-9 September 2015 is analyzed based on hourly observed precipitation data obtained from weather stations and NCEP FNL data. Two moist dynamic parameters, i.e., moist vorticity （mζ and moist divergence （mδ）, are used to diagnose this heavy precipitation event. Results show that the topography over southwestern China has a significant impact on the ability of these two parameters to diagnose precipitation. When the impact of topography is weak （i.e., low altitude）, rn（ cannot exactly depict the location of precipitation in the initial stage of the event. Then, as the precipitation develops, its ability to depict the location improves significantly. In particular, m（ coincides best with the location of precipitation during the peak stage of the event. Besides, the evolution of the m（ center shows high consistency with the evolution of the precipitation center. For mδ, although some false-alarm regions are apparent, it reflects the location of precipitation almost entirely during the precipitation event. However, the mδ center shows inconsistency with the precipitation center. These results suggest that both m（ and mδ have a significant ability to predict the location of precipitation. Moreover, m（ has a stronger ability than mδ in terms of predicting the variability of the precipitation center. However, when the impact of topography is strong （i.e., high altitude）, both of these two moist dynamic parameters are unable to depict the location and center of precipitation during the entire precipitation event, suggesting their weak ability to predict precipitation over complex topography.

Influences of Vorticity Source and Momentum Source on Atmospheric Circulation

A simplified one-dimensional barotropic vorticity equation is used to study the influences of the vorticity and the momentum source on the large scale wave. Both vorticity source and momentum source can cause the formation of the large scale wave, but the former can produce large scale wave only under the condition that there is apparent basic flow acting on it, while the latter can produce the large scale wave even when tends to be zero. Furthermore, the amplitude of steady wave caused by the former is proportional to , while the amplitude caused by the latter has no relation to , instead it depends only on the magnitude of the perturbation of momentum.

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.