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Helicity is defined as H = V · ω, where V and ω velocity and vorticity vectors, respectively. Many works have pointed out that the larger the helicity is, the longer the life cycle of the weather system is. However, the direct relationship of the helicity to the evolution of the weather system is not quite clear. In this paper, the concept of helicity is generalized as shearing wind helicity (SWH). Dynamically, it is found that the average SWH is directly related to the increase of the average cyclonic rotation of the weather system. Physically, it is also pointed out that the SWH, as a matter of fact, is the sum of the torsion terms and the divergence term in the vorticity equation. Thermal wind helicity (TWH), as a derivative of SWH, is also discussed here because it links the temperature field and the vertical wind field. These two quantities may be effective for diagnosing a weather system. This paper applies these two quantities in cylindrical coordinates to study the development of Hurricane Andrew to validate their practical use. Through analyzing the hurricane, it is found that TWH can well describe the characteristics of the hurricane such as the strong convection and release of latent heat, SWH is not only a good quantity for diagnosing the weather system, but also an effective one for diagnosing the development of the hurricane.

On the basis of the MM5 simulation data of the severe storm that occurred over the southeastern part of Hubei province on 21 July 1998, the interaction of mesoscale convection and frontogenesis is dealt with using the thermodynamical equation and frontogenetical function. The results show that the outbreak of the severe storm is closely related to the local frontogenesis. In fact, the interaction between the shearing instability of the low-level jet (LLJ) and the topographic forcing generates an gravity-inertia wave as well as local frontogenesis (the first front), which consequently induce the onset of the severe storm. From then on, owing to the horizontal and vertical advection of the potential temperature, the new frontogenesis (the second front) is formed to the northeast side of the severe storm, which initiates the second rain belt. Meanwhile, a two-front structure emerges over the southeastern part of Hubei province. Accompanied with the further intensification of the convection, the rain droplets evaporation cooling strengthens the first front and weakens the second front, resulting in single front structure over the southeastern part of Hubei province in the period of the strong convection.

The characteristics of helicity in a hurricane are presented by calculating the MM5 model output in addition to theoretical analysis. It is found that helicity in a hurricane mainly depends on its horizontal component, whose magnitude is about 100 to 1000 times larger than its vertical component. It is also found that helicity is approximately conserved in the hurricane. Since the fluid has the intention to adjust the wind shear to satisfy the conservation of helicity, the horizontal vorticity is even larger than the vertical vorticity, and the three-dimensional vortices slant to the horizontal plane except in the inner eye. There are significant horizontal vortices and inhomogeneous helical flows in the hurricane. The formation of the spiral rainband is discussed by using the law of horizontal helical flows. It is closely related to the horizontal strong vortices and inhomogeneous helical flows.

Energetics of geostrophic adjustment in rotating flow is examined in detail with a linear shallow water model. The initial unbalanced flow considered first falls tinder two classes. The first is similar to that adopted by Gill and is here referred to as a mass imbalance model, for the flow is initially motionless but with a sea surface displacement. The other is the same as that considered by Rossby and is referred to as a momentum imbalance model since there is only a velocity perturbation in the initial field. The significant feature of the energetics of geostrophic adjustment for the above two extreme models is that although the energy conversion ratio has a large case-to-case variability for different initial conditions, its value is bounded below by 0 and above by 1 / 2. Based on the discussion of the above extreme models, the energetics of adjustment for an arbitrary initial condition is investigated. It is found that the characteristics of the energetics of geostrophic adjustment mentioned above are also applicable to adjustment of the general unbalanced flow under the condition that the energy conversion ratio is redefined as the conversion ratio between the change of kinetic energy and potential energy of the deviational fields.

Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive error source in the numerics. This paper presents an optimization of centered finite-difference operator based on the principle of constrained cost function, which can reduce the truncation error to minimum. In the optimization point of view, such optimal operator is in fact an attempt to minimize spatial truncation er-rors in atmospheric modeling, in a simple way and indeed a quite innovative way to implement Variational Continuous Assimilation (VCA) technique.

Three-dimensional simulation of cold-front rain-band (NCFR) associated with a straight cold front has been studied by use of a non-hydrostatic, full compressible storm-scale model (ARPS) including multi-phase microphysical parameterization. The dynamical and physical features of the frontal cloud de-velopment have been well simulated and analyzed. It is in evidence that the frontal cloud is triggered by the updraft of the secondary frontal circulation. However, the long persistence of diabatic frontogenesis only can be attributed to positive feedback between the frontal baroclinicity and the prefrontal latent heat release. The simulations indeed demonstrate that the potential temperature gradient enhancement in front zone is strongly related with the re-distribution of cloud moisture, by the action of tilted updraft. In conse-quence, the splice of cooling and heating pool that is respectively created from the evaporation of cloud wat-er and condensing J freezing of water vapor J rain droplet, wich is in favor of the strong contrast of cool and warm air mass across the frontal zone to diabatic frontogenesis.

Theoretical argumentation for so-called suitable spatial condition is conducted by the aid of homotopy framework to demonstrate that the proposed boundary condition does guarantee that the over-specification boundary condition resulting from an adjoint model on a limited-area is no longer an issue, and yet preserve its well-poseness and optimal character in the boundary setting. The ill-poseness of over-specified spatial boundary condition is in a sense, inevitable from an adjoint model since data assimilation processes have to adapt prescribed observations that used to be over-specified at the spatial boundaries of the modeling domain.

Three conservative principles: potential vorticity, absolute momentum and potential temperature are used to study the influence of topography on the local frontogenesis and geostrophic adjustment, which are induced by the inhomogeneous thermal fields. It is found that the horizontal distribution of the initial potential temperature and its position relative to the mountain play important roles during the geostrophic adjustment and local frontogenesis. The frontogenesis is weakened by the mountain when the initial thermal perturbation is located at the base of the upwind slope. The frontal discontinuity cannot occur unless the horizontal contrast of the initial potential temperature is great enough. Whereas, the situation is opposite when the initial thermal disturbance is main-ly situated near the peak of the mountain. Complementary to the aforementioned cases, the effect of topog-raphy on the frontogenesis depends on the stratification of the flow when the initial thermal disturbance lies at the foot of lee slope. For weak stratification, topography is favorable to the formation of frontal discontinuity, vice versa. This discrepancy is attributed to the difference of subsidence warming, caused by the mountain, when the stratification is either strong or weak. Furthermore, the energy conversion ratio between the kinetic and potential energy during the geostrophic adjustment process is also affected by the topography. In contrast to the flat bottom case, the ratio is reduced (increased) when the initial thermal perturbation lies in the up-wind slope (lee slope). The reason is that the gravity force does negative work in the former case while does positive work in the latter case.

The final balanced state of an initial unbalanced flow is discussed with the same method as Vallis (1992). For the two-dimensional, inviscid, rotating and nonlinear model, the final state of the flow depends on the initial conditions. If the initial potential vortcity of the flow is non-uniform, the final state is not necessarily geostrophic. However, for the zero and uniform potential vorticity flow, the final state will satisfy the thermal wind relation when the length scale of the initial disturbance is large enough. Otherwise, discontinuity will occur in the geostrophic solution. In this case, the final balanced state will not be geostrophic any longer and an extended momentum coordinate is introduced to overcome the mult-value problem.

In four—dimensional variational data assimilation (4DVAR) technology, how to calculate the optimal step size is always a very important and indeed difficult task. It is directly related to the computational efficiency. In this research, a new method is proposed to calculate the optimal step size more effectively. Both nonlinear one—dimensional advection equation and two—dimensional inertial wave equation are used to test and compare the influence of different methods of the optimal step size calculations on the iteration steps, as well as the simulation results of 4DVAR processes. It is in evidence that the different methods have different influences. The calculating method is very important to determining whether the iteration is convergent or not and whether the convergence rate is large or small. If the calculating method of optimal step size is properly determined as demonstrated in this paper, then it can greatly enlarge the convergence rate and further greatly decrease the iteration steps. This research is meaningful since it not only makes an important improvement on 4DVAR theory, but also has useful practical application in improving the computational efficiency and saving the computational time.

If the initial fields are not in geostrophic balance, the adjustment and evolution will occur in the stratified fluid, and the frontogenesis will occur under suitable conditions. The evolution is studied here with a nonhydrostatic fully compressible meso—scale model (Advanced Regional Prediction System, ARPS). Four cases are designed and compared: (i) control experiment; (ii) with different initial temperature gradient; (iii) with vapor distribution; (iv) with orographie forcing. The results show that: (1) there is an inertial oscillation in the evolution of the imbalanced flow with the frequency of the local Coriolis ƒ, and with its amplitude decreasing with time. The stationary balanced state can only be approached as it cannot be reached in the limit duration of time. The energy conversion ratio varies in the range of [0, 1 / 3]; (2) the stronger initial temperature gradient can make the final energy conversion ratio higher, and vice versa; (3) suitable vapor distribution is favorable for the frontogenesis. It will bring forward the time of the frontogenesis, strengthen the intensity of the cold front, and influence the final energy conversion ratio; (4) the orographie forcing has an evidently strengthening effect on the frontogenesis. The strengthening effect on the frontogenesis and the influence on the final energy conversion ratio depend on the relative location of the mountain to the cold front.

The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are used. One is the conjugate code method-direct approach, and another is the numerical backward integration of analytical adjoint equation—indirect approach. Theoretical derivation and sensitivity tests are conducted in order to verify the consistency and inconsistency of the two algorithms under the semi-Lagrangian framework. On the other hand, the sensitivity of the perfect and imperfect initial condition is also tested in both direct and indirect approaches.

The interaction of orographic disturbance with front is investigated with a nonhydrostatic fully compressible mesoscale model (ARPS). It is shown that the front is dominated mainly by the orographic disturbance if the front is weak. Firstly, because the stratified airstream is forced to flow along the topographic surface, the topographic surface almost coincides with the lowest isentrope for the barotropic flow. The potential temperature gradients are opposite on upwind slope and downwind slope. As the cold front moves across the mountain, its intensity decreases on the upwind side and increases on the downwind side due to the thermal superposition. Conversely, the warm front is strengthened on the upwind slope and weakened on the downwind slope. This is the thermal superposition effect. Secondly, the mountain-forced circulation and orographic waves, which depend on the shape and size of topography and characteristics of airflow, contribute to frontogenesis and / or frontolysis. This is referred as dynamical action. For the mesoscale mountain ridge of gentle slope, the dynamical action weakens the cold front on the upwind slope, and strengthens the cold front on the lee side. While for the mesoscale mountain of steep slope, the dynamical effect weakens the cold front on the upwind side and strengthens the cold front on the mountain top, the frontal intensity is decreased when front moves downslope rapidly. As front moves into the convergent zone near the mountain base, its intensity is enhanced severely. If the front is intensive, there is strong interaction between the orographic disturbance and the front. The cold front dramatically increases downslope wind and lee side gravity wave activity. And these in turn act upon the frontal intensity and frontal structure. For the baroclinic basic flow, the southerly warm advection on the upwind side makes the cold front less frontolysis; the northerly on the lee side violently intensifies the clod front.

Using the PSU / NCAR Mesoscale Model version four(MM4), the frontogenesis and geostrophic adjustment problem in atmosphere with imbalance initial ideal data and conditions are studied. Based on results of experiments, it is found that the objective analysis and initialization procedure of the Model are not sensitive to the initial conditions used in this study. The final state of atmosphere, through process of adjustment, depends on the temperature gradient intensity of initial imbalance conditions. The front can be formed with appropriate condition. The processes of the frontogenesis are studied. It is also found that the response of the model to the ideal initial data used in this investigation is sensitive to the selected lateral boundary condition. The time-dependent inflow / outflow lateral boundary Condition is the best implemented option for this numerical study. Energetic study of the experiments shows that the front is formed after the initial transient stage when there is no exchange of energy between the kinetic and potential energy. The time needed for the formation of the front is longer than that predicted theoretically. The ratio of kinetic energy to the released potential energy is considered. This ratio varies with the temperature gradient intensity and the type of used wind for computing kinetic energy (geostrophic or geostrophic plus ageostrophic wind). The larger temperature gradient, the larger magnitude of this ratio. A maximum value of energy in either type of computed kinetic energies (geostrophic wind kinetic energy and actual wind kinetic energy) for cases that the fronts are observed whereby, and its magnitude and occurrence time depend on initial data distribution. The variation of the computed kinetic energies with time, after transition time, is reasonable and no significant conversion of the energy between kinetic and potential energy goes on, however, stability within variables is not achieved.

Observational study shows that, in some cases, the frontal structure displays the features of gravitative flows. It seems that the formation of discontinuity is an important problem in the study of the frontogenesis which is usually defined as an increasing of the scalar gradient. In this paper, the characteristic features of air flow with initial imbalance between the wind and the density fields are studied. Much attention is paid on the condition for the formation of discontinuity and its time scale. It is found that the initial distribution of density plays an important role in the formation of the discontinuity which happens in short time duration.

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 ū tends to be zero. Furthermore, the amplitude of steady wave caused by the former is proportional to \(\sqrt {\overline u } \), while the amplitude caused by the latter has no relation to ū, instead it depends only on the magnitude of the perturbation of momentum.

In order to study the characteristic features of the frontal motion over mountains, a frontal model is designed in this paper. The analytical solution of the model with the assumption of semigeostrophic approximation and no friction is obtained and compared with numerical solution without the assumption. It assumes that the front is a free surface between two fluid layers with different densities. It also assumes that the mountain and the front are indefinitely long. Therefore, the motion of such a front can be determined by the one-dimensional shallow water equation system. By making a series of experiments, we confirm the rule further that front can be retarded when climbing the mountain and accelerated when going down the mountains. We also found some interesting characteristics of frontal structure influenced by topography in addition.

Helicity is an important physical variable which is similar to the energy and enstrophy in three-dimensional fluid. It can be used to describe the motion in the direction of fluid rotation and also can be regarded as a new physical variable in turbulence theory. In recent years, it has been used in atmospheric dynamics. In this paper, helicity of atmospheric flow, especially helicity in the boundary layer and in the vicinity of front was discussed. These results show that helicity is usually positive in the boundary layer due to the effect of friction. The helicity of boundary layer flow is larger in anticyclone than that in cyclone, resulting from the different wind structures of boundary layers in anticyclone and cyclone under the geostrophic momentum approximation. It is possible that the helicity is negative at certain height in the baroclinic boundary layer. The influences of nonlinearity and baroclinity on the helicity are important. The so called “Cloud Street” in the boundary layer is related to the dynamics of helicity. Helicity in the atmosphere can be expressed as the temperature advection under some conditions, so helicity would be allowed to describe the frontogenesis and development of frontal structure. The amplitude of helicity increases with time in the frontogenesis. A large gradient of helicity is generated in the region located to the northeast of the surface low and in which the front is formed. In warm frontal region, as well as behind the trough of temperature, the helicity is positive, while the helicity is negative in cold frontal sector and in the ahead ridge of temperature. The largest helicity occurs in the boundary.

In the boundary layer, the flow is basically an equilibrium of three forces: Coriolis, pressure gradient and frictional. This means that it is an Ekman flow while the basic flow in the free atmosphere is an equilibrium of two forces: Coriolis and pressure gradient, and is a geostrophic flow. Therefore, it is natural to try to modify the geostrophic momentum approximation in the free atmosphere to become an Ekman momentum approximation in the boundary layer. The physical explanation and foundation of the Ekman momentum approximation are discussed.

In order to study the characteristics of cold frontal motion over the arbitrary topography, the velocity of cold frontal movement is derived by using the one layer shallow-water model. The results show that there exist the retardation in upwind side and rapid descent in the lee slope when the cold front crosses the topography.

The flow over mountain is quite complicated. There are a lot of papers on this problem and a lot of progresses have been made. However, in the most of these papers, just the dynamics contributions of mountain have been analysed; the effect of the friction is often neglected. Since the frictional effect is always associated with flow, especially when it flows over the mountain. The study shows that the friction is small in the magnitude but it is not a negligible effect because it changes the features of the flow. In the case of super- or sub-critical flow, there are two extremes: one maximum, one minimum of the fluid surface on the lee-side of themountain, while in the inviscid fluid, there is just one extreme. The frictional effect should neither be too strong nor too weak to make the situation happened according to the investigation of this paper.