Newtonian Jerky Dynamics and Inertial Instability

Newtonian jerky dynamics is applied to inertial instability analysis to study the nonlinear features of atmospheric motion under the action of variable forces. Theoretical analysis of the Newtonian jerky function is used to clarify the criteria for inertial instability, including the influences of the meridional distributions of absolute vorticity （ζg） and planetary vorticity （the ζ effect）. The results indicate that the meridional structure of absolute vorticity plays a fundamental role in the dynamic features of inertial motion. Including only the ζ effect （with the assumptionof constant ζg） does not change the instability criteria or the dynamic features of the flow, but combining the β effect with meridional variations of ζg introduces nonlinearities that significantly influence the instability criteria. Numerical analysis is used to derive time series of position, velocity, and acceleration under different sets of parameters, as well as their trajectories in phase space. The time evolution of kinematic variables indicates that a regular wave-like change in acceleration corresponds to steady wave-like variations in position and velocity, while a rapid growth in acceleration （caused by a rapid intensification in the force acting on ,the parcel） corresponds to track shifts and abrupt changes in direction. Stable limiting cases under the f- and f-plane approximations yield periodic wave-like solutions, while unstable limiting cases yield exponential growth in all variables. Perturbing the value of absolute vorticity at the initial position （ζ0） results in significant changes in the stability and dynamic features of the motion. Enhancement of the nonlinear term may cause chaotic behavior to emerge, suggesting a limit to the predictability of inertial motion.

Rayleigh–Taylor instability at spherical interfaces of incompressible fluids

Rayleigh–Taylor instability（RTI） of three incompressible fluids with two interfaces in spherical geometry is derived analytically. The growth rate on the two interfaces and the perturbation feedthrough coefficients between two spherical interfaces are derived. For low-mode perturbation, the feedthrough effect from outer interface to inner interface is much more severe than the corresponding planar case, while the feedback from inner interface to the outer interface is smaller than that in planar geometry. The low-mode perturbations lead to the pronounced RTI growth on the inner interface of a spherical shell that are larger than the cylindrical and planar results. It is the low-mode perturbation that results in the difference between the RTI growth in spherical and cylindrical geometry. When the mode number of the perturbation is large enough, the results in cylindrical geometry are recovered.

A Diagnostic Case Study on the Comparison Between the Frontal and Non-Frontal Convective Systems

Two major mesoscale convective clusters of different characters occurred during the heavy rainfall event in Guangxi Region and Guangdong Province on 20 June 2005,and they are preliminarily identified as a frontal mesoscale convective system（MCS1;a frontal cloud cluster） and a non-frontal MCS（MCS2;a warm sector cloud cluster）.Comparative analyses on their convective intensity,maintenance mechanism, and moist potential vorticity（MPV） structure were further performed.The convective intensity analysis suggests that the ascending motion in both the frontal MCS1 and the warm sector MCS2 was strong,so it is hard to conclude whether the intensity of the frontal convective cluster was stronger than that of the nonfrontal convective cluster,and their difference in precipitation might result from differences in their moisture conditions.The comparative analysis of the maintenance mechanisms of matured MCS1 and MCS2 show that in MCS1 there were strong northerly inflows at middle and upper levels,and the convection was mainly maintained through convective-symmetric instability;while in MCS2,the water vapor was abundant,and the convection was maintained by moist convective instability.The structural analysis of MPV indicates that（1） the two clusters were both potentially symmetric unstable at middle and low levels;（2） there were interactions between the cold/dry air and the warm/wet air in the frontal MCS1,and the interactions between the upper- and low-level jets in the warm sector MCS2;（3） the high- and low-level jets and moisture condition nearby the convective clusters exerted different impacts on the two types of convective systems, respectively.