NONLINEAR INSTABILITY OF WAVETRAIN UNDER INFLUENCES OF SHEAR CURRENT WITH VARYING VORTICITY AND AIR PRESSURE

Under the assumption of weak shear current with varying vorticity in water and weak air pressure the Zakharov theory is extended to include the effects of vorticity and air pressure on the modulation of water waves. This new equation is used to examine the influence of current and wind on the Benjamin-Feir sideband instability and long-time evolution of wavetrain. As strength of the current increases the bandwidth is found broadened, and the maximum growth rate of sidebands decreased. Periodic solution of sidebands in the presence of current is indicated, which means that shear current does not affect the downshift of wave spectrum peak. Energy input by imposing the air pressure leads to the enhancement of the lower sideband, which is in agreement with the finding of Hara and Mei (1991).

THE USE OF SHEAR GRADIENT VORTICITY IN TROPICAL CYCLONE HEAVY PRECIPITATION PREDICTION:A HIGH-RESOLUTION NUMERICAL CASE STUDY

This study introduces a new dynamical quantity, shear gradient vorticity (SGV), which is defined as vertical wind shear multiplying the horizontal component of vorticity gradient, aiming to diagnose heavy precipitation induced by some strong convective weather systems. The vorticity gradient component can be used to study the collision or merging process between different vortexes or the deformation of a vortex with a sharp vorticity gradient. Vertical wind shear, another contributed component of SGV, always represents the environmental dynamical factor in meteorology. By the combined effect of the two components, overall, SGV can represent the interaction between the environmental wind shear and the evolution of vortexes with a large vorticity gradient. Other traditional vorticity-like dynamical quantities (such as helicity) have the limitation in the diagnosis of the convection, since they do not consider the vorticity gradient. From this perspective, SGV has the potential to diagnose some strong convective weather processes, such as Extratropical Transition (ET) of tropical cyclones and the evolution of multicell storms. The forecast performance of SGV for the numerical ET case of Typhoon Toraji (0108) has been evaluated. Compared with helicity, SGV has shown a greater advantage to forecast the distribution of heavy precipitation more accurately, especially in the frontal zone.

A NOVEL METHOD FOR CALCULATING VERTICAL VELOCITY:A RELATIONSHIP BETWEEN HORIZONTAL VORTICITY AND VERTICAL MOVEMENT

The present work provides a novel method for calculating vertical velocity based on continuity equations in a pressure coordinate system.The method overcomes the disadvantage of accumulation of calculating errors of horizontal divergence in current kinematics methods during the integration for calculating vertical velocity,and consequently avoids its subsequent correction.In addition,through modifications of the continuity equations,it shows that the vorticity of the vertical shear vector(VVSV) is proportional to-ω,the vertical velocity in p coordinates.Furthermore,if the change of ω in the horizontal direction is neglected,the vorticity of the horizontal vorticity vector is proportional to-ω.When ω is under a fluctuating state in the vertical direction,the updraft occurs when the vector of horizontal vorticity rotates counterclockwise;the downdraft occurs when rotating clockwise.The validation result indicates that the present method is generally better than the vertical velocity calculated by the ω equation using the wet Q-vector divergence as a forcing term,and the vertical velocity calculated by utilizing the kinematics method is followed by the O'Brien method for correction.The plus-minus sign of the vertical velocity obtained with this method is not correlated with the intensity of d BZ,but the absolute error increases when d BZ is >=40.This method demonstrates that it is a good reflection of the direction of the vertical velocity.