Mesoscale Barotropic Instability of Vortex Rossby Waves in Tropical Cyclones

In this study, the barotropic stability of vortex Rossby waves （VRWs） in 2D inviscid tropical cyclone （TC）-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable conditions are discovered： （a） there must be at least one zero point of basic vorticity gradient in the radial scope; and （b） the relative propagation velocity of perturbations must be negative to the basic vorticity gradient, which reflects the restriction relationship of instable energy. The maximum growth rate of instable waves depends on the peak radial gradient of the mean vorticity and the tangential wavenumber （WN）. The vortex-semicircle theorem is also derived to provide bounds on the growth rates and phase speeds of VRWs. The typical basic states and different WN perturbations in a tropical cyclone （TC） are obtained from a high resolution simulation. It is shown that the first necessary condition for vortex barotropic instability can be easily met at the radius of maximum vorticity （RMV）. The wave energy tends to decay （grow） inside （outside） the RMV due mainly to the negative （positive） sign of the radial gradient of the mean absolute vorticity. This finding appears to help explain the developemnt of strong vortices in the eyewall of TCs.

The Instability of the Vortex Sheet along the Shear Line

The traditional Kelvin-Helmholtz notion of studying the shear instability is not suitable for the case associated with shear line with the strong wind shear in the vortex sheet. Since then, the shear instability becomes theinstability of the vortex sheet. If the velocity is induced by the vortex sheet, the inequalities (1? R r + Ri d)> 0 and U(v,t)> U(A(t)) become the criterion of the vortex sheet instability. This criterion indicates that 1) the disposition of environment field restrains the disturbance developing along the shear line. 2) There exist multi—scale interactions in the unstable process of the shear line. The calculation of the necessary condition for the instability is also presented in this paper. Key words Shear line - Induced velocity - Instability of the vortex sheet This work was supported by the project on the study of the formative mechanism and predictive theory of the significant climate and weather disaster in China under Grant G 1998040907 and by the key project on the Dynamic Study of Severe Mesoscale Covective Systems sponsored by the National Natural Science Foundation of China under Grant No.49735180.

The energy transfer mechanism of a perturbed solid-body rotation flow in a rotating pipe

Three-dimensional direct numerical simulations of a solid-body rotation superposed on a uniform axial flow entering a rotating constant-area pipe of finite length are presented. Steady in time profiles of the radial, axial, and circumferential velocities are imposed at the pipe inlet. Convective boundary conditions are imposed at the pipe outlet. The Wang and Rusak (Phys. Fluids 8:1007-1016, 1996.) axisymmetric instability mechanism is retrieved at certain operational conditions in terms of incoming flow swirl levels and the Reynolds number. However, at other operational conditions there exists a dominant, three-dimensional spiral type of instability mode that is consistent with the linear stability theory of Wang et al. (J. Fluid Mech. 797: 284-321, 2016). The growth of this mode leads to a spiral type of flow roll-up that subsequently nonlinearly saturates on a large amplitude rotating spiral wave. The energy transfer mechanism between the bulk of the flow and the perturbations is studied by the Reynolds-Orr equation. The production or loss of the perturbation kinetic energy is combined of three components: the viscous loss, the convective loss at the pipe outlet, and the gain of energy at the outlet through the work done by the pressure perturbation. The energy transfer in the nonlinear stage is shown to be a natural extension of the linear stage with a nonlinear saturated process.