ASYMMETRIC DYNAMIC INSTABILITY OF AXISYMMETRIC POLAR DIMPLING OF THIN SHALLOW SPHERICAL SHELLS

If the parameter , which measures the thickness-to-rise of the sliell, is small, the axismnnetrie polar dimpling oj .shallow .spherical .shell due to quadratic pressure distribution i.s dynamic instability, i.e., a small perturbation can change il to an asymmetric polar dimple mode. In two cases, the problem can be reduced to an eigenvalue problem where T can approximately be reduced to a Sturm-Liouvi/le operator if The existence of at least one real eigenvalue of T, which means that the axisyntmetric polar dimpling is dynamically unstable, i.s proved by spectral theorem or Hilbert theorem. Furthermore, an eigenfunction, which represents one of the asymmetric modes of the unstable dimple shell, belonging to an eigenvalue of T, is found.

The effects of asymmetric potential vorticity forcing on the instability of South Asia High and Indian summer monsoon onset

Based on the theory of potential vorticity(PV),the unstable development of the South Asia High(SAH)due to diabatic heating and its impacts on the Indian Summer Monsoon(ISM)onset are studied via a case diagnosis of 1998.The Indian Summer Monsoon onset in 1998 is related to the rapidly strengthening and northward moving of a tropical cyclone originally located in the south of Arabian Sea.It is demonstrated that the rapid enhancement of the cyclone is a consequence of a baroclinic development characterized by the phase-lock of high PV systems in the upper and lower troposphere.Both the intensification of the SAH and the development of the zonal asymmetric PV forcing are forced by the rapidly increasing latent heat released from the heavy rainfall in East Asia and South East Asia after the onsets of the Bay of Bengal(BOB)monsoon and the South China Sea(SCS)monsoon.High PV moves southwards along the intensified northerlies on the eastern side of the SAH and travels westwards on its south side,which can reach its northwest.Such a series of high PV eddies are transported to the west of the SAH continuously,which is the main source of PV anomalies in the upper troposphere over the Arabian Sea from late spring to early summer.A cyclonic curvature on the southwest of the SAH associated with increasing divergence,which forms a strong upper tropospheric pumping,is generated by the anomalous positive PV over the Arabian Sea on 355 K.The cyclone in the lower troposphere moves northwards from low latitudes of the Arabian Sea,and the upper-layer high PV extends downwards and southwards.Baroclinic development thus occurs and the tropical low-pressure system develops into an explosive vortex of the ISM,which leads to the onset of the ISM.In addition,evolution of subtropical anticyclone over the Arabian Peninsula is another important factor contributing to the onset of the ISM.Before the onset,the surface sensible heating on the Arabian Peninsula is very strong.Consequently the subtropical anticyclone which dominated the Arabian Sea in spring retreats westwards to the Arabian Peninsula and intensifies rapidly.The zonal asymmetric PV forcing develops gradually with high PV eddies moving southwards along northerlies on the eastern side of the anticyclone,and a high PV trough is formed in the middle troposphere over the Arabian Sea,which is favorable to the explosive barotropic development of the tropical cyclone into the vortex.Results from this study demonstrate that the ISM onset,which is different from the BOB and the SCS monsoon onset,is a special dynamical as well as thermodynamic process occurring under the condition of fully coupling of the upper,middle,and lower tropospheric circulations.