The stability of monsoon depression

Abstract

SummaryThe object of the present paper is to study the stability of a monsoon depression which is a low level wave disturbance over the Indian region during summer. The stability of a wave disturbance depends intimately on the phase velocity. Again, the phase velocity of Rossby-gravity wave does not explain the phase velocity of a monsoon depression. Thus, knowing that the convective activity plays an important role in the development of a monsoon depression, one modifies the phase velocity of zonally propagating Rossbygravity waves, i. e. one obtains the modified dispersion relation considering the effect of convective heating in the equivalent barotropic model which is derived for the low levels in tropics. The modified dispersion relation explains the phase velocity of monsoon depression. Beyond the limiting stage, there is no further depression of the central pressure. So, it is essential to study the stability of a monsoon depression at the limiting stage. The stability analysis shows that the monsoon depression is neutral (i. e.; does not break down) as long as there is convective activity. But the monsoon depression becomes unstable (i. e.; breaks down) if the convective activity ceases. In the latter case, one obtains a possible stream of zonal wind. Zusammenfassung Die Stabilitiit von MonsundepressionenIn der vodiegenden Arbeit wird die Stabilitiit yon Monsundepressionen untersucht, die durch Wellenst6Iungen in der unteren Atmosph~ire Indiens im Sommer dargestellt werden k6nnen. Die Stabilit~t dieser Wellenst6mngen h~ingt in grot~em Ma~e yon deren Phasengeschwindigkeit ab. Diese jedoch ist nicht mit der Phasengeschwindigkeit yon RossbySchwerewellen identisch. Im Hinblick auf die Tatsache, daft die Konvektion eine bedeutende Rolle in der Entwicklung einer Monsundepression spielt, kann die Phasengeschwindigkeit yon zonal sich fortpflanzenden Rossby-Schwerewellen dahingehend modifiziert werden, daf~ man eine ge~inderte Dispersionsbeziehung ethiitt, welche den Einflut~ konvektiver Erw~irmung in das fiir die unteren Atmosphiirenschichten entwickelte ~iquivaient-barotrope Model1 einbezieht.

Die Entstehung tropischer Störungen

“…(6) and the subsequent results remain unaltered). At the limiting stages of the disturbances, 6--e = --rr/2 [ 12]. So, at the limiting stages, eqs.…”

“…k and rn are the zonal and meridional wave numbers respectively, v is the frequency, and * stands for the complex conjugate, e and 6 are the phase angles. It is considered that, throughout the depth of the atmosphere, e and g have their same values as those of the equivalent barotropic level [ 12]. Under these circumstances, eqs.…”

“…These models, however, relate the tendency of vorticity with the effect of diabatic heating directly and so it appears that these models can serve the previous requirements satisfactorily. The tropical disturbance is now considered as a pressure wave, and the diabatic heating effect due to the ensemble of cumulas clouds associated with the disturbance is taken as a wave which propagates with the pressure wave with an equal velocity [12]. The problem is now to show that the mutual interaction between the pressure wave and diabatic heating wave can explain the amplifications and movements of tropical disturbances, depending on the observed values of parameters.…”

“…However, previously, there were no such efficient models which would satisfy the above requirements. Recently, Mahanti [11,12] has derived a pair of equivalent barotropic models for tropics. One model is for the upper troposphere while the other model is for the lower troposphere.…”

A study on Indian monsoon disturbances

“…Depending on Krishnamurti's version, Mahanti [5] has made an attempt to introduce the concept of wave instability problems in tropics (at the limiting stage). Also, in [ 1] is calculated the ratio of incipient amplitudes by taking the ratio of developed amplitudes at nor nearby the limiting stage.…”