A study of the instability of the meridional flow: Part 2

Abstract

In an earlier study [6] the author has shown that the time-dependent meridional flow can be expressed as superimposition of a number of easterly Rossby-gravity waves of infinite lateral extent. Using an equivalent barotropic model, it has been further shown that the short waves of the time-dependent meridional flow are unstable, releasing their kinetic energy to the tropical zonal flow. This is favourable for the generation of the tropical easterly jet. There are, however, some points which have not been fully discussed in the earlier study [6]. This paper deals with the following points: (1) the equivalent barotropic model has been fully derived; (2) it has been shown that short waves have greater contribution to the meridional wind than long waves; (3) the time-dependent meridional wind is quite strong during the disturbed condition of the upper atmosphere in the tropics during summer; (4) the amplitude of wave number 8 is calculated depending on observational facts; (5) the vanishing of modified beta is further discussed. ZusammenfassungUntersuchung der Instabilitfit der Meridionalstr6mung: Tell 2In einer bereits ver6ffentlichten Studie [6] zeigte der Verfasser, daft die zeitabh~ngige Meridionalstr6mung als eine Ubedagerung einer Anzahl yon Rossby-Schwerwellen mit unendlicher lateraler Ausdehnung ausgedriickt werden kann. Unter Verwendung eines ~quivalent-barotropen Modells konnte ferner gezeigt werden, daft die kurzen Wellen der zeitabh~ingigen Meridionalstr6mung instabil sind und ihre kinetische Energie an die tropische Zonalstr6mung abgeben. Es verbleiben jedoch efliche Punkte, die in der ursprtinglichen Studie [6] nicht yoU diskutiert wurden. Die vorliegende Arbeit betrachtet folgende Gesichtspunkte: 1. Das ~iquivalent-ba~otrope Modell wurde vollstiindig abgeleitet; 2. es wird gezeigt, dal~ kurze Wellen einen gr6t~eren Beitrag zur meridionalen Windkomponente liefern als lange Wellen; 3. die zeitabMngige Meridionalstr6mung ist w~ihrend St6rungsperioden in der h6heren tropischen Atmosph~ire im Sommer verh~ilt-nism~igig stark; 4. die Amplitude der Wellenzahl 8 wurde auf Grund von Beobachtungsdaten ermittelt; 5. die Tatsache, dag der modifizierte Beta-Weft (der meridionale Gradient der potentiellen Vorticity) die Gr6ge Null erreicht, wird welter diskutiert.

Die Entstehung tropischer Störungen

“…(12), (13), (15), and (16) clearly show that the growth rate and phase velocity of tropical disturbances are expressed in terms of the phase difference 6 --e (between the mutually interacting pressure wave and diabatic heating wave) and several other parameters. From these equations, one easily finds that westward, standing and eastward movements as well as amplifying, neutral and damping natures of tropical disturbances may be adequately explained using suitable values of 6 --e and other parameters.…”

“…The wave number 8 is associated with a transient motion, propagating westward with a velocity -8 to -12 msec -1 12" 170 A.C. Mahanti nearly. The seasonal average value of the amplitude of meridional wind is nearly 4.5 msec-1 [ 15 ]. The amplitude of wave number 8 grows and breaks down within a period of 3 to 5 days.…”

“…These waves appear to be stationary throughout the summer season. The seasonal mean values of the amplitudes of meridional wind are 1.5 msec -I and 1 msec -1 for wave number 1 and 2 respectively [ 15 ]. The African high and Pacific trough are associated with wave number 1 while the Atlantic trough, Tibetan high, Pacific trough and Mexican high are associated with wave number 2.…”

The stability of monsoon depression

“…This fact is rather justified for the tropical atmosphere where thermal advection is generally considered as small especially beyond the friction level. Mahanti [9,10] has expressed the stream function as a product of a function ofp and a function of x, y and t in order to obtain a zero value of thermal advection. This, however, gives a sufficient condition for the vanishing of thermal advection and such a condition is not always necessary for the same.…”

“…The lateral extent is infinite due to the absence of zonal wind. Thus, one may consider that the zonal harmonics of the meridional flow with zonal shear give nearly the meridional wind components of several Rossby-gravity waves [10]. Thus, the instability of the time-dependent meridional flow with zonal shear has been reduced to the instability of easterly Rossby-gravity waves of infinite lateral extent.…”