Low Level Jet stream of Asian Summer Monsoon and its Variability

The main objective of the of present study are to study the intraseasonal variability of LLJ and its relation with convective heating of the atmosphere, to establish whether LLJ splits into two branches over the Arabian sea as widely believed, the role of horizonatal wind shear of LLJ in the episodes of intense rainfall events observed over the west coast of India, to perform atmospheric modeling work to test whether small (meso) scale vortices form during intense rainfall events along the west coast; and to study the relation between LLJ and monsoon depression genesis. The results of a study on the evolution of Low Level Jetstream (LLJ) prior to the formation of monsoon depressions are presented. A synoptic model of the temporal evolution of monsoon depression has been produced. There is a systematic temporal evolution of the field of deep convection strength and position of the LLJ axis leading to the genesis of monsoon depression. One of the significant outcomes of the present thesis is that the LLJ plays an important role in the intraseasonal and the interannual variability of Indian monsoon activity. Convection and rainfall are dependent mainly on the cyclonic vorticity in the boundary layer associated with LLJ. Monsoon depression genesis and the episodes of very heavy rainfall along the west coast of India are closely related to the cyclonic shear of the LLJ in the boundary layer and the associated deep convection. Case studies by a mesoscale numerical model (MM5) have shown that the heavy rainfall episodes along the west coast of India are associated with generation of mesoscale cyclonic vortices in the boundary layer.

Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

A Study On Vortex Knots

In this thesis an attempt is made to study vortex knots based on the work of Keener . It is seen that certain mistakes have been crept in to the details of this paper. We have chosen this study for an investigation as it is the first attempt to study vortex knots. Other works had given attention to this. In chapter 2 we have considered these corrections in detail. In chapter 3 we have tried a simple extension by introducing vorticity in the evolution of vortex knots. In chapter 4 we have introduced a stress tensor related to vorticity. Chapter 5 is the general conclusion.Knot theory is a branch of topology and has been developed as an independent branch of study. It has wide applications and vortex knot is one of them. As pointed out earlier, most of the studies in fluid dynamics exploits the analogy between vorticity and magnetic induction in the case of MHD. But vorticity is more general than magnetic induction and so it is essential to discuss the special properties of vortex knots, independent of MHD flows. This is what is being done in this thesis.

Sea Surface Temperature-Convection Relationship in Tropical Oceans with Special Emphasis to Intraseasonal Variability of Indian Summer Monsoon

The SST convection relation over tropical ocean and its impact on the South Asian monsoon is the first part of this thesis. Understanding the complicated relation between SST and convection is important for better prediction of the variability of the Indian monsoon in subseasonal, seasonal, interannual, and longer time scales. Improved global data sets from satellite scatterometer observations of SST, precipitation and refined reanalysis of global wind fields have made it possible to do a comprehensive study of the SST convection relation. Interaction of the monsoon and Indian ocean has been discussed. A coupled feedback process between SST and the Active-Break cycle of the Asian summer monsoon is a central theme of the thesis. The relation between SST and convection is very important in the field of numerical modeling of tropical rainfall. It is well known that models generally do very well simulating rainfall in areas of tropical convergence zones but are found unable to do satisfactory simulation in the monsoon areas. Thus in this study we critically examined the different mechanisms of generation of deep convection over these two distinct regions.The study reported in chapter 3 has shown that SST - convection relation over the warm pool regions of Indian and west Pacific oceans (monsoon areas) is in such a way that convection increases with SST in the SST range 26-29 C and for SST higher than 29-30 C convection decreases with increase of SST (it is called Waliser type). It is found that convection is induced in areas with SST gradients in the warm pool areas of Indian and west Pacific oceans. Once deep convection is initiated in the south of the warmest region of warm pool, the deep tropospheric heating by the latent heat released in the convective clouds produces strong low level wind fields (Low level Jet - LLJ) on the equatorward side of the warm pool and both the convection and wind are found to grow through a positive feedback process. Thus SST through its gradient acts only as an initiator of convection. The central region of the warm pool has very small SST gradients and large values of convection are associated with the cyclonic vorticity of the LLJ in the atmospheric boundary layer. The conditionally unstable atmosphere in the tropics is favorable for the production of deep convective clouds.

Water characteristics and current structure of the intermediate waters in the arabian sea

At intermediate depths of the Arabian Sea, the circulation and characteristics of water are more influenced by the high saline waters from the north and low saline waters from the south of equator. The interaction of these waters which greatly differ in characteristics is less understood compared to that at the upper layers. An understanding of the nature of the intermediate waters is of vital importance not only because of the unusual characteristics of the waters but also due to the influx of the different water masses from the neighbouring Red Sea and Persian Gulf. Hence, in the present investigation, it is proposed to study the water characteristics and current structure of the intermediate waters in the Arabian Sea through the distribution of the water properties on the isanosteric surfaces of 100, 80, 60 and 4O—cl/t, vertical sections, and scatter diagrams An attempt is also made to present the potential vorticity between different steric levels to understand the circulation and mixing processes. Data collected during and subsequent to International Indian Ocean Expedition (IIOE) are used for this study. The thesis has been divided into six chapters with further sub divisions

Circulation in the indian ocean in relation to the monsoon circulation of the atmosphere

The present thesis is an attempt by the researcher to Investigate the surface circulation of the Indian Ocean, north of 2095 in relation to the atmospheric circulation over the ocean. The aim is achieved by working out the circu1ation pattern and correlating it with the computed wind stress and its vorticity. The month wise surface circulation is arrived by drawing the streamlines, using freshand method with superimposed isotache. The zonal ad meridional componance of the wind stress and the curl of the wind stress are computed for each month over 2° latitude longitude quadrangle from the bulk aerodynamic formula, using a computer program. The data for drawing the surface circu1ation and for computing the wind stress and its curl have come from the Dutch Atlas.

SST–convection relation over tropical oceans

According to current knowledge, convection over the tropical oceans increases with sea surface temperature (SST) from 26 to 29 °C, and at SSTs above 29 °C, it sharply decreases. Our research shows that it is only over the summer warm pool areas of Indian and west Pacific Oceans (monsoon areas) where the zone of maximum SST is away from the equator that this kind of SST-convection relationship exists. In these areas (1) convection is related to the SST gradient that generates low-level moisture convergence and upward vertical motion in the atmosphere. This has modelling support. Regions of SST maxima have low SST gradients and therefore feeble convection. (2) Convection initiated by SST gradient produces strong wind fields particularly cross-equatorial low-level jetstreams (LLJs) on the equator-ward side of the warm pool and both the convection and LLJ grow through a positive feedback process. Thus, large values of convection are associated with the cyclonic vorticity of the LLJ in the atmospheric boundary layer. In the inter-tropical convergence zone (ITCZ) over the east Pacific Ocean and the south Pacific convergence zone (SPCZ) over the west Pacific Ocean, low-level winds from north and south hemisphere converge in the zone of maximum SST, which lies close to the equator producing there elongated bands of deep convection, where we find that convection increases with SST for the full range of SSTs unlike in the warm pool regions. The low-level wind divergence computed using QuikSCAT winds has large and significant linear correlation with convection in both the warm pool and ITCZ/SPCZ areas. But the linear correlation between SST and convection is large only for the ITCZ/SPCZ. These findings have important implications for the modelling of largescale atmospheric circulations and the associated convective rainfall over the tropical oceans

Some conservation laws of fluid mechanics

This thesis contains a study of conservation laws of fluid mechanics. These conservation laws though classical, have been put to extensive studies in t:he past many decades