African monsoons, Part 2: Synoptic-scale wave disturbances in the intertropical convergence zone over north Africa

In this part, the paper discusses several aspects of the origin, structure, development and movement of wave disturbances over the North African tropical zone during the northern summer. Analyzing the cases often actual wave disturbances which later in their life cycles developed into hurricanes over the Atlantic, it finds that though the horizontal and vertical shear of the mean zonal wind associated with the mid-tropospheric easterly jet over Africa satisfies the condition of dynamical instability under certain restrictive boundary conditions, it is the influence of a large-amplitude baroclinic wave in mid-latitude westerlies upon a stationary wave in the mountainous region of the east-central north Africa that appears to trigger the birth of a wave disturbance in the intertropical convergence zone over the Nile valley of Sudan between the Marra and the Ethiopian mountains. Physical processes likely to be important in the formation, development and movement of the disturbances are pointed out.

Some Theoretical and Experimental Extensions Based on the Properties of the Intrinsic Transfer Matrix

The work approaches new theoretical and experimental studies in the elastic characterization of materials, based on the properties of the intrinsic transfer matrix. The term ‘intrinsic transfer matrix’ was firstly introduced by us in order to characterize the system in standing wave case, when the stationary wave is confined inside the sample. An important property of the intrinsic transfer matrix is that at resonance, and in absence of attenuation, the eigenvalues are real. This property underlies a numerical method which permits to find the phase velocity for the longitudinal wave in a sample. This modal approach is a numerical method which takes into account the eigenvalues, which are analytically estimated for simple elastic systems. Such elastic systems are characterized by a simple distribution of eigenmodes, which may be easily highlighted by experiment. The paper generalizes the intrinsic transfer matrix method by including the attenuation and a study of the influence of inhomogeneity. The condition for real eigenvalues in that case shows that the frequencies of eigenmodes are not affected by attenuation. For the influence of inhomogeneity, we consider a case when the sound speed is varying along the layer’s length in the medium of interest, with an accompanying dispersion. The paper also studies the accuracy of the method in estimating the wave velocity and determines an optimal experimental setup in order to reduce the influence of frequency errors.

The Australian monsoon, Part 2 : Depressions and cyclones

A study of the NCEP/NCAR Reanalysis for the Australian region during the southern summer reveals that most of the depressions and cyclones over the region form and develop in a stationary wave that develops along the continent's northern coastline during this period due to land-sea thermal contrast. The structure and properties of the stationary wave are brought out in detail and internal and external forcings that lead to its development into depressions and cyclones are discussed. Environmental factors that appear to influence the movement and recurvature of cyclones over the region are discussed with two case studies.

On the onset of summer monsoon over India in relation to interactions of the monsoon stationary wave with transient baroclinic waves leading to monsoon cyclogenesis

The important problem of the early or late onset of summer monsoon over India is addressed in the present study and found to be related to the structure and behaviour of a monsoon stationary wave that forms over the region due to land-sea thermal contrast and interacts with travelling wave disturbances in the westerlies and the easterlies associated with the subtropical belt over Asia. Depending upon the type of coupling and decoupling that occurs between the interacting waves, monsoon advances towards India either slowly or speedily. Since northward-propagating monsoon depressions are found to accelerate the onset processes. the study carries out a detailed analysis of the interaction processes which give rise to such disturbances and determine their development and movement.

Role of tropical mid-latitude interaction in the genesis of a monsoon depression - A detailed case study

During northern summer, a monsoon stationary wave which maintains as part of its baroclinic structure three well-defined troughs, one each in the region of the Arabian sea, the Bay of Bengal and South China sea, frequently interacts with the mid-latitude baroclinic waves which amplify during their eastward passage with profound influence on the development of the monsoon troughs. The paper discusses the mechanism of this wave-wave interaction as suggested by the temporal evolution of the themla1 and wind fields associated with the waves and reports the findings of a detailed study of a case of tropical-mid latitude interaction in which the development of a monsoon trough led to the birth of a westward-propagating monsoon depression over South China.

Structure and properties of summer monsoon stationary B,"Operational use of Ozone over .southern Asia: an observational study

A study of ten-year (1976-1985) mean July climatology of southern Asia and adjoining ocean areas confirms the presence of a well-defined stationary wave, believed to be due mainly to land-sea thermal contrast over the region, in the fields of several meteorological variables. The wave extends laterally over about 10 degrees of latitude with maximum intensity along about 20° N and vertically from surface to about 300 hPa. Its zonal wavelength is about 2000-2500 km and its amplitude in the field of zonal anomaly of temperature and meridional component of wind is 1 oC and 4ms-l respectively. The trough-ridge system of the wave appears to tilt eastward with height from surface to about 700 hPa and westward aloft up to about 300 hPa, while the warmest-coldest anomaly system appears to tilt eastward all the way from surface to about 300 hPa. A phase difference appears to exist between the geopotential and the temperature fields in both the lower and the upper tropospheres. The aforesaid zonal-vertical tilt of the monsoon trough and phase difference between the geopotential and the temperature fields appears to be compatible, through thermal advection, With a direct conversion of eddy available potential energy into eddy kinetic energy via a west-east (clockwise) overturning with warm air rising in the west and cold air sinking in the east in the case of the eastward-tilting lower-tropospheric trough and an east-west (anti-clockwise) overturning with warm air rising in the east and cold air sinking in the west in the case of the westward-tilting middle and upper-tropospheric trough, An enhancement of the thermal advection and hence the vertical circulation may occasionally lead to development of the trough into a I(JW or depression. However, the question of development of the trough and physical factors, which may contribute to such development, needs to be examined by further study.

QUASI-STATIONARY PLANETARY WAVES IN MID-LATITUDE STRATOSPHERE–MESOSPHERE IN WINTER 2011-2020

The 10-year climatology (2011–2020) of quasi-stationary planetary waves in the mid-latitude stratosphere and mesosphere (40–50N, up to 90 km) has been analyzed. Longitude–altitude sections of geopotential height and ozone have been obtained using the Aura MLS satellite data. It is found that stationary wave 1 propagates into the mesosphere from the North American High and Icelandic Low, which are adjacent surface pressure anomalies in the structure of stationary wave 2. Unexpectedly, the strongest pressure anomaly in the Aleutian Low region does not contribute to the stationary wave 1 formation in the mesosphere. The vertical phase transformations of stationary waves in geopotential height and ozone show inconsistencies that should be studied separately.

Localized stationary seismic waves predicted using a nonlinear gradient elasticity model

This paper aims at investigating the existence of localized stationary waves in the shallow subsurface whose constitutive behavior is governed by the hyperbolic model, implying non-polynomial nonlinearity and strain-dependent shear modulus. To this end, we derive a novel equation of motion for a nonlinear gradient elasticity model, where the higher-order gradient terms capture the effect of small-scale soil heterogeneity/micro-structure. We also present a novel finite-difference scheme to solve the nonlinear equation of motion in space and time. Simulations of the propagation of arbitrary initial pulses clearly reveal the influence of the nonlinearity: strain-dependent speed in general and, as a result, sharpening of the pulses. Stationary solutions of the equation of motion are obtained by introducing the moving reference frame together with the stationarity assumption. Periodic (with and without a descending trend) as well as localized stationary waves are found by analyzing the obtained ordinary differential equation in the phase portrait and integrating it along the different trajectories. The localized stationary wave is in fact a kink wave and is obtained by integration along a homoclinic orbit. In general, the closer the trajectory lies to a homoclinic orbit, the sharper the edges of the corresponding periodic stationary wave and the larger its period. Finally, we find that the kink wave is in fact not a true soliton as the original shapes of two colliding kink waves are not recovered after interaction. However, it may have high amplitude and reach the surface depending on the damping mechanisms (which have not been considered). Therefore, seismic site response analyses should not a priori exclude the presence of such localized stationary waves.

Vortex Layer on the β-Plane in the Miles – Ribner Formulation. Pole on the Real Axis

Purpose. The problem of a non-zonal vortex layer on the β-plane in the Miles – Ribner formulation is considered. It is known that in the absence of the β-effect, the vortex layer has no neutral eigenmodes, and the available two ones (varicose and sinusoidal) are unstable. Initially, generalization of the problem to the β-plane concerned only the zonal case. The problem for a non-zonal vortex layer is examined for the first time in the paper. It is known that in the WKB approximation for the linear wave disturbances (regardless of whether a zonal or non-zonal background flow is considered), there is an adiabatic invariant in the form of the law of the enstrophy (vorticity) conservation. For the zonal vortex layer, the enstrophy conservation law also holds, and no vorticity exchange occurs between the waves and the flow in the zonal case. The non-zonal vortex layer has qualitatively different features; particularly, it does not retain enstrophy. Thus, as a result, there appears a new class of solutions which can be interpreted as pure radiation of the Rossby waves by a non-zonal flow. Generalizing the vortex layer problem on the β-plane to the non-zonal case constitutes the basic aim of the present study. Methods and Results. A new class of linear stationary wave solutions, namely the Rossby waves, is found. It is shown a non-zonal flow can be directed in one way, whereas the stationary wave disturbances can move in the opposite (contrary) direction. The coexistence of such solutions for the shear non-zonal flow and stationary wave disturbances takes place due to the influence of the external force and mathematically comes from a non-self-adjoining character of the linear operator for a non-zonal background flow. Conclusions. There exists a new class of solutions that can be interpreted as pure radiation of the Rossby waves by a non-zonal flow. There is no such solution for a zonal flow. It is just non-zoning that gives the effect of pure radiation and corresponds to the classical definition of radiation. This approach makes it possible to eliminate inconsistency in terminology, when instabilities are mistakenly called radiation, and radiation – pure radiation.