A linear, uniformly stratified ocean model is used to investigate propagation of baroclinic Kelvin waves in a cylindrical basin. It is found that smaller wave amplitudes are inherent to higher mode individual terms of the obtained solutions that are also evanescent away of a costal line toward the center of the circular basin. It is also shown that the individual terms if the obtained solutions can be visualized as spinning patterns in rotating stratified fluid confined in a circular basin. Moreover, the fluid patterns look rotating in an anticlockwise sense looking above the North Pole and that spinning is more intensive for smaller mode numbers. Finally, we observe the existence of the oceanic region where the pressure increases relatively rapidly with the depth.

Today engineering and science researchers routinely confront problems in mathematical modeling involving solutions techniques for differential equations. Sometimes these solutions can be obtained analytically by numerous traditional ad hoc methods appropriate for integrating particular types of equations. More often, however, the solutions cannot be obtained by these methods, in spite of the fact that, e.g. over 400 types of integrable second-order ordinary differential equations were summarized in voluminous catalogues. On the other hand, many mathematical models formulated in terms of nonlinear differential equations can successfully be treated and solved by Lie group methods. Lie group analysis is especially valuable in investigating nonlinear differential equations, for its algorithms act here as reliably as for linear cases. The aim of this article is, from the one hand, to provide the wide audience of researchers with the comprehensive introduction to Lie’s group analysis and, from the other hand, is to illustrate the advantages of application of Lie group analysis to group theoretical modeling of internal gravity waves in stratified fluids.

Analysis of high-resolution data from slow-ascent radiosondes released at Halley station, Antarctica (75°38′S, 26°40′W), shows that internal gravity wave phenomena are frequently present in the lower troposphere. There is a strong tendency for these waves to induce a vertical transport of the SE-NW component of momentum, this being the component perpendicular to the alignment of regular ridges in the ice shelf on which the base is built and is independent of the mean wind direction. A method for estimating the variation of the momentum fluxes with height is described. Results show that momentum flux divergences equivalent to accelerations of about 10 ms−1 per day are common at Halley.

We give local and global well-posedness results for a system of twoKadomtsev-Petviashvili (KP) equations derived by R. Grimshaw and Y. Zhuto model the oblique interaction of weakly nonlinear, two dimensional,long internal waves in shallow fluids. We also prove a smoothing effect for the amplitudes of the interacting waves.We use the Fourier transform restriction norms introduced by J. Bourgain and the Strichartz estimates for the linear KP group. Finallywe extend the result of [3] for lower order perturbationof the system in the absence of transverse effects.