We report on experimentally observed addition, subtraction, and cancellation of orbital angular momentum (OAM) in the process of parametric four-wave mixing that results in frequency up- and down-converted emission in Rb vapor. Specific features of OAM transfer from resonant laser fields with different optical topological charges to the spatially and temporally coherent blue light (CBL) have been considered. We have observed the conservation of OAM in nonlinear wave mixing in a wide range of experimental conditions, including a noncollinear geometry of the applied laser beams, and furthermore, that the CBL accumulates the total OAM of the applied laser light. Spectral and power dependences of vortex and plane wavefront blue light beams have been compared.

We have examined the linear stability of the fully developed natural convection flow in a differentially heated tall vertical enclosure under non-Boussinesq conditions. The three-dimensional analysis of the stability problem was reduced to a two-dimensional one by the use of Squire's theorem. The resulting eigenvalue problem was solved using an integral Chebyshev collocation method. The influence of non-Boussinesq effects on the stability was studied. We have investigated the dependence of the critical Rayleigh number on the temperature difference. The results show that two different modes of instability are possible, one of which is new and due entirely to non-Boussinesq effects. Both types of instability are oscillatory, and the critical disturbance wave speed is zero only in the Boussinesq limit

Microbubble clustering may occur when bubbles become bound to targeted surfaces or are grouped by acoustic radiation forces in medical diagnostic applications. The ability to identify the formation of such clusters from the ultrasound echoes may be of practical use. Nonlinear numerical simulations were performed on clusters of microbubbles modeled by the modified Keller-Miksis equations. Encapsulated bubbles were considered to mimic practical applications but the aim of the study was to examine the effects of inter-bubble spacing and bubble size on the dynamical behavior of the cluster and to see if chaotic or bifurcation characteristics could be helpful in diagnostics. It was found that as microbubbles were clustered closer together, their oscillation amplitude for a given applied ultrasound power was reduced, and for inter-bubble spacing smaller than about ten bubble radii nonlinear subharmonics and ultraharmonics were eliminated. For clustered microbubbles, as for isolated microbubbles, an increase in the applied acoustic power caused bifurcations and transition to chaos. The bifurcations preceding chaotic behavior were identified by Floquet analysis and confirmed to be of the period-doubling type. It was found that as the number of microbubbles in a cluster increased, regularization occurred at lower ultrasound power and more windows of order appeared.

Linear stability of convection flow of ferromagnetic fluid between two vertical differentially heated plates placed in a uniform external magnetic field perpendicular to the plates is studied. Complete stability diagrams for two- and three-dimensional disturbances are presented. It is shown that two distinct mechanisms, thermogravitational and magnetic, are responsible for the appearance of three instability modes. The physical nature of all three modes is investigated in detail and the most prominent features are identified to provide guidance for future experimental investigation. Depending on the governing parameters, the instability patterns are shown to consist of vertical stationary magnetoconvection rolls and/or vertically or obliquely counterpropagating thermogravitational or thermomagnetic waves.

We have examined the linear stability of the fully developed mixed-convection flow in a differentially heated tall vertical channel under non-Boussinesq conditions. The Three-dimensional analysis of the stability problem was reduced to an equivalent two-dimensional one by the use of Squire's transformation. The resulting eigenvalue problem was solved using an integral Chebyshev pseudo-spectral method. Although Squire's theorem cannot be proved analytically, two-dimensional disturbances are found to be the most unstable in all cases. The influence of the non-Boussinesq effects on the stability was studied. We have investigated the dependence of the critical Grashof and Reynolds numbers on the temperature difference. The results show that four different modes of instability are possible, two of which are new and due entirely to non-Boussinesq effects.