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In this work, we analyze numerically the dynamics of one-dimensional gaseous detonations propagating in a mixture with periodically varying properties such as density, temperature, or mixture composition. It is found that periodic upstream variations can lead to resonant amplification of intrinsic oscillations and to mode locking whereby the detonation oscillations are controlled more by the imposed mixture nonuniformities than by the detonation intrinsic instability. The results are consistent with predictions made in the recent work (Kasimov and Gonchar, Proceedings of 27th ICDERS, 2019; Proc Combust Inst 38(3):3725–3732, 2021) that analyzed the same problem in the framework of reactive Burgers’ equation.

Equations describing the flow of an incompressible viscoelastic polymer fluid in the presence of a magnetic field are considered. The symmetrization of this system of equations is discussed.

Under discussion is the the so-called acoustic systems (in linear and nonlinear cases) for the system of equations describing the movement of incompressible viscoelastic polymer fluid. We also consider some approximations of these systems.

We consider a one-dimensional gaseous detonation wave propagating in a channel with a spatially periodic friction factor with the purpose of understanding how non-uniform momentum losses affect the detonation dynamics. The problem is investigated by means of the shock-fitting numerical integration of reactive Euler equations. We examine in detail the detonation velocity oscillations for a range of wavelengths of the variation of the friction factor. It is found that such periodic momentum losses lead to mode locking whereby the oscillations of the detonation velocity are locked into particular simple modes imposed by the variable friction. Outside of the mode locking regions, the dynamics is found to be highly irregular. For such regimes, we estimate the largest Lyapunov exponents of the detonation-velocity signal that points to the presence of friction-driven chaotic solutions.

The temporally growing particular solutions of linearized equations of an incompressible polymeric liquid with strong discontinuities were constructed.

An approach to constructing two-phase state regions for real gases, the state of which is described by the modified van der Waals equation in the form proposed by R.L. Fogel’son and E.R. Likhachev, has been discussed.

Computation of ocean currents in the Drake Passage is carried out with variational assimilation of the data of the hydrographical section across the Drake Passage carried out on December 11-15, 2003, and other data. A stream-eddy structure of the easterly Antarctic Circumpolar Current and a westerly current on the Antarctic Slope are obtained. Water transports by the different current field components and the integral trans- port across the Drake Passage are estimated. The necessity of direct current measurements in the Drake Passage for a correct estimate of the transport is confirmed.