Abstract
In the article the dynamics of free interface of heavy fluid is studied. Namely, the Rayleigh-Taylor instability (RTI) in the case of incompressible fluids under the gravitation g is investigated and the theory of asymptotical stage of RTI is proposed. Flows periodic in space and steady-state in time are considered. Both two-dimensional (2D) and three-dimensional (3D) cases are presented. In 20 the how is described by the famous periodic chain of smooth bubbles (like billows or swells) intermitted with jets (like planes or walls). In 3D we consider the spatially periodic flow of bubbles and jets with the elementary square lattice (i.e. flow with the axis symmetry C-4). The solution is based on an expansion of a velocity potential in a Fourier series and subsequent re-expansion in a Taylor series near the top of the bubble. Very high non-linear orders are considered. A sequence of solutions at different values of a truncation number, which equals the number of harmonics involved, is presented. The convergence of these solutions is shown and proved. Accurate data about all physical characteristics of the flows are given. A comparison of these analytic solutions with results of the numerical simulation is presented also.
| Original language | English |
|---|---|
| Pages (from-to) | 339-341 |
| Number of pages | 3 |
| Journal | Physica D |
| Volume | 87 |
| Issue number | 1-4 |
| DOIs | |
| Publication status | Published - 15 Oct 1995 |
| Event | Conference on the Nonlinear Schrodinger Equation - CHERNOGOLOVKA Duration: 25 Jul 1994 → 3 Aug 1994 |