Analytical study of the buoyancy–drag equation

✍ Scribed by Serge Bouquet; Pierre Gandeboeuf; Pierre Pailhoriès

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 114 KB
• Volume: 30
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.944

✦ Synopsis

Abstract

The buoyancy–drag equation (BDE) is used for describing the time evolution of the mixing zone, between two fluids, due to Rayleigh–Taylor instabilities in a highly non‐linear regime. The BDE is similar to an equation of motion for each fluid and, in addition to the inertial term, it contains a buoyancy term (proportional to the external acceleration experienced by the system) and a friction proportional to the square of the velocity. In this paper, the integrability of the BDE is studied using Lie point symmetries. Two relevant situations are studied analytically. First, for a constant acceleration, the general solution with two arbitrary constants is derived. On the other hand, for accelerations varying like a power of time, we obtain a one‐parameter family of solutions. These theoretical results can be compared with the various experimental results published in the current literature. Copyright © 2007 John Wiley & Sons, Ltd.