2D Rayleigh-Taylor instability: Interfacial arc-length vs. deformation amplitude

¹ FAST Laboratory, Université Pierre et Marie Curie-Paris 6/CNRS - Campus Universitaire, 91400 Orsay, France, EU
² Department of Physics, Case Western Reserve University - Cleveland, OH 44106-7079 USA

Received: 6 August 2012
Accepted: 7 February 2013

Abstract

Fluid interface instabilities are usually studied through the time evolution of the amplitude of deformation of the interface. While this approach is convenient, it often fails to fully describe the evolution of a deforming interface, especially when the interface cannot be represented as a single-valued function of a space coordinate. Here, we present new experimental data on Rayleigh-Taylor 2D instability for immiscible fluids, obtained through the use of magnetic levitation. We observe that new information can be retrieved by using an alternate metric to the amplitude, viz., the total arc-length of the interface (in 2D), or equivalently its total surface area (in 3D). In particular, we identify a master curve for the evolution of the arc-length over time, following three different regimes and on which all our data points fall. We conjecture that the exploration of such alternate metrics will yield equally promising results on a broad range of interface instabilities.