Centrifugally forced viscous Rayleigh-Taylor instability:growth of the varicose modes
Abstract
The study of the classical Rayleigh-Taylor instability has wide-ranging applications in day-to-day observed phenomena involving the mixing of two fluids of differing densities in a gravitational field e.g. from small scale examples such mixing milk in coffee to large scales including, for example, the formation of cloud patterns in the sky. The growth of this instability and its inhibition in presence of rotation has recently been studied in both experiments [1,2] and numerical simulations [3]. The present study is primarily motivated by the recent work of [3] on the growth of Rayleigh-Taylor instabilities in a rotating cylindrical geometry (as illustrated in Figure) for a two-fluid setup in absence of a gravitational field. The work considered the case of azimuthal perturbations to the interface in a two-dimensional setup. Here we explore the full three-dimensional problem taking into account both the azimuthal and axial (varicose) perturbations of the interface using linear stability theory to predict initial growth rates of the unstable modes. Through numerical simulations we test the predictions of the linear theory and gain insights into the full non-linear evolution of the growing instabilities in the system. We present our model setup for the 3D-"varicose centrifuge" problem followed by the analytical tools used to perform a linear stability analysis (both for inviscid and viscous setups) that are subsequently compared with numerical simulations performed with the help of the open-source software package Open-Foam. We conclude with some interesting observations from the set of numerical simulations performed which seem to hint at the emergence of an inherent length scale in the problem independent of initial conditions and various parameters of the system. These parameters were studied systematically to quantify any influence on the growth of the varicose modes in the system.
References: [1] K. A. Baldwin, M. M. Scase, and R. J. A. Hill, The Inhibition of the Rayleigh-Taylor Instability by Rotation, Scientific Reports, 5 (2015), p. 11706. [2] M. M. Scase, K. A. Baldwin, and R. J. A. Hill, Rotating Rayleigh-Taylor instability, Physical Review Fluids, 2 (2017), p. 024801. [3] M. M. Scase and R. J. A. Hill, Centrifugally forced Rayleigh-Taylor instability, Journal of Fluid Mechanics, 852 (2018), pp. 543-577.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFMNG43A0899S
- Keywords:
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- 4415 Cascades;
- NONLINEAR GEOPHYSICS;
- 4568 Turbulence;
- diffusion;
- and mixing processes;
- OCEANOGRAPHY: PHYSICAL;
- 5405 Atmospheres;
- PLANETARY SCIENCES: SOLID SURFACE PLANETS;
- 5430 Interiors;
- PLANETARY SCIENCES: SOLID SURFACE PLANETS