The Inhibition of the Rayleigh-Taylor Instability by Rotation

Abstract

It is well-established that the Coriolis force that acts on fluid in a rotating system can act to stabilise otherwise unstable flows. Chandrasekhar considered theoretically the effect of the Coriolis force on the Rayleigh-Taylor instability, which occurs at the interface between a dense fluid lying on top of a lighter fluid under gravity, concluding that rotation alone could not stabilise this system indefinitely. Recent numerical work suggests that rotation may, nevertheless, slow the growth of the instability. Experimental verification of these results using standard techniques is problematic, owing to the practical difficulty in establishing the initial conditions. Here, we present a new experimental technique for studying the Rayleigh-Taylor instability under rotation that side-steps the problems encountered with standard techniques by using a strong magnetic field to destabilize an otherwise stable system. We find that rotation about an axis normal to the interface acts to retard the growth rate of the instability and stabilise long wavelength modes; the scale of the observed structures decreases with increasing rotation rate, asymptoting to a minimum wavelength controlled by viscosity. We present a critical rotation rate, dependent on Atwood number and the aspect ratio of the system, for stabilising the most unstable mode.

Incompressible Rayleigh–Taylor Turbulence

“…The e↵ect of rotation on Rayleigh-Taylor instability was first considered by Chandrasekhar (1961), who concluded that it slows down the instability, and later extended by Tao et al (2013) to the nonlinear stage. These predictions have been confirmed by numerical simulations by Carnevale et al (2002) and more recently by the experiments by Baldwin et al (2015). The e↵ect of rotation on the turbulent phase is less clear.…”

“…In the case Figure 7 Rotating RT turbulence. The two images on the left show the evolution of the RT instability of a paramagnetic liquid (pink) above a diamagnetic liquid (clear) without rotation (upper) and with ⌦ = 4.6 rad s 1 (lower) (Figure taken from Baldwin et al (2015)). The two images on the right represent the temperature field, at the same time t = 20⌧ , for two simulations of the OB equations with the Coriolis force starting from the same initial condition, with ⌦ = 0 (left) and with ⌦⌧ = 20 (right) (⌧ = (Lz/Ag) 1/2 ).…”

“…Another, and promising technique developed by Huang et al (2007) makes use of a strong magnetic field gradient to stabilize a paramagnetic (heavy) fluid over a diamagnetic (light) one. In yet another variant, the initial configuration is opposite (and stable) and the magnetic field is used to produce the instability (Baldwin et al 2015). point nonlinear e↵ects emerge and the RT flow develops into a di↵erent, nonlinear phase.…”

“…We cite surface tension and viscosity (see, e.g., Bellman & Pennington (1954); Mikaelian (1993) ;Chertkov et al (2005); Celani et al (2009) ;Bo↵etta et al (2010c)), magnetic fields (Kruskal & Schwarzschild 1954;Peterson et al 1996), spherical geometries (Plesset 1954;Sakagami & Nishihara 1990), finite-amplitude perturbations (Chang 1959), bubbles (Garabedian 1957;Hecht et al 1994;Goncharov 2002), rotation (Chandrasekhar 1961;Baldwin et al 2015), and compressibility (Newcomb 1983;Scagliarini et al 2010).…”

Effects of rotation on the bulk turbulent convection

“…In the case of RT convection, the effect of rotation has been studied more recently by means of both experiments (Baldwin et al 2015) and DNS within the Boussinesq approximation (Boffetta et al 2016). The main result is that rotation always reduces the turbulent heat transfer in this case.…”