Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids

Abstract

A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number A_{T}=1, the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998)10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.

Magneto-Rayleigh–Taylor instability in an elastic finite-width medium overlying an ideal fluid

“…These limit show that (4.23) describes several different behaviours depending on the values of β 0 and A T which are discussed below: (i) For A T = 1 and β 0 = 0 we retrieve, as expected, the pure elastic case with a cut-off given by (4.31) (Bakhrakh et al1997, Plohr & Sharp 1998, Piriz, Piriz & Tahir 2017a, 2017b [see figure 6(a), and (4.31)]…”

“…Figures 5(c) and 5(d) show the same cases as before but for the marginal stability wavenumber κ c as a function of dimensionless thickness α. The behaviour is qualitatively the same for any Atwood number except for the fact that, for the purely elastic case (β 3 = 0), there is no instability threshold when A T = 1 (Plohr & Sharp 1998, Piriz, Piriz & Tahir 2017a, 2017b.…”

“…This is also the scenario in some recent laboratory experiments (Adkins et al 2017) involving viscous fluids, a situation that has also been studied theoretically by and previously, for some particular limits, by Lister & Kerr (1989), and Wilcock & Whitehead (1991). For the case of finite-width elastic-media with no presence of rigid boundaries RT instability has been studied by Bakhrakh et al (1997), Plohr & Sharp (1998), and by Piriz, Piriz & Tahir (2017a, 2017b. When magnetic fields are present the instability is known as the magneto-Rayleigh-Taylor (MRT) instability.…”

“…This competition phenomenon is connected with the fact that the magnetic field stabilising effect is determined by the local strain kξ a at y = 0, while the stabilising effect of the elasticity depends on the total strain which, for relatively thin slabs, is of the order of (ξ a − ξ b )/h (Piriz, Piriz & Tahir 2017a, 2017b. For the very thick slabs the total strain coincides with the local one, and the stabilising effects of the magnetic field add to the ones of the elasticity.…”

Finite-thickness effect of the fluids on bubbles and spikes in Richtmyer–Meshkov instability for arbitrary Atwood numbers

“…RMI is very important to the fields, such as inertial confinement fusion and astrophysical problems [5,6]. In a wide range of engineering, geophysical, and astrophysical flows, the RMI is one of the triggering events that, in many cases, can lead to large-scale turbulent mixing, see in the recent two-part comprehensive reviews [7,8] where the concerns over the past 140 years on Rayleigh-Taylor [9][10][11][12][13][14][15][16][17][18] and RM instabilities have been introduced in details. The Rayleigh-Taylor instability (RTI) occurs when a light fluid supports or accelerates a heavy one.…”