Effect of magnetic field on temporal development of Rayleigh–Taylor instability induced interfacial nonlinear structure

Abstract

The effect of magnetic field on the nonlinear growth rate of Rayleigh -Taylor instability induced two fluid interfacial structures has been investigated. The magnetic field is assumed to be parallel to the plane of the two fluid interface and acts in a direction perpendicular to the wave vector. If magnetic field is restricted only to either side of the interface the growth rate may be depressed (may almost disappear) or be enhanced depending on whether the magnetic pressure on the interface opposes the instability driving pressure difference g(ρ h − ρ l )y or acts in the same direction. If magnetic field is present on both sides of the two fluid interface, stabilization * e-mail: mrgupta − cps@yahoo.co.in † e-mail: laba.kanta@yahoo.com ‡ e-mail: phy.sou82@gmail.com § e-mail: mkhan − ju@yahoo.com 1 may also take place in the sense that the surface of separation undulates periodically when the force due to magnetic pressure on two sides are such as to act in opposite direction. This result differs from the classical linear theory result which predicts that the magnetic field parallel to the surface has no influence on the growth rate when the wave vector is perpendicular to its direction.2

Combined Effect of Magnetic Field and Compressibility on Rayleigh Taylor Instability

“…According to the linear analysis,when the externally applied magnetic field is parallel to the interface of separation of the two fluid system (heavier fluid lies over the lighter fluid under the action of gravity), the RTI remain unaffected [22]. However, nonlinear analysis shows a decreasing nature of RTI growth rate for the above configuration [27]. It was shown that, compressibility also decreases the growth rate of RTI [26] [32].…”

“…In all the above studies, the RTI was studied in linear approximation. However, in nonlinear theory, it has been studied separately, the evolution of the interfacial fluid structure due to RTI in compressible fluids [26] and that due to presence of magnetic field [27]. The present paper is addressed to the problem of the evolution of the nonlinear interfacial structure caused by RTI in presence of a magnetic field parallel to the surface of separation of the two compressible fluids.…”

“…In presence of only magnetic field [27], there exists a magnetic pressure in addition to the usual hydrodynamic pressure. As a result, the RTI driving pressure difference ( )…”

“…[the suffix h(l) corresponds to the dynamical variable associated with the heavier (lighter) fluid]. In our earlier study [27] it has been shown that, the growth rate of RTI may be enhanced or depressed according to whether the extra contribution is positive or negative. Moreover, stabilization may occur in the sense that the surface of separation executes periodic undulation resulting from time lag in the temporal variation of h B and l B .…”

Combined effect of viscosity and vorticity on single mode Rayleigh–Taylor instability bubble growth

“…with η 0 (t) > 0 and η 2 (t) < 0 (terms O(x 2+i )(i ≥ 1) are neglected as we are interested only in the motion very close to the tip of the bubble |x| ≪ 1) [6] .…”