Related papers: Linear Theory of Visco-Resistive Tearing Instabili…
The linear perturbation equation of the tearing instability derived in LSC theory (Loureiro, Schekochihin, and Cowley, PoP2007) is numerically examined as an initial value problem, where the inner and outer regions are seamlessly solved…
The plasmoid instability in visco-resistive current sheets is analyzed in both the linear and nonlinear regimes. The linear growth rate and the wavenumber are found to scale as $S^{1/4} {\left( {1 + {P_m}} \right)}^{-5/8}$ and $S^{3/8}…
We study the linear and nonlinear evolution of the tearing instability on thin current sheets by means of two-dimensional numerical simulations, within the framework of compressible, resistive magnetohydrodynamics. In particular we analyze…
Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…
Magnetohydrodynamic simulations have shown that a non-unique critical Lundquist number $S_c$ exists, hovering around $S_c \sim 10^4$, above which threshold Sweet-Parker type stationary reconnecting configurations become unstable to a fast…
Sweet-Parker current sheets in high Lundquist number plasmas are unstable to tearing, suggesting they will not form in physical systems. Understanding magnetic reconnection thus requires study of the stability of a current sheet as it…
The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for a Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can…
Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the {\it uniform shear} flow with constant viscosity, and (b) the {\it non-uniform shear} flow…
We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear…
The scaling of plasmoid instability maximum linear growth rate with respect to Lundquist number $S$ in a Sweet-Parker current sheet, $\gamma_{max}\sim S^{1/4}$, indicates that at high $S$, the current sheet will break apart before it…
Recently, the existence and properties of unbounded cavity modes, resulting in extensive plastic deformation failure of two-dimensional sheets of amorphous media, were discussed in the context of the athermal Shear-Transformation-Zones…
In this paper we study the nonlinear stability of a shear layer profile for Navier Stokes equations near a boundary. This question plays a major role in the study of the inviscid limit of Navier Stokes equations in a bounded domain as the…
Classical MHD reconnection theories, both the stationary Sweet-Parker model and the tearing instability, are known to provide rates which are too slow to explain the observations. However, a recent analysis has shown that there exists a…
It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate, or the flow in a Taylor-Couette geometry, can become unstable to a…
In this paper, we studied the long-wave instability of the shear flows. When the wavenumber of perturbation is larger than the critical value, the flow is always neutrally stable. First, we obtain a new upper bound for the neutral…
In this study, the evolution of a highly unstable m = 1 resistive tearing mode, leading to plasmoid formation in a Harris sheet is studied in the framework of full MHD model using the NIMROD simulation. Following the initial nonlinear…
We establish criteria of stability and instability for the stratified compressible magnetic Rayleigh--Taylor (RT) problem. More precisely, if under the stability condition $\Xi <1$, we show the existence of unique solution with algebraic…
The linearized Navier-Stokes equations for a system of superposed immiscible compressible ideal fluids are analyzed. The results of the analysis reconcile the stabilizing and destabilizing effects of compressibility reported in the…
Submesoscale currents in the ocean's mixed layer (ML), consisting of fronts, eddies, and filaments, are characterized by order one Rossby (Ro) and Richardson (Ri) numbers. These currents play a crucial role in mediating vertical exchange…
Elastic turbulence has been found in computations of planar viscoelastic Taylor-Couette flow using the Oldroyd-B model, apparently generated by a linear instability (van Buel et al. Europhys. Lett., 124, 14001, 2018). We demonstrate that no…