In the presence of a vertically varying horizontal current (background shear), the salt-fingering instability is supplanted by the salt-sheet instability. Previous direct numerical simulation (DNS) experiments on salt sheets revealed that flow becomes turbulent via secondary instabilities. We call these instabilities zig-zag and tip modes. Here, we investigate the physics of these modes using l...

Since Rayleigh’s early work on shear-flow driven instabilities in fluids, it has been known that sheared flows are usually unstable only in the presence of an inflection point in the velocity profile. However, in magnetohydrodynamics, there are important instabilities for which no inflection point is required. In tokamak experiments, strongly sheared flows are associated with transport barriers...

Despite the importance of the magnetorotational instability (MRI) as a fundamental mechanism for angular momentum transport in magnetized accretion disks, it has yet to be demonstrated in the laboratory. A liquid sodium αω dynamo experiment at the New Mexico Institute of Mining and Technology provides an ideal environment to study the MRI in a rotating metal annulus (Couette flow). A local stab...

Uniform shear flow is a prototype non-equilibrium state admitting detailed study at both the macroscopic and microscopic levels via theory and computer simulation. It is shown that the hydrodynamic equations for this state have a long wavelength instability. This result is obtained first from the NavierStokes equations and shown to apply at both low and high densities. Next, higher order rheolo...

The linear marginal instability of an axisymmetric MHD Taylor-Couette flow of infinite vertical extension is considered. For flows with a resting outer cylinder there is a well-known characteristic Reynolds number even without magnetic field but for sufficiently weak magnetic fields there are solutions with smaller Reynolds numbers so that a characteristic minimum exists. The minimum only exist...

The Rayleigh–Taylor instability (RTI) is a fundamental fluid instability that occurs when a light fluid is accelerated into a heavier one. While techniques for observing the RTI in classical fluids continue to improve, the instability has not been demonstrated in quantum fluids. Here, we exploit the formal equivalence between condensed matter and coherent nonlinear optics to observe the superfl...

Analysis of the linear theory of capillary instability of threads of Maxwell fluids of diameter D is carried out for the unapproximated normal mode solution and for a solution based on viscoelastic potential flow. The analysis here extends the analysis of viscous potential flow [Int. J. Multiphase Flow 28 (2002) 1459] to viscoelastic fluids of Maxwell type. The analysis is framed in dimensionle...

We study the effect of velocity shear on the spectrum of MHD surface waves. A nonuniform intermediate region is taken into account, so that the surface wave can be subject to resonant absorption. In order to deal in a mathematically and also physically consistent manner with the resonant wave excitation, we analytically derive the dissipative solution around the resonant surface in resistive MH...

The intent of this short note is to provide an independent proof of the unpublished discovery of Klaus Kröncke [Kro13] that complex projective space with its canonical Fubini–Study metric is dynamically unstable under Ricci flow in all complex dimensions N ≥ 2. The unstable perturbation is not Kähler. This provides a counterexample to a well known conjecture widely attributed to Hamilton. Moreo...

We present stability analyses for the boundary-layer flow over broad cones (half-angle ψ > 40◦) rotating in imposed axial flows. Preliminary convective instability analyses are presented that are based on the Orr–Sommerfeld equation for a variety of axial-flow speeds. The results are discussed in terms of the limited existing experimental data and previous stability analyses on related bodies. ...