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The intent of this short note is to provide an independent proof of the unpublished discovery of Klaus Kröncke [Kro13] that complex projective space with its canonical Fubini–Study metric is dynamically unstable under Ricci flow in all complex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. ...

I Research on fundamentals for multiphase pipelining ................................................... 1 II Accomplishments of our previous DOE/DE-FG02-87ER 13798, 9/1/98--8/31/01...... 2 III Lubricated transport of viscous oils. Friction factor efficiency ratio......................... 5 IV Numerical simulation of laminar wavy core flow...........................................................

Plane Couette flow of viscoelastic fluids is shown to exhibit a purely elastic subcritical instability at a very small-Reynolds number in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette flow of the Upper-Convected Maxwell fluid is presented. Above a critical Weissenberg number, a small finite-size perturbation i...

The onset of instability induced by impulsively started rotating cylinder was first investigated experimentally by Chen and Christensen [1]. The initial laminar flow evolves into a secondary flow pattern which consists of a series of Taylor-like vortices. In this transient boundary-layer system the critical time tc to mark the onset of secondary motion becomes an important question. This proble...