Related papers: Linear and nonlinear instability in vertical count…
We consider the conceptual two-layered oscillating tank of Inoue & Smyth (2009), which mimics the time-periodic parallel shear flow generated by low-frequency (e.g. semi-diurnal tides) and small-angle oscillations of the density interface.…
Shear-thinning fluids flowing through pipes are crucial in many practical applications, yet many unresolved problems remain regarding their turbulent transition. Using highly robust numerical tools for the Carreau-Yasuda model, we…
An asymptotic interface equation for directional solidification near the absolute stabiliy limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts…
The effect of magnetic shear and shear flow on local gravitationally induced instabilities is investigated. A simple model is constructed allowing for an arbitrary entropy gradient and a shear plasma flow in the Boussinesq approximation. A…
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results…
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…
The current work analyses the onset characteristics of buoyancy and thermocapillary-driven instabilities in two-layer binary fluid systems near their upper critical solution temperature (UCST). The dynamics of the binary fluids are modelled…
Particles in pressure-driven channel flow are often inhomogeneously distributed. Two modes of low-Reynolds number instability, absent in Poiseuille flow of clean fluid, are created by inhomogeneous particle loading, and their mechanism is…
A modal stability analysis shows that pressure-driven pipe flow of an Oldroyd-B fluid is linearly unstable to axisymmetric perturbations, in stark contrast to its Newtonian counterpart which is linearly stable at all Reynolds numbers. The…
We study an instability of thin liquid-vapor layers bounded by rigid parallel walls from both below and above. In this system, the interfacial instability is induced by lateral vapor pressure fluctuation, which is in turn attributed to the…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…
This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…
We consider here the effects of inertia on the instability of a flat liquid film under the effects of capillary and intermolecular forces (van der Waals interaction). Firstly, we perform the linear stability analysis within the long wave…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…
Flow of a thin viscous film down a flat inclined plane becomes unstable to long wave interfacial fluctuations when the Reynolds number based on the mean film thickness becomes larger than a critical value (this value decreases as the angle…
We study the instability of a thin membrane (of zero bending rigidity) to out-of-plane deflections, when the membrane is immersed in an inviscid fluid flow and sheds a trailing vortex-sheet wake. We solve the nonlinear eigenvalue problem…
We present a comprehensive framework for gravity-driven, surfactant-laden thin films flowing over slippery substrates, elucidating how wall slip modifies the coupled hydrodynamics and interfacial transport. A long-wave model is formulated…
Three-dimensional direct numerical simulations of an incompressible open square cavity flow are conducted. Features of the permanent (non-linear) regime together with the linear stability analysis of a two-dimensional steady base flow are…