Nonlinear stability in three-layer channel flows

Nonlinear Stability of Two – Layer Flows ∗

We study the dynamics of two–layer, stratified shallow water flows. This is a model in which two scenarios for eventual mixing of stratified flows (shear-instability and internal breaking waves) are, in principle, possible. We find that unforced flows cannot reach the threshold of shearinstability, at least without breaking first. This is a fully nonlinear stability result for a model of strati...

Studies on stability in three-layer Hele-Shaw flows

We consider a setup in a Hele-Shaw cell where a fluid of constant viscosity l occupying a near-half-plane pushes a fluid of constant viscosity l occupying a layer of length L which in turn pushes another fluid of constant viscosity r occupying the right half-plane. The fluid upstream has a velocity U. Careful analysis of the dispersion relation arising from linear stability of the three-layer H...

Linear instability, nonlinear instability, and ligament dynamics in three-dimensional laminar two-layer liquid/liquid flows

We consider the linear and nonlinear stability of two-phase density-matched but viscosity-contrasted fluids subject to laminar Poiseuille flow in a channel, paying particular attention to the formation of three-dimensional waves. A combination of Orr–Sommerfeld–Squire analysis with direct numerical simulation of the three-dimensional two-phase Navier–Stokes equations is used. For the parameter ...

Boundary Layer Associated with a Class of 3d Nonlinear Plane Parallel Channel Flows

Single phase three-layer channel routing algorithms

We present a simple three-layer assignment algorithm for planar layouts generated by a class of layout algorithms. This class of algorithms includes simple variations of the following algorithms developed by Mehlhorn et al. (1986): (i) The algorithm that generates planar layouts for the two-terminal net CRP with dmax tracks. (ii) The algorithm that generates planar layouts for the twoand three-...