Showing papers by "Yuriko Renardy published in 1988"

Stability of the interface in two-layer couette flow of upper convected maxwell liquids

Abstract: The linear stability of a two-layer Couette flow of upper convected Maxwell liquids is considered. The fluids have different densities, viscosities, and elasticities, with surface tension at the interface. At low speeds, the interfacial mode may become unstable, while other modes stay stable. The shortwave asymptotics of the interfacial mode is analyzed. It is found that an elasticity difference can stabilize or destabilize the flow even in the absence of a viscosity difference. As the viscosity difference increases, the range of elasticities for which there is shortwave stability widens. A linearly stable arrangement can be achieved by placing the less viscous fluid in a thin layer to stabilize longwaves and using elasticities to stabilize shortwaves. Such an arrangement can be stable even when the density stratification is adverse.

Effectiveness and robustness with respect to time delays of boundary feedback stabilization in one-dimensional viscoelasticity

Abstract: The damping effect of a boundary feedback mechanism on torsional vibrations of a homogeneous viscoelastic rod is examined. A characteristic equation is derived for the oscillatory modes, and the solutions of this equation are studied by analytic and numerical methods, as functions of the feedback gain parameter and of a parameter for feedback delay. Results are compared to recent studies of elastic materials, where a feedback delay can cause exponential instability; here this phenomenon depends significantly on the short-time behavior of the viscoelastic memory kernel. Finally, an existence result is given, showing that the behavior of a weak solution corresponds in the expected way to the location of the characteristic roots.