Filipe S. Cal

TL;DR: In this paper, a linear system of equations governing the interaction of water waves with partially or totally submerged freely floating structures in a two-layer fluid is derived and conditions for the stability of equilibrium are established.

TL;DR: In this paper, a dimensionally reduced Reynolds type equation for thin film flow lubrication of a class of viscoelastic fluids was derived by employing a perturbation analysis on the upper-convected Maxwell model in natural orthogonal coordinates.

Abstract: We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing.

TL;DR: Under symmetry assumptions on the geometry of the fluid domain, conditions guaranteeing the existence of trapped modes in a two-layer fluid channel are presented and numerous examples of floating bodies supporting trapped modes are given.

TL;DR: In this article, the authors studied the existence of solutions for the problem of interaction of linear water waves with an array of three-dimensional fixed structures in a density-stratified multi-layer fluid, where in each layer the density is assumed to be constant.