Related papers: Scale-critical curve diffusion flows
We identify incompressible planar linear flows that are generalizations of the well known one-parameter family characterized by the ratio of in-plane extension to (out-of-plane) vorticity. The latter `canonical' family is classified into…
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…
We study flows generated within a two-dimensional corner by the chemical activity of the confining boundaries. Catalytic reactions at the surfaces induce diffusioosmotic motion of the viscous fluid throughout the domain. The presence of…
We study flow driven through a finite-length planar rigid channel by a fixed upstream flux, where a segment of one wall is replaced by a pre-stressed elastic beam subject to uniform external pressure. The steady and unsteady systems are…
The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity…
This paper examines the linearized stability of plane Couette flow for stress-power law fluids, which exhibit non-monotonic stress-strain rate behavior. The constitutive model is derived from a thermodynamic framework using a non-convex…
We investigate existence, stability, and instability of anchored rotating spiral waves in a model for geometric curve evolution. We find existence in a parameter regime limiting on a purely eikonal curve evolution. We study stability and…
In order to investigate the emergence of periodic oscillations of rimming flows, we study analytically the stability of steady states for the model of (Benilov, Kopteva, O'Brien, 2005), which describes the dynamics of a thin fluid film…
Separated flows past complex geometries are modelled by discrete vortex techniques. The flows are assumed to be rotational and inviscid, and a new technique is described to determine the streamfunctions for linear shear profiles. The…
The main part of this contribution to the special issue of EJM-B/Fluids dedicated to Patrick Huerre outlines the problem of the subcritical transition to turbulence in wall-bounded flows in its historical perspective with emphasis on plane…
The emergence of large-scale spatial modulations of turbulent channel flow, as the Reynolds number is decreased, is addressed numerically using the framework of linear stability analysis. Such modulations are known as the precursors of…
The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe…
Incompressible flows of an ideal two-dimensional fluid on a closed orientable surface of positive genus are considered. Linear stability of harmonic, i.e. irrotational and incompressible, solutions to the Euler equations is shown using the…
Flow-stabilized solids are a class of fragile matter that forms when a dense suspension of colloids accumulates against a semi-permeable barrier, for flow rates above a critical value. In order to probe the effect of particle size on the…
This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…
Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a sub-critical…
We study stable surfaces, i.e., second order minima of the area for variations of fixed volume, in sub-Riemannian space forms of dimension $3$. We prove a stability inequality and provide sufficient conditions ensuring instability of…
We study the meandering instability during growth of an isolated nanostructure, a crystalline cone, consisting of concentric circular steps. The onset of the instability is studied analytically within the framework of the standard…
The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies…
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric…