Related papers: Pressure transfer functions for interfacial fluid …
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
Shear flow of dense, non-Brownian suspensions is simulated using the discrete element method, taking particle contact and hydrodynamic lubrication into account. The resulting flow regimes are mapped in the parametric space of solid volume…
Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for…
We study the dynamics of the interface given by two incompressible viscous fluids in the Stokes regime filling a 2D horizontally periodic strip. The fluids are subject to the gravity force and the density difference induces the dynamics of…
A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and/or the presence of a plane wall. The Lorentz reciprocal theorem is used to…
Two-dimensional turbulence governed by the so-called $\alpha$ turbulence equations, which include the surface quasi-geostrophic equation ($\alpha=1$), the Navier--Stokes system ($\alpha=2$), and the governing equation for a shallow flow on…
The two-phase horizontally periodic quasistationary Stokes flow in $\mathbb{R}^2$, describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, which is parameterized as the graph of a…
In this paper we study the homogenization of the Dirichlet problem for the Stokes equations in a perforated domain with multiple microstructures. First, under the assumption that the interface between subdomains is a union of Lipschitz…
This paper is on the effect of nonlinearity in the equations for propagation of disturbances on transition in the class of Spiral Poiseuille Flows. The problem is approached from the fundamental point of view of following the growth of…
In this paper, we study two-dimensional steady solitary gravity waves propagating along the surface of a fluid of finite depth. In particular, we can deal with general vorticity distributions and overhanging wave profiles. By conformal…
We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalise the…
Frequently encountered in nature, internal solitary waves in stratified fluids are well-observed and well-studied from the experimental, the theoretical, and the numerical perspective. From the mathematical point of view, these waves are…
A homogenised model is developed to describe the interaction between aligned strings and an incompressible, viscous, Newtonian fluid. In the case of many strings, the ratio of string separation to domain width gives a small parameter which…
The leading-order far-field scattered flow produced by a particle in a parallel-wall channel under creeping flow conditions has a form of the parabolic velocity field driven by a 2D dipolar pressure distribution. We show that in a system of…
In this article we apply local bifurcation theory to prove the existence of small-amplitude steady periodic water waves, which propagate over a flat bed with a specified fixed mean-depth, and where the underlying flow has a discontinuous…
Numerical simulations of a thin layer of turbulent flow in stably stratified conditions within the Boussinesq approximation have been performed. The statistics of energy transfer among scales have been investigated for different values of…
We investigate the interaction of waves with surface flows by considering the full set of conserved quantities, subtle but important surface elevation changes induced by wave packets and by directly considering the necessary forces to…
For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families…
The subject of this work is the instability mechanism of simple shear flows, like Hagen-Poiseuille pipe flow, which is a long-standing problem in fluid mechanics [1,2]. A possible analogy with phenomenological theory of ideal plasticity in…
The article provides an analytical solution of the Navier-Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of…