Related papers: Stokes flows in a two-dimensional bifurcation
Singular solutions of the Stokes equations play important roles in a variety of fluid dynamics problems. They allow the calculation of exact flows, are the basis of the boundary integral methods used in numerical computations, and can be…
We present a combined experimental and theoretical study of the primary and secondary instabilities in a Kolmogorov-like flow. The experiment uses electromagnetic forcing with an approximately sinusoidal spatial profile to drive a…
The understanding and prediction of sudden changes in flow patterns is of paramount importance in the analysis of geophysical flows as these rare events relate to critical phenomena such as atmospheric blocking, the weakening of the Gulf…
We consider Stokes water waves on the vorticity flow in a two-dimensional channel of finite depth. In the paper "V.Kozlov, On first subharmonic bifurcations in a branch of Stokes waves, JDE, 2024," it was proved existence of subharmonic…
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…
We investigate the behaviour of flux-driven flow through a single-phase fluid domain coupled to a biphasic poroelastic domain. The fluid domain consists of an incompressible Newtonian viscous fluid while the poroelastic domain consists of a…
Particulate Stokesian flows describe the hydrodynamics of rigid or deformable particles in Stokes flows. Due to highly nonlinear fluid-structure interaction dynamics, moving interfaces, and multiple scales, numerical simulations of such…
In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in [50] is a…
In this article, two novel numerical methods have been developed for simulating fluid/porous particle interactions in three-dimensional (3D) Stokes flow. The Brinkman-Debye-Bueche model is adopted for the fluid flow inside the porous…
Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of…
We study magnetic geodesic flows invariant under rotations on the 2-sphere. The dynamical system is given by a generic pair of functions $(f,\Lambda)$ in one variable. Topology of the Liouville fibration of the given integrable system near…
Solutions to the Stokes equations written in terms of a small number of hydrodynamic image singularities have been a useful tool in theoretical and numerical computations for nearly fifty years. In this article, we extend the catalogue of…
It is vital important in material sciences and fluid mechanics to study the field enhancements in the narrow region between two inclusions. Complex fluids including particle suspensions usually result in complicated flow behavior. In this…
Flow interaction between a plain-fluid region in contact with a porous layer attracted significant attention from modelling and analysis sides due to numerous applications in biology, environment and industry. In the most widely used…
We consider the interaction between an incompressible, viscous fluid modeled by the dynamic Stokes equation and a multilayered poroelastic structure which consists of a thin, linear, poroelastic plate layer (in direct contact with the free…
Particles whose shapes couple translation to rotation display a rich array of behaviors as they sediment at low Reynolds number. We introduce a unifying perspective in which the possible dynamical regimes and bifurcations between them can…
Electron transport in two-dimensional conducting materials such as graphene, with dominant electron-electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the…
We study the modulational stability problem for the traveling periodic waves (called Stokes waves) in an infinitely deep fluid by using pseudo-differential operators in conformal variables. We derive the criteria and the normal forms for…
In this paper, we construct a simple and robust two-point finite volume discretization applicable to isotropic linearized elasticity, valid in also in the incompressible Stokes' limit. The discretization is based only on co-located,…
Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic…