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We study large traveling surface waves within a two-dimensional finite depth, free boundary, homogeneous, incompressible and viscous fluid governed by Darcy's law. The fluid is bound by a gravitational force to a flat rigid bottom and meets…

We investigate steady symmetric gravity water waves on finite depth. For non-positive vorticity it is shown that the particles display a mean forward drift, and for a class of waves we prove that the size of this drift is strictly…

Consider the dynamics of a layer of viscous incompressible fluid under the influence of gravity. The upper boundary is a free boundary with the effect of surface tension taken into account, and the lower boundary is a fixed boundary on…

Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates…

In this paper, we consider a layer of viscous incompressible isotropic micropolar fluid in a uniform gravitational field of finite depth, lying above a flat rigid bottom and below the atmosphere in a three-dimensional horizontally periodic…

We consider the governing equations for the motion of compressible fluid on an evolving surface from both energetic and thermodynamic points of view. We employ our energetic variational approaches to derive the momentum equation of our…

Use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil strict conservative form. If one is willing to work in…

In this article we consider the multi-layer shallow water system for the propagation of gravity waves in density-stratified flows, with additional terms introduced by the oceanographers Gent and McWilliams in order to take into account…

A two-dimensional steady problem of a potential free-surface flow of an ideal incompressible fluid caused by a singular sink is considered. The sink is placed at the horizontal bottom of the fluid layer. With the help of the Levi-Civita…

Concept of curvature of liquid surrounding a spherical surface seems obvious in daily life, but based on earthly conditions everywhere. However, our understanding about the concept seems more transparent when we keep the system out of the…

The instability of non-homoentropic axisymmetric flow of perfect fluid with respect to non-axisymmetric infinitesimal perturbations was investigated by numerical integration of hydrodynamical differential equations in two-dimensional…

We provide a rigorous mathematical study of an asymptotic model describing Darcy flow with free boundary in a low amplitude/large wavelength approximation. In particular, we prove several well-posedness results in critical spaces.…

The unsteady electrorotation of a drop of a viscous weakly conducting polarizable liquid suspended in another viscous weakly conducting polarizable liquid immiscible with the former in an applied constant uniform electric field is…

We consider the motion of the interface separating a vacuum from an inviscid, incompressible, and irrotational fluid, subject to the self-gravitational force and neglecting surface tension, in two space dimensions. The fluid motion is…

We present the results of a combined theoretical and experimental investigation into the vertical dynamics of floating discs subjected to an imposed time-periodic forcing. The axisymmetric and inviscid wavefield is governed by a linear…

The macroscale structure and microscale fluctuation statistics of late-time asymptotic steady state flows in cylindrical geometries is studied using the methods of equilibrium statistical mechanics. The axisymmetric assumption permits an…

Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. The coupling of electric…

In this paper, we study the two phase flow problem with surface tension in the ideal incompressible magnetohydrodynamics. We first prove the local well-posedness of the two phase flow problem with surface tension, then demonstrate that as…

In order to describe behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the…

In geophysical environments, wave motions that are shaped by the action of gravity and global rotation bear the name of gravito-inertial waves. We present a geometrical description of gravito-inertial surface waves, which are low-frequency…