Related papers: Steady bubbles and drops in inviscid fluids
This study presents a first-principles model to predict the two-phase pressure drop in gas-liquid intermittent flow through round capillaries, which serve as the simplest analogous of a porous medium. Building upon the classical capillary…
In this study, we examine the linear stability of an axisymmetric Taylor bubble moving steadily in a flowing liquid enclosed in a circular tube. Linearisation is performed about axisymmetric base states obtained in Part I of this study by…
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the…
The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
We study a model for the evolution of an axially symmetric bubble of inviscid fluid in a homogeneous porous medium otherwise saturated with a viscous fluid. The model is a moving boundary problem that is a higher-dimensional analogue of…
In this paper, we study two-dimensional steady incompressible Euler flows in which the vorticity is sharply concentrated in a finite number of regions of small diameter in a bounded domain. Mathematical analysis of such flows is an…
We study stationary hollow vortices with surface tension in two dimensions. Such objects solve an overdetermined elliptic free boundary problem in an exterior domain, with an additional boundary condition involving mean curvature and the…
We prove non-existence of nontrivial uniformly subsonic inviscid irrotational flows around several classes of solid bodies with two protruding corners, in particular vertical and angled flat plates; horizontal plates are the only case where…
We derive the vorticity equation for an incompressible fluid on a 2-dimensional surface with arbitrary topology embedded in 3-dimensional Euclidean space by using a tailored Clebsch parametrization of the flow. In the inviscid limit, we…
We consider the relativistic Euler equations governing spherically symmetric, perfect fluid flows on the outer domain of communication of Schwarzschild spacetime, and we introduce a version of the finite volume method which is formulated…
The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler-Coriolis fluids respectively…
In this paper, we present a theoretical, experimental, and numerical study of the dynamics of cavitation bubbles inside a droplet suspended in another host fluid. On the theoretical side, we provided a modified Rayleigh collapse time and…
This paper studies the dynamics of an incompressible fluid driven by gravity and capillarity forces in a porous medium. The main interest is the stabilization of the fluid in Rayleigh-Taylor unstable situations where the fluid lays on top…
We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of…
We are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of…
A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and…
In this paper, we study nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler flows. We construct a family of steady vortex rings (with and without swirl) which constitutes a desingularization of the…
We hypothesize that dynamical systems concepts used to study the transition to turbulence in shear flows are applicable to other transition phenomena in fluid mechanics. In this paper, we consider a finite air bubble that propagates within…
In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…