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We study the volume preserving mean curvature flow of a surface immersed in an asymptotically flat $3$-manifold modeling an isolated gravitating system in General Relativity. We show that, if the ambient manifold has positive ADM mass and…
In this paper, we consider an incompressible viscous flow without surface tension in a finite-depth domain of three dimensions, with free top boundary and fixed bottom boundary. This system is governed by a Naiver-Stokes equation in above…
The rheology of surface granular flows is investigated by means of measurements of velocity and number density profiles in a quasi-two-dimensional rotating cylinder, half-filled with mono-disperse steel balls. The measurements are made at…
The standard analytical approach for studying gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its…
We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…
Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al. 2021). We consider the linear stability of the steady two-dimensional flow…
Random organizing hyperuniform fluid induced by reciprocal activation is a non-equilibrium fluid with vanishing density fluctuations at large length scales like crystals. Here we extend this new state of matter to a closed manifold, namely…
Osmotically driven flow across a semi-permeable membrane under a constant static pressure difference is revisited with referring to the previous reports for reverse osmosis. A few mathematical techniques for obtaining the approximate…
We report on progress on the free surface flow in the presence of submerged oscillating line sources (2D) or point sources (3D) when a simple shear flow is present varying linearly with depth. Such sources are in routine use as Green…
We investigate the processes that lead to the generation of mean flows in two-dimensional anelastic convection. The simple model consists of a plane layer that is rotating about an axis inclined to gravity. The results are two-fold: firstly…
In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the…
A plane non-parallel vortex flow in a square fluid domain is examined. The energy dissipation of the flow is dominated by viscosity and linear friction effect of a Hartmann layer. This is a traditional Navier-Stokes flow when the linear…
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 consider the sloshing problem for an incompressible, inviscid, irrotational fluid in an open container, including effects due to surface tension on the free surface. We restrict ourselves to a constant contact angle and seek…
We report and analyze the results of numerical studies of dense granular flows in two and three dimensions, using both linear damped springs and Hertzian force laws between particles. Chute flow generically produces a constant density…
A certain class of surface motions, including those of a relativistic membrane minimizing the 3-dimensional volume swept out in Minkowski-space, is shown to be equivalent to 3-dimensional steady-state irrotational inviscid isentropic…
We study the statistics of free-surface turbulence at large Reynolds numbers produced by direct numerical simulations in a fluid layer at different thickness with fixed characteristic forcing scale. We observe the production of a transient…
In continuum thermodynamics, models of two-phase mixtures typically obey the condition of pressure equilibrium across interfaces between the phases. We propose a new non-equilibrium model beyond that condition, allowing for microinertia of…
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present in this paper several new forms of open boundary conditions for…
Regularizing effects of surface tension are studied for interfacial waves between a two-dimensional, infinitely-deep and irrotational flow of water and vacuum. The water wave problem under the influence of surface tension is formulated as a…