Related papers: Models for Free Granular Surfaces
Granular flows through pipes show interesting phenomena, e.g. clogging and density waves, 1/f-noise. These things are fairly good studied by computer-experiments, but there is a lack in theoretical and analytical consideration. We introduce…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible…
A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven…
Many turbulent flows encountered in nature -- seas, oceans and rivers -- are bounded by a deformable free surface. A question that remained to be fully explored is to what extent the underlying turbulent flow field can be revealed solely by…
We present a short review of recent theoretical descriptions of flows occuring at the surface of granular piles, and focus mainly on two models: the phenomenological ``BCRE'' model and the hydrodynamic model, based on Saint-Venant…
We present simulations of granular flows in a modified Couette cell, using a continuum model recently proposed for dense granular flows. Based on a friction coefficient, which depends on an inertial number, the model captures the positions…
The dynamics of the development of instability of the free surface of liquid helium, which is charged by electrons localized above it, is studied. It is shown that, if the charge completely screens the electric field above the surface and…
We consider dry granular flow down an inclined chute with a localised contraction theoretically and numerically. The flow regimes are predicted through a novel extended one-dimensional hydraulic theory. A discrete particle method validated…
Oscillating shape motion of a freely falling water droplet has long fascinated and inspired scientists. We propose dynamic non-linear equations for closed, two dimensional surfaces in gravity and apply it to analyze shape dynamics of freely…
A continuum theory of partially fluidized granular flows is developed. The theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order parameter equation which describes the transition…
We study a 2D potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of Euler equations having a pair of square-root branch points…
Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…
We show how the motion of free material test particles in arbitrary spatial flows is easily determined within the context of ordinary vector calculus. This may be useful for everyone, including engineers and other non-specialists, when…
Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…
Gravity-driven thick granular flows are relevant to many industrial and geophysical processes. In particular, it is important to know and understand the particle velocity distributions as we get deeper into the flow from the free surface.…
We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…
We investigate the impact of a free-falling water drop onto a granular layer. First, we constructed a phase diagram of crater shapes with two control parameters, impact speed and grain size. A low-speed impact makes a deeper cylindrical…
In this paper, we determine an exact solution to the governing equations in spherical coordinates for an inviscid, incompressible fluid. This solution describes a steady, purely azimuthal equatorial flow with an associated free surface.…
We study the morphological evolution of surfaces during ion sputtering and we compare their dynamical roughening with aeolian ripple formation in sandy deserts. We show that, although the two phenomena are physically different, they must…