Geophysical granular and particle-laden flows: review of the field

2005 ◽  
Vol 363 (1832) ◽  
pp. 1497-1505 ◽  
Author(s):  
Kolumban Hutter
Keyword(s):  
Turbulent Flows ◽  
Granular Flows ◽  
Gravity Currents ◽  
Two Dimensional ◽  
Theme Issue ◽  
Aeolian Transport ◽  
Particle Laden Flows ◽  
Granular Base ◽  
Sand Dust ◽  
Dimensional Surface

An introduction is given to the title theme, in general, and the specific topics treated in detail in the articles of this theme issue of the Philosophical Transactions . They fit into the following broader subjects: (i) dense, dry and wet granular flows as avalanche and debris flow events, (ii) air-borne particle-laden turbulent flows in air over a granular base as exemplified in gravity currents, aeolian transport of sand, dust and snow and (iii) transport of a granular mass on a two-dimensional surface in ripple formations of estuaries and rivers and the motion of sea ice.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170220 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Water Waves ◽  
Two Dimensional ◽  
Physical Plane ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Dimensional Gravity ◽  
Irrotational Motion ◽  
Exact Relations

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

scholarly journals GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO

2011 ◽  
Vol 21 (03) ◽  
pp. 421-457 ◽  
Author(s):  
RAPHAËL DANCHIN ◽  
MARIUS PAICU
Keyword(s):  
Global Existence ◽  
Turbulent Flows ◽  
Vertical Direction ◽  
Boussinesq System ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Incompressible Euler Equation ◽  
Navier Stokes Equation ◽  
Transport Diffusion ◽  
Anisotropic Viscosity

Models with a vanishing anisotropic viscosity in the vertical direction are of relevance for the study of turbulent flows in geophysics. This motivates us to study the two-dimensional Boussinesq system with horizontal viscosity in only one equation. In this paper, we focus on the global existence issue for possibly large initial data. We first examine the case where the Navier–Stokes equation with no vertical viscosity is coupled with a transport equation. Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transport–diffusion equation with diffusion in the horizontal direction only. For both systems, we construct global weak solutions à la Leray and strong unique solutions for more regular data. Our results rest on the fact that the diffusion acts perpendicularly to the buoyancy force.

Asymptotic analysis of some two-dimensional diffusion problems

1995 ◽  
Vol 448 (1933) ◽  
pp. 213-236 ◽  
Keyword(s):  
Linear Problem ◽  
Vacancy Concentration ◽  
Surface Concentration ◽  
Two Dimensional ◽  
Surface Source ◽  
Dimensional Diffusion ◽  
Equilibrium Vacancy ◽  
Equilibrium Vacancy Concentration ◽  
Dimensional Surface ◽  
Diffusion Problems

In this paper we discuss two-dimensional surface source and implant problems for a substitutional-interstitial diffusion model. We present asymptotic solutions in the limit of the surface concentration of impurity (or peak concentration of the implant) being far greater than the equilibrium vacancy concentration. Using leading order composite solutions we plot contours of constant impurity concentration. Some of these contours differ markedly from those of the corresponding linear problem, having the ‘bird’s beak’ shape which is frequently observed in experiments. We also discuss a two-dimensional surface source problem for a va­cancy model.

Anisotropic Coarsening of Two-Dimensional Surface Domains in Copolymer Thin Films

1999 ◽  
Vol 32 (26) ◽  
pp. 9007-9012 ◽  
Author(s):  
Jakob Heier ◽  
Easan Sivaniah ◽  
Edward J. Kramer
Keyword(s):  
Thin Films ◽  
Two Dimensional ◽  
Surface Domains ◽  
Dimensional Surface
Sign in / Sign up

Export Citation Format

Share Document