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Notation

 

 
 tex2html_wrap_inline12303  		 damping parameter

tex2html_wrap_inline12303 half of the ratio density difference/ mean density

tex2html_wrap_inline13275 constants in a linear sum of the collision invariants

tex2html_wrap_inline14649 fluid mobility

tex2html_wrap_inline12083 density difference between two fluids, also known as the order parameter

tex2html_wrap_inline14617 distribution function for tex2html_wrap_inline12083

tex2html_wrap_inline14639 equilibrium distribution function for tex2html_wrap_inline12083

tex2html_wrap_inline17803 ath order approximation to tex2html_wrap_inline14617

tex2html_wrap_inline17809 collision function for link i

tex2html_wrap_inline14651 chemical potential

tex2html_wrap_inline14557 change in momentum

tex2html_wrap_inline12127 density relative to a constant density

tex2html_wrap_inline12127 density difference between simulations performed using different models

tex2html_wrap_inline13299 Knudsen number

tex2html_wrap_inline13299 small number

tex2html_wrap_inline14593 function of the deviation of the density from its equilibrium value

tex2html_wrap_inline14593 small displacement

tex2html_wrap_inline15677 displacement at interface

tex2html_wrap_inline12063 scattering angle

tex2html_wrap_inline12063 angle between velocity and x-axis

tex2html_wrap_inline12063 angle between x-axis and x'-axis

tex2html_wrap_inline14279 angle of the colour gradient

tex2html_wrap_inline14303 angle between tex2html_wrap_inline13399 and x-axis

tex2html_wrap_inline12095 interfacial energy

tex2html_wrap_inline14663 strength of free energy, binary fluid interaction

tex2html_wrap_inline12727 wavelength

tex2html_wrap_inline12727 mean free path

tex2html_wrap_inline12727 eigenvalue of the enhanced collision matrix

tex2html_wrap_inline12375 kinematic shear viscosity

tex2html_wrap_inline12883 kinematic bulk viscosity

tex2html_wrap_inline17865 momentum flux tensor

tex2html_wrap_inline12075 density

tex2html_wrap_inline15749 mean density

tex2html_wrap_inline15725 density fluctuation about mean

potential density

tex2html_wrap_inline13605 initial density

tex2html_wrap_inline13605 constant density

tex2html_wrap_inline15837 complex time scale of a wave in a viscous fluid

tex2html_wrap_inline15837 differential cross section

tex2html_wrap_inline15837 eigenvalue of the enhanced collision matrix

tex2html_wrap_inline13341 relaxation time

tex2html_wrap_inline14897 value of the order parameter relaxation time which gives Galilean

invariance

tex2html_wrap_inline13341 eigenvalue of the enhanced collision matrix

tex2html_wrap_inline15035 gravitational potential

tex2html_wrap_inline13163 irrotational velocity potential

tex2html_wrap_inline13163 azimuthal angle

tex2html_wrap_inline15621 salinity

tex2html_wrap_inline17899 free energy

tex2html_wrap_inline14603 bulk free energy

tex2html_wrap_inline14481 effective mass of ath component

tex2html_wrap_inline13049 collision invariant

tex2html_wrap_inline14603 rotational part of velocity solution

tex2html_wrap_inline14603 phase factor

tex2html_wrap_inline12901 collision function

tex2html_wrap_inline13155 solid angle

tex2html_wrap_inline12301 wave frequency

tex2html_wrap_inline15669 wave frequency in an inviscid fluid

tex2html_wrap_inline15853 viscous correction to the inviscid frequency

tex2html_wrap_inline12427 frequency of a wave in an inviscid fluid at a continuous density change

tex2html_wrap_inline12425 frequency of a wave in a viscous fluid at a sharp interface

A initial amplitude of wave

A constant determining strength of surface tension

A coefficient of the equilibrium distribution function

A amplitude term of the velocity potential

tex2html_wrap_inline14705 coefficient of the equilibrium distribution function

tex2html_wrap_inline17937 probability of tex2html_wrap_inline17939 in a collision

tex2html_wrap_inline17941 amplitude term

A constant

a amplitude of inviscid interfacial perturbation

a coefficient of the equilibrium distribution function

tex2html_wrap_inline14737 coefficient of the equilibrium distribution function

tex2html_wrap_inline14013 component of the enhanced collision function tex2html_wrap_inline13975

a constant determining strength of free energy liquid-gas interaction

tex2html_wrap_inline17957 bubble diameter in direction i

B blue particle

B coefficient of the equilibrium distribution function

tex2html_wrap_inline16003 amplitude term

b number of links

b component of the enhanced collision function tex2html_wrap_inline13975

b impact parameter

b coefficient of the equilibrium distribution function

b constant determining strength of free energy liquid-gas interaction

tex2html_wrap_inline13449 collision operator

tex2html_wrap_inline13729 colour density

C coefficient of the equilibrium distribution function

tex2html_wrap_inline14707 coefficient of the equilibrium distribution function

tex2html_wrap_inline13755 constant

tex2html_wrap_inline17989 constant

tex2html_wrap_inline13449 amplitude term

tex2html_wrap_inline12921 particle velocity

c wave celerity

c mean depth of lower fluid, found from curve fitting

tex2html_wrap_inline13535 speed of sound

c coefficient of the equilibrium distribution function

tex2html_wrap_inline14739 coefficient of the equilibrium distribution function

c component of the enhanced collision function tex2html_wrap_inline13975

D dimension of space

D diffusion coefficient

D coefficient of the equilibrium distribution function

tex2html_wrap_inline15989 phase term

D distance OP

d mean density per link

d vertical distance between the peaks of |u|

tex2html_wrap_inline14157 constant

d coefficient of the equilibrium distribution function

d distance of a point from the origin

E equilibrium distribution

tex2html_wrap_inline18035 evolution operator

E tex2html_wrap_inline18039 in the Strum-Liouville equation

tex2html_wrap_inline13399 unit vector in the direction of link i

tex2html_wrap_inline15265 unit vector in the vertical direction

e internal energy

e sum of the squares of the deviation between the data points and the

fitted curve, also known as the error parameter

tex2html_wrap_inline12895 body force per unit mass

tex2html_wrap_inline18051 force on ath component in local interaction model

F Froude number

F coefficient of the equilibrium distribution function

tex2html_wrap_inline12899 distribution function

tex2html_wrap_inline13269 equilibrium distribution function

tex2html_wrap_inline18063 non-equilibrium component of the distribution function

tex2html_wrap_inline18065 ath order approximation to f

tex2html_wrap_inline18071 distribution function for `red' fluid

tex2html_wrap_inline18073 distribution function for `blue' fluid

tex2html_wrap_inline18075 distribution function of link i when u = 0

tex2html_wrap_inline18081 distribution function of link 1 - 6 when u = 0

tex2html_wrap_inline18085 distribution function of link 0 when u = 0

f ratio of fluid densities, tex2html_wrap_inline18091

f' above ratio multiplied by tex2html_wrap_inline18095

tex2html_wrap_inline18097 colour gradient

f coefficient of the equilibrium distribution function

f Fermi-Dirac function

G Galilean invariance factor

tex2html_wrap_inline18105 Greens function

tex2html_wrap_inline18107 local component of Greens function

G coefficient of the equilibrium distribution function

g acceleration due to gravity

g' reduced gravity

tex2html_wrap_inline16017 strength of gravity in fluid i

tex2html_wrap_inline13827 Galilean invariance term

g magnitude of particles relative velocity before a binary collision

g coefficient of the equilibrium distribution function

H function of the distribution function

H amplitude term

H constant

tex2html_wrap_inline17003 depth of fluid i

tex2html_wrap_inline18135 Lagrange multiplier

tex2html_wrap_inline13825 identity operator

tex2html_wrap_inline18139 mean mass current

tex2html_wrap_inline18141 implementation operator for the long range interaction

k wavenumber

tex2html_wrap_inline13039 Boltzmann's constant

L representative length scale

l interface thickness

l typical microscopic length

l size of the grid

tex2html_wrap_inline13679 the ith moment of the equilibrium distribution

M number of particles in an averaging cell

tex2html_wrap_inline13679 number of particles on link i in an averaging cell

m particle mass

tex2html_wrap_inline18167 exponential vertical decay factor for the viscous part of the fluid velocity

m number of links including rest links

m gradient of line

tex2html_wrap_inline18173 mean population of link i

tex2html_wrap_inline13503 equilibrium mean population of link i

tex2html_wrap_inline18181 ath order approximation to tex2html_wrap_inline18173

N(z) Brunt-Väisälä frequency

N total number of points considered

N number of points considered in curve fitting

tex2html_wrap_inline18193 occupation number of link i

O origin

tex2html_wrap_inline13125 pressure tensor

tex2html_wrap_inline18201 momentum

P function in the Strum-Liouville equation

P point just within the boundary

P pressure incorporating a gravitational potential

p pressure

tex2html_wrap_inline15635 isotropic part of tex2html_wrap_inline13125

tex2html_wrap_inline15635 reference pressure

tex2html_wrap_inline18217 stress tensor

tex2html_wrap_inline18219 tensor

Q function in the Strum-Liouville equation

tex2html_wrap_inline13129 heat flux

q concentration of particles

tex2html_wrap_inline13129 local colour flux

tex2html_wrap_inline18229 Lagrange multiplier

Re Reynolds number

R red particle

R function in the Strum-Liouville equation

R separation of sites participating in the long range interaction

tex2html_wrap_inline12911 position vector

tex2html_wrap_inline13451 streaming operator

tex2html_wrap_inline18243 tensor containing the viscous terms in the lattice gas Navier-Stokes

equation

S number of fluid components

S entropy

tex2html_wrap_inline18249 gravitational strength parameter in fluid i

s in-state of a collision

s' out-state of a collision

tex2html_wrap_inline18257 ith component of in-state

tex2html_wrap_inline18261 ith component of out-state

tex2html_wrap_inline13201 infinitesimal surface

T wave period

T temperature

tex2html_wrap_inline18271 four-dimensional tensor

t time

tex2html_wrap_inline15883 rotational velocity

U horizontal component of tex2html_wrap_inline15883

tex2html_wrap_inline18281 amplitude of the horizontal velocity for a wave on a continuous density

gradient

U representative velocity scale

tex2html_wrap_inline12875 fluid velocity

u horizontal component of tex2html_wrap_inline12875

tex2html_wrap_inline13033 inviscid velocity

tex2html_wrap_inline12179 horizontal component of tex2html_wrap_inline13033

tex2html_wrap_inline13033 peculiar velocity

tex2html_wrap_inline18299 horizontal velocity magnitude

tex2html_wrap_inline14459 dimensionless horizontal velocity, tex2html_wrap_inline17479

u' dimensionless horizontal velocity, u/c

tex2html_wrap_inline18309 equilibrium velocity

tex2html_wrap_inline14459 common equilibrium velocity

tex2html_wrap_inline12875 mean velocity

tex2html_wrap_inline12169 velocity component parallel to x-axis

tex2html_wrap_inline18319 velocity component parallel to y-axis

tex2html_wrap_inline16997 horizontal velocity for a wave on a large grid

tex2html_wrap_inline15995 horizontal velocity for a wave on a small grid

V interaction potential

tex2html_wrap_inline15103 fluid velocity when the introduction of a body force is being considered

W vertical component of tex2html_wrap_inline15883

tex2html_wrap_inline18335 amplitudeoftheverticalvelocityforawaveonacontinuousdensity

gradient

W work done by colour flux on colour gradient

w vertical component of tex2html_wrap_inline12875

tex2html_wrap_inline12185 vertical component of tex2html_wrap_inline13033

tex2html_wrap_inline18347 vertical velocity magnitude

w' dimensionless vertical velocity, w/c

tex2html_wrap_inline17011 vertical velocity for a wave on a large grid

tex2html_wrap_inline15997 vertical velocity for a wave on a small grid

x coordinate of the lattice

x horizontal coordinate

x' coordinate at an angle to the standard x axis

y coordinate of the lattice

y' coordinate at an angle to the standard y axis

Z(z) z-dependence of the velocity potential

z vertical coordinate

z' dimensionless vertical displacement, tex2html_wrap_inline12737


next up previous contents
Next: FHP-III Collisions Up: No Title Previous: References

James Buick
Tue Mar 17 17:29:36 GMT 1998