damping parameterhalf of the ratio density difference/ mean density
constants in a linear sum of the collision invariants
fluid mobility
density difference between two fluids, also known as the order parameter
distribution function for
equilibrium distribution function for
ath order approximation to
collision function for link i
chemical potential
change in momentum
density relative to a constant density
density difference between simulations performed using different models
Knudsen number
small number
function of the deviation of the density from its equilibrium value
small displacement
displacement at interface
scattering angle
angle between velocity and x-axis
angle between x-axis and x'-axis
angle of the colour gradient
angle between and x-axis
interfacial energy
strength of free energy, binary fluid interaction
wavelength
mean free path
eigenvalue of the enhanced collision matrix
kinematic shear viscosity
kinematic bulk viscosity
momentum flux tensor
density
mean density
density fluctuation about mean
potential density
initial density
constant density
complex time scale of a wave in a viscous fluid
differential cross section
eigenvalue of the enhanced collision matrix
relaxation time
value of the order parameter relaxation time which gives Galilean
invariance
eigenvalue of the enhanced collision matrix
gravitational potential
irrotational velocity potential
azimuthal angle
salinity
free energy
bulk free energy
effective mass of ath component
collision invariant
rotational part of velocity solution
phase factor
collision function
solid angle
wave frequency
wave frequency in an inviscid fluid
viscous correction to the inviscid frequency
frequency of a wave in an inviscid fluid at a continuous density change
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
coefficient of the equilibrium distribution function
probability of in a collision
amplitude term
A constant
a amplitude of inviscid interfacial perturbation
a coefficient of the equilibrium distribution function
coefficient of the equilibrium distribution function
component of the enhanced collision function
a constant determining strength of free energy liquid-gas interaction
bubble diameter in direction i
B blue particle
B coefficient of the equilibrium distribution function
amplitude term
b number of links
b component of the enhanced collision function
b impact parameter
b coefficient of the equilibrium distribution function
b constant determining strength of free energy liquid-gas interaction
collision operator
colour density
C coefficient of the equilibrium distribution function
coefficient of the equilibrium distribution function
constant
constant
amplitude term
particle velocity
c wave celerity
c mean depth of lower fluid, found from curve fitting
speed of sound
c coefficient of the equilibrium distribution function
coefficient of the equilibrium distribution function
c component of the enhanced collision function
D dimension of space
D diffusion coefficient
D coefficient of the equilibrium distribution function
phase term
D distance OP
d mean density per link
d vertical distance between the peaks of |u|
constant
d coefficient of the equilibrium distribution function
d distance of a point from the origin
E equilibrium distribution
evolution operator
E in the Strum-Liouville equation
unit vector in the direction of link i
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
body force per unit mass
force on ath component in local interaction model
F Froude number
F coefficient of the equilibrium distribution function
distribution function
equilibrium distribution function
non-equilibrium component of the distribution function
ath order approximation to f
distribution function for `red' fluid
distribution function for `blue' fluid
distribution function of link i when u = 0
distribution function of link 1 - 6 when u = 0
distribution function of link 0 when u = 0
f ratio of fluid densities,
f' above ratio multiplied by
colour gradient
f coefficient of the equilibrium distribution function
f Fermi-Dirac function
G Galilean invariance factor
Greens function
local component of Greens function
G coefficient of the equilibrium distribution function
g acceleration due to gravity
g' reduced gravity
strength of gravity in fluid i
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
depth of fluid i
Lagrange multiplier
identity operator
mean mass current
implementation operator for the long range interaction
k wavenumber
Boltzmann's constant
L representative length scale
l interface thickness
l typical microscopic length
l size of the grid
the ith moment of the equilibrium distribution
M number of particles in an averaging cell
number of particles on link i in an averaging cell
m particle mass
exponential vertical decay factor for the viscous part of the fluid velocity
m number of links including rest links
m gradient of line
mean population of link i
equilibrium mean population of link i
ath order approximation to
N(z) Brunt-Väisälä frequency
N total number of points considered
N number of points considered in curve fitting
occupation number of link i
O origin
pressure tensor
momentum
P function in the Strum-Liouville equation
P point just within the boundary
P pressure incorporating a gravitational potential
p pressure
isotropic part of
reference pressure
stress tensor
tensor
Q function in the Strum-Liouville equation
heat flux
q concentration of particles
local colour flux
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
position vector
streaming operator
tensor containing the viscous terms in the lattice gas Navier-Stokes
equation
S number of fluid components
S entropy
gravitational strength parameter in fluid i
s in-state of a collision
s' out-state of a collision
ith component of in-state
ith component of out-state
infinitesimal surface
T wave period
T temperature
four-dimensional tensor
t time
rotational velocity
U horizontal component of
amplitude of the horizontal velocity for a wave on a continuous density
gradient
U representative velocity scale
fluid velocity
u horizontal component of
inviscid velocity
horizontal component of
peculiar velocity
horizontal velocity magnitude
dimensionless horizontal velocity,
u' dimensionless horizontal velocity, u/c
equilibrium velocity
common equilibrium velocity
mean velocity
velocity component parallel to x-axis
velocity component parallel to y-axis
horizontal velocity for a wave on a large grid
horizontal velocity for a wave on a small grid
V interaction potential
fluid velocity when the introduction of a body force is being considered
W vertical component of
amplitudeoftheverticalvelocityforawaveonacontinuousdensity
gradient
W work done by colour flux on colour gradient
w vertical component of
vertical component of
vertical velocity magnitude
w' dimensionless vertical velocity, w/c
vertical velocity for a wave on a large grid
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,