Symbols
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This page contains an alphabetic list of symbols used in the documentation

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Symbol         Description
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$A_H$          Lateral friction coefficient
$\\mathrm{Bi}$ Biot number $\\mathrm{Bi} = hD/k$
$C_p$          Heat capacity
$d$            Distance between two cylinders in Taylor-Couette flow $d = r_o - r_i$
$D$            Depth of the domain/typical length scale
$e_z$          Unit vector in the $z$-direction
$f_0$          Coriolis paramter $f_0 = 2 \\Omega \\sin{\\theta_0}$
$F$            $F = f_0^2 L^2 / (g D)$
$g$            Gravitational constant
$\\mathrm{Gr}$ Grashof number $\\mathrm{Gr} = \\mathrm{Ra} / \\mathrm{Pr}$
$h$            Surface heat transfer coefficient
$k$            Thermal conductivity
$L$            Length of the domain/typical length scale. Height of the cylinders for Taylor-Couette flow
$\\mathrm{Le}$ Lewis number $\\mathrm{Le} = \\kappa_T / \\kappa_S$
$p$            Pressure
$Q_S$          Spatial structure of the surface salinity flux
$r$            Radius. First component in the cylindrical coordinate system
$r_0$          Bottom friction parameter $r_0 = \\epsilon_0 L / U$
$r_i$          Radius of the inner cylinder. Used as typical length scale
$r_o$          Radius of the outer cylinder
$\\mathrm{Pr}$ Prandtl number $\\mathrm{Pr} = \\nu / \\kappa_T$
$\\mathrm{Ra}$ Rayleigh number $\\mathrm{Ra} = (\\alpha_T g \\Delta T D^3) / (\\nu \\kappa)$
$\\mathrm{Re}$ Reynolds number $\\mathrm{Re} = UL / \\nu$ or $\\mathrm{Re} = UL / A_H$
$t$            Time
$T$            Temperature
$T_S$          Surface temperature
$\\Delta T$    Temperature difference
$\\mathrm{Ta}$ Taylor number $\\mathrm{Ta} = v_i r_i / \\nu = \\mathrm{Re}_i r_i / d = \\mathrm{Re}_i (\\eta^{-1} - 1)^{-1}$
$\\mathbf{u}$  Velocity vector $(u, v, w)$ in 3D and $(u, v)$ in 2D
$u$            Horizontal velocity in the $x$-direction
$U$            Typical velocity/lid velocity for the lid-driven cavity
$v$            Horizontal velocity in the $y$-direction
$v_i$          Angular velocity of the inner cylinder. Used as typical velocity scale
$w$            Vertical velocity in the $z$-direction
$\\alpha$      Wind stress parameter $\\alpha = \\tau_0 L / (\rho D U^2)$
$\\alpha_S$    Solutal coefficient
$\\alpha_T$    Thermal compressibility coefficient
$\\beta$       Planetary vorticity gradient $\\beta = \\beta_0 L^2 / U$
$\\beta_0$     Meridional variation of the Coriolis parameter $f_0$ at $\\theta_0$.
$\\epsilon_0$  Damping coefficient
$\\zeta$       Vorticity
$\\eta$        Radius ratio of the two cylinders in Taylor-Couette flow $\\eta = r_i / r_o$
$\\theta$      Azimuth. Second component in the cylindrical coordinate system
$\\theta_0$    Central latitude
$\\kappa_S$    Saline diffusivity
$\\kappa_T$    Thermal diffusivity $\\kappa_T = k / (\\rho_0 C_p)$
$\\lambda$     Buoyancy ratio $\\lambda = \\alpha_S \\Delta S / (\\alpha_T \\Delta T)$
$\\lambda_0$   $\\lambda_0 = f_0^2 / (g D)$
$\\mu$         Dynamic viscosity
$\\nu$         Kinematic viscosity $\\mu / \\rho_0$
$\\rho$        Density
$\\rho_0$      Reference density
$\\sigma$      Surface heat flux strength
$\\tau$        Wind stress
$\\tau_0$      Characteristic wind stress amplitude
$\\psi$        Stream function
$\\omega_i$    Angular frequency of the inner cylinder
$\\omega_o$    Angular frequency of the outer cylinder
$\\Omega$      Rotation rate of the earth
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