Symbols

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

Symbol	Description
$A_H$	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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