A.1 Notation

Table 1:

Definition of symbols used throughout the paper.

Symbol

Units $a$

Definition

$B(r, h,f, t)$

$G$

Magnetic field

$CP$

$-1 -1 erg g K$

Specific heat per unit mass at constant pressure

$CV$

$erg g -1K -1$

Specific heat per unit mass at constant volume

$D(r, h, f,t)$

Viscous stress tensor with elements $Dij$ [Equation (44 )]

$eij$

$-1 s$

Strain rate tensor

$F$

Energy flux due to radiative diffusion [Equation (55 )]

$F$

Angular momentum flux [Equation (67 )-(73 )]

$G$

$g cm- 2s-2$

Flux term for maintenance of the meridional circulation [Equations (15 )-(80 )]

$g$

$cm s-2$

Gravitational acceleration

$H T$

$cm$

Temperature scale height: $- 1 HT = - (@ ln T/@r)$

$J (r,h,f,t)$

$statamp cm - 2$

Current density [Equation (46 )]

$L o .$

$erg s- 1$

Solar luminosity: $33 -1 Lo . = 3.846 × 10 erg s$

$L$

$cm2 s-1$

Angular momentum per unit mass

$-- P (r)$ , $P (r,h,f,t)$

$-2 dyn cm$

Reference and perturbation pressure

$Ro .$

$cm$

Solar radius: $R o. = 6.960 × 1010cm$

$rt$

$cm$

Radial location of the center of the tachocline: $rt ~ 0.7Ro .$ (Section 3.2)

$-- S(r)$ , $S(r, h,f,t)$

$erg g -1K -1$

Specific entropy per unit mass for the reference state and perturbation

$g$

…

Adiabatic exponent $= C /C P V$

$Dt$

$cm$

Tachocline thickness

$d$

…

Tachocline aspect ratio $d = Dt/rt$

$e$

…

Perturbation parameter [see Equation (35 )]

$-- T (r)$ , $T (r,h,f,t)$

$K$

Reference and perturbation temperature

$v(r,h, f,t)$

$cm s-1$

Fluid velocity relative to the rotating reference frame

$-- r(r)$ , $r(r,h, f,t)$

$- 3 g cm$

Reference and perturbation density

$kr(r)b$

$cm2 s- 1$

Radiative thermal diffusion

$c$

$cm$

Distance from the rotation axis (radius in cylindrical coordinates): $c = r sin h$

$n(r)b$

$cm2 s- 1$

Kinematic viscosity attributed either to molecular diffusion or to unresolved motions in a numerical model

$Y$

$g cm- 5s-1$

Meridional circulation streamfunction [Equation (13 )

$w(r, h,f,t)$

$s-1$

Fluid vorticity relative to the rotating coordinate system

$_O_0$

$-1 rad s$

Angular velocity of the rotating reference frame: $( ) _O_0 = _O_0 cos h^r- sin h^h$

$_O_$

$-1 rad s$

Angular velocity: $_O_ = _O_0 + <vf>/c$

$p$

$g cm- 3 s- 1$

Curl of the axisymmetric mass flux in the meridional plane [Equation (12 )]

$a$ Unless otherwise noted.

$b$ $n$ and $kr$ may in general vary with space and time but in this paper and in many other practical applications, only their radial dependence is taken into account.