Go to previous page Go up Go to next page

A.1 Notation

Throughout this paper we refer to the anelastic equations in spherical coordinates, with r, h, and f representing the radius, colatitude, and longitude, respectively, and t representing the time. The corresponding unit vectors are denoted as ^r, ^ h, and ^ f and the three spatial components of vector quantities are identified using subscripts as follows:
v = vr^r + vh^h + vf^f. (34)
The magnitude of vector quantities is denoted by removing the bold-face type, for example v is the magnitude of v. Furthermore, throughout the text, angular brackets <> denote averages over longitude, f, unless they have subscripts which indicate other averaging dimensions. The Lagrangian derivative is defined as D/Dt = @/@t + v. \~/. Other symbols used in this paper are defined in Table 1.
Table 1: Definition of symbols used throughout the paper.



Symbol

Unitsa

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 (44View Equation)]

eij

-1 s

Strain rate tensor

F

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

F

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

G

g cm- 2s-2

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

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 (46View Equation)]

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 (35View Equation)]

-- 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 (13View Equation)

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 (12View Equation)]




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.


  Go to previous page Go up Go to next page