*Astron. Astrophys. 359, 788-798 (2000)*
## 5. The flux vector in moving 3D media
It is obvious from Eqs. (4) and (5) that the direction dependence of
*w* induces a complicated dependence of the flux vector
(I:11) on the directions of the
velocity vector and of the temperature gradient. In particular, it
appears possible that in case these directions do not coincide there
is a flux component perpendicular to the temperature gradient.
While it seems impossible to derive an explicit expression for the
flux vector analytically in the general case, this could be done in
the limit of small . However, even in
this case the general expressions are quite lengthy and very difficult
to interpret.
In order to discuss the essential effects we therefore consider
here as example a *plane-parallel* medium with a temperature
gradient in the normal direction (taken to be the *z*-direction)
and with a velocity field () which
is assumed to vary only with the *z* coordinate in the
neighborhood of the point of
interest, i.e. in cartesian coordinates
For the direction one now
obtains from Eq. (2)
and the integration over all directions (see Eq. I:12) of Eq. (18)
yields
where all coefficients are to be taken at
.
It is seen that the classical result for static media is fully
regained for . If the velocity
vector is in the *z* direction
(), i.e. if it is parallel to the
temperature gradient, the *x* and *y* components of the flux
vector are still zero, but the *z* component is modified by the
velocities as has been discussed in Sect. 4.1:
The coefficients of the terms
are just given by the two angle averages
and
, respectively.
If the flow direction and the temperature gradient are *not*
parallel (), the comparison of
Eq. (55) with (54) shows that the flux component in *z* direction
is not changed in first order but it is increased in second order.
More significantly, however, we find also non-zero flux components in
the *x* and *y* directions, i.e. there is now a radiative
flux perpendicular to the temperature gradient.
© European Southern Observatory (ESO) 2000
Online publication: July 7, 2000
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