scholarly journals A General Formulation of the Transfer Equation. II. Line Formation with General Redistribution

1972 ◽  
Vol 25 (2) ◽  
pp. 177 ◽  
Author(s):  
CJ Cannon
Keyword(s):  
Velocity Field ◽  
Spectral Line ◽  
Transfer Equation ◽  
Functional Form ◽  
System Of Equations ◽  
Line Formation ◽  
Line Radiation ◽  
Multidimensional Equation

The multidimensional equation of transfer for spectral line radiation under a general redistribution law is studied. It is shown that the equation may be rewritten as a system of equations of the "Feautrier" form, which are known to be exceedingly stable and efficient under numerical reduction. It is also shown that the inclusion of a multidimensional differential macroscopic velocity field does not alter the functional form of the equations obtained and therefore may also be treated by the general Feautrier technique.

scholarly journals Effects of Acoustic Waves on Spectral Line Profiles

1980 ◽  
Vol 51 ◽  
pp. 211-211
Author(s):  
Lawrence E. Cram
Keyword(s):  
Velocity Field ◽  
Spectral Line ◽  
Acoustic Waves ◽  
Line Shift ◽  
Solar Photosphere ◽  
Line Formation ◽  
Thermal Velocity ◽  
State Variables ◽  
Velocity Amplitude ◽  
Short Period

AbstractAlmost all studies of spectral line formation in the presence of non-thermal velocity fields have been made assuming that the only effect of the velocity field is to produce a Doppler shift of the absorption and emission coefficients. However, a non-thermal velocity field will entail velocity-correlated fluctuations in temperature, pressure, level populations, and other parameters of the line formation problem. Using a time-dependent dynamical calculation describing the propagation of non-linear, radiatively-damped short period (P = 30s) acoustic waves in the solar photosphere, Cram, Keil and Ulmschneider (1980) have shown that velocity-correlated fluctuations in state variables (particularly the temperature) may lead to important effects in line broadening, line shifts and asymmetries, and in line-shift oscillations. Upwardly propagating waves generally produce significant redshifts in the cores of medium-strong Fe I lines, and the increased ratio of observed line shift to wave velocity amplitude would significantly modify the results of kinematic studies of high frequency line shifts such as those of Deubner (1976) and Keil (1980).Cram (1980) has further explored dynamical effects in the formation of Fe I and Fe II lines by using the “microturbulence” limit, wherein an average is made over the phase of the wave before the transfer equation is solved. Except for weak, high EP Fe II lines, the predicted solar lines are redshifted and show a “red” asymmetry. For a model of Arcturus the lines are often shifted to the blue, but it does not appear that this model can account for the observed differences between solar and Arcturan line asymmetries (Gray 1980).

scholarly journals Mesoturbulence

1980 ◽  
Vol 51 ◽  
pp. 172-182
Author(s):  
G. Traving
Keyword(s):  
Velocity Field ◽  
Transfer Equation ◽  
Line Radiation ◽  
Scale Length

AbstractThe influence of a stochastic velocity field with a finite scale length 1 on the transfer of line radiation is described by means of a generalization of the transfer equation. Micro- and macroturbulence are contained in this mesoturbulence approach as limiting cases 1 → O and 1 → ∞ respectively.

scholarly journals Influence of turbulence on the shape of a spectral line: the analytical approach

2007 ◽  
Vol 3 (S242) ◽  
pp. 32-33
Author(s):  
N. A. Silant'ev ◽  
E. E. Lekht ◽  
J. E. Mendoza-Torres ◽  
G. M. Rudnitskij
Keyword(s):  
Radiative Transfer ◽  
Spectral Line ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Simple Analytical Expression ◽  
Line Radiation ◽  
Explicit Analytical Solution ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Factor Α

AbstractWe consider the propagation of spectral-line radiation in a correlated turbulent atmosphere. The ensembles of turbulent velocities u(r,t) and optical depths, τν, are assumed to be Gaussian. We investigate the explicit analytical solution of the stochastic radiative transfer equation for the intensity Iν of radiation. The scattering term is not taken into account. It is shown that, in addition to the usual Doppler broadening of the spectral line, correlated turbulent motions of atoms and molecules give rise to considerable changes in the shape of a spectral line. We find that the mean intensity I(0)ν (Iν=I(0)ν+I′ν, I′ν = 0) obeys the usual radiative transfer equation with renormalized extinction factor αeffν if the correlation length R0 of the turbulence is small as compared to a photon free path. A simple analytical expression for αeffν is given. This expression integrally depends on the two-point correlation function of the turbulent velocity field.

Wavelets in the Solution of Nongray Radiative Heat Transfer Equation

1998 ◽  
Vol 120 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Y. Bayazitoglu ◽  
B. Y. Wang
Keyword(s):  
Transfer Equation ◽  
Solution Method ◽  
Radiative Heat ◽  
Radiative Transfer Equation ◽  
Basis Functions ◽  
Wavelet Basis ◽  
System Of Equations ◽  
Heat Transfer Equation ◽  
One Dimensional ◽  
The One

The wavelet basis functions are introduced into the radiative transfer equation in the frequency domain. The intensity of radiation is expanded in terms of Daubechies’ wrapped-around wavelet functions. It is shown that the wavelet basis approach to modeling nongrayness can be incorporated into any solution method for the equation of transfer. In this paper the resulting system of equations is solved for the one-dimensional radiative equilibrium problem using the P-N approximation.

scholarly journals Neutral oxygen spectral line formation revisited with new collisional data: large departures from LTE at low metallicity

2009 ◽  
Vol 500 (3) ◽  
pp. 1221-1238 ◽  
Author(s):  
D. Fabbian ◽  
M. Asplund ◽  
P. S. Barklem ◽  
M. Carlsson ◽  
D. Kiselman
Keyword(s):  
Spectral Line ◽  
Line Formation ◽  
Spectral Line Formation ◽  
Low Metallicity

scholarly journals Calculation of turbulent diffusion jets under effects of gravity and moving surrounding air

2001 ◽  
Vol 23 (2) ◽  
pp. 87-94
Author(s):  
Bui Van Ga ◽  
Nhan Hong Quang ◽  
Jean Marc Vignon
Keyword(s):  
Velocity Field ◽  
Turbulent Diffusion ◽  
Concentration Field ◽  
Integral Model ◽  
System Of Equations ◽  
Kutta Method ◽  
Air Velocity ◽  
Runge Kutta Method ◽  
Jet Axis ◽  
General Conditions

The basis theory for the turbulent diffusion of jet and flame has been presented previously [1, 2]. But that one applies only in quiet surrounding air with the effects of buoyancy neglected. In the present paper, the theory is developed further by establishing an integral model for a jet in more general conditions with variable inclined angles, under effects of gravity and surrounding air velocity in any direction compared to the jet axis. The system of equations is closed by turbulence k-E model and is solved by 4th order Runge-Kutta method. In the first stage, the model is applied to predict the velocity field, the concentration field and with development of a 0.3 m diameter jet.

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