The stream-stream interaction between a slow solar wind and its leading faster solar wind is considered. A hydrodynamic model comprising double-layered rarefactions and recompressions is proposed toward understanding the observed large-scale structure near the trailing portion of a high-speed stream

Lee, T. S.

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THE NATURE OF STREAM-STREAM INTERACTION IN 
THE LARGE-SCALE STRUCTURE OF THE SOLAR WIND T. S. Lee 
ABSTRACT Th stream-stream interaction between a slow solar wind and its leading faster solar wind 
is considered. A hydrodynamic model comprising double-layered rarefactions and 
recompressions is proposed toward understanding the observed large-scale structure near 
the trailing portion of a high-speed stream. 
This paper considers the problem of solar wind stream- 
stream interaction, and introduces additional discussions 
concerning the interpretation of the quasistatic large- 
scale solar wind structure. 
It is now well inferred from near-earth direct monitor- 
ing measurements that, over several consecutive rota- 
tions of the sun the solar wind, at times, may possess a 
near-stable corotating structure. Longitudinal and, to a 
much lesser extent, latitudinal variations in the solar 
wind strength appear to be the basic cause. Geomagnetic 
disturbances often exhibit periodicities, some of which 
implicate a clear association with solar rotation. Long 
sequences of the stronger among these-the recurrent 
storms-were first attributed to the so-called M regions 
on the solar surface by Bartels [1932]. His view, which 
incorporates quasipermanent narrow beams of corpus- 
cular radiation, was long held although observational 
identifications of these regions were lacking. Dessler and 
Fejer [ 19631 reconsidered this view and proposed that 
these storms are generated by corotating nonunifor- 
mities resulting from the interaction between a slow- 
wind region and an overtaking-wind region. Razdan et 
al. [1965] e x a m i d  their model hypothesis and 
showed that the basic idea is hydrodynamically viable 
with respect to the expected implications at 1 AU. 
The general premise of regarding longitudinal gradients 
in solar wind strength near the sun responsible for the 
corotating wind variations in the interplanetary region is 
?he author is at the Electrikal Engineering Department, Univer- 
sity of Minnesota, Minneapolis, Minn. 
very reasonable. In addition, the particular picture of 
one steady wind overtaking another appears to provide 
useful clues to the dynamical complexities near the 
leading portion of a high speed stream. Here, the key 
ideas of a solar wind interface (tangential discontinuity) 
and accompanying compressions, bounded by perhaps 
two shock waves, go far toward giving overall interpreta- 
tions to many observations, as discussed by Dr. Davis in 
his presentation yesterday. 
Phenomena related to the trailing portion of a strong 
wind have not received adequate considerations in the 
literature. Surabhai [ 19633 thought that the decrease in 
velocity results in the formation of a cavity, or region of 
reduced density, behind the M region beam. Although 
the suggestion is inherently interesting, it is actually 
difficult to see how the model is arrived at through his 
given hydrodynamic arguments. We would like to reopen 
the discussion and try to indicate a different model 
concept for limited considerations in the following. 
The question is raised: what appropriate hydrodynam- 
ic structures may connect two steady solar winds, 
departing from each other? If we allow ourselves the 
luxury of disregarding the secondary nonradial motions 
generated in the context of corotating interactions 
viewed in the solar equatorial plane, then the problem is 
grossly similar to its sister problem in the context of 
spherical flow in which a fast steady expanding flow 
pulls away from a trailing slow steady expanding flow. 
Here, one is easily tempted to argue that a more or less 
simple and smooth rarefaction region would be created, 
a conclusion generally associated with experiences with 
laboratory planar flows. However, the conditions of the 
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solar wind are sufficiently different to warrant separate 
considerations for this type of stream-stream interaction. 
It is interesting to point out that there exist classes of 
hydrodynamic solutions to the spherical problem men- 
tioned above [Lee, to be published]. They correspond 
to specific model assumptions made on the solar winds: 
invariant mass flow rate per steradian and invariant 
streaming and sound velocities. Not all of these have 
been scrutinized and cataloged, but one has sufficient 
bearing on our present consideration that a qualitative 
description of its main features may shed some light on 
the original problem. 
When a fast wind moves ahead, leaving a trailing slow 
wind behind, it tends to expand inward on account of its 
inherent specific thermal energy density. At the same 
time, the slower wind left behind tends to expand 
outward. Thus rarefaction waves of respectively deceler- 
ative and accelerative nature are generated. First con- 
sider the drastic case where the separation of the two 
steady winds takes .place at a sufficiently high relative 
velocity. Since the specific thermal energy densities for 
the two winds are both finite, the edges of the 
two expansion waves cannot meet, thus creating a 
vacuum. . This sequence of wind-rarefaction-vacuum- 
rarefaction-wind would characterize the structure of the 
basic stream-stream “noninteraction.” [The reader will 
find it interesting to compare this picture with Sarab- 
hais, 1963, picture.] Consider next the probably more 
realistic case where the relative separating velocity is less 
drastic so that the two rarefaction waves begin to 
interfere with each other. In figure 1 ,  we have sketched 
the configuration of the total interaction as projected on 
the solar equitorial plane. Here, we consider the interfer- 
ence to be only moderate such that it is confined 
spatially to the regions to the two sides of the interface 
discontinuity (tangential discontinuity as shown). We 
note that the interference interaction is basically analo- 
gous to the leading edge interaction discussed earlier, 
except that the double-layered recompression here re- 
sults from a collision between the expanded extensions 
of the two winds which, if it were not for compres- 
sibility, would depart from each other permanently. It 
follows that respectively inward-looking and outward- 
looking shock waves are expected in the flow. Thus the 
trailing-edge interaction may have a structure composed 
of regions of fast wind region-rarefied region (fast 
wind)-recompressed region (fast wind)-recompressed 
region (slow wind)-rarefied region (slow wind)-slow wind 
region. In this model picture, five flow discontinuities- 
two rarefaction fronts, two shock waves and an interface 
discontinuity-combine to give demarcations to the flow 
field. 
Figure 1. Configuration of stream-stream interaction at 
the trailing portion of a fast steady wind. This wind and 
its following slow steady wind are joined through an 
assemblage of unsteady wave regions encompassing 
dou ble-layered expansions and recompressions. The 
discontinuities comprise the sequence of rarefaction 
front -shock wave - tangential discontinuity - shock 
wave - rarefaction front. 
In the above, we have outlined the essential physical 
arguments for a specific class of stream-stream interac- 
tion. Depending on quantitative specifications on the 
two interacting solar winds, other possible modes of 
flow connections may be predicted. We refrain from 
discussing them here. 
If the more complete view is taken that close to the 
sun the longitudinal strength of the solar wind varies 
alternately from strong to weak, to strong, and so forth, 
we should see, of course, leading-edge and trailing-edge 
types of stream-stream interaction, According to our 
discussions, plasma compression can be expected at both 
the leading and trailing portions of a stream. Thus, the 
mere presence of locally high density does not neces- 
sarily imply the arrival of any new enhanced “stream” or 
“beam.” Here, we are being reminded that the occa- 
sional detections of density enhancement occur near the 
minimum of the corresponding time-profiles of the 
velocity, an interesting fact already observed by 
Dr. Smith in a comment following Dr. Wolfe’s paper 
yesterday. Finally, the durations of density enhance- 
ments of both leading-edge and trailing-edge interactions 
473 
are expected from our model considerations to be 
followed by high (by local comparisons) velocities in the 
solar wind, in good agreement with the usual observa- 
tions. 
REFERENCES 
Bartels, J.; Terrestrial Magnetic Activity and Its Rela- 
tions to Solar Phenomena. Tern. Magn., Vol. 37,1932, 
pp. 1-52. 
Dessler, A.J.; and Fejer, J. A.: Interpretation of K p  
Index and M-Region Geomagnetic Storms. Pknet. 
Space Sci. , Vol. 11 , 1963, pp. 505-5 11. 
Razdan, H., Colburn, D. S.; and Sonett, C. P.: Recurrent 
Sp - SI- Impulse Pairs and Shock Structure in 
M-Region Beams. Planet. Space Sci., Vol. 13, 1965, 
Sarabhai, V.: Some Consequences of Nonuniformity of 
Solar Wind Velocity. J. Geophys. Res., Vol. 68, 1963, 
pp. 11 11-1 123. 
pp. 1555-1557. 
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The nature of stream-stream interaction in the large-scale structure of the solar wind

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