Small-scale Turbulent Motions Research Articles

Evidence for the Hydrodynamic Character of Microturbulence

Worrall and Wilson1 have questioned the validity of determinations of the chemical composition of stellar atmospheres from observations of absorption lines in stellar spectra. Their main argument is directed against the concept of “microturbulence”, which has been used for several decades to explain the high level of the flat part of the curve of growth. It was first introduced by Struve and Elvey2 to account for the apparent systematic variation of the abundances with the total amount of absorption (equivalent width) of the spectral lines from which they are derived. Microturbulence is thought of as a statistical velocity field in the stellar atmosphere, with moving gas elements whose optical depths for the photons to be absorbed are smaller than unity. This small scale velocity field widens the frequency interval for the absorption of photons; this has no influence on the strength of the weak lines, but the equivalent width of saturated lines is increased. In the curve of growth, which represents the relation between the effective number of absorbing particles in the stellar atmosphere and the equivalent width of the absorption line, the flat part of the saturated lines is lifted. Thermal motion of the absorbing atoms frequently fails to account for the level of the flat part of the curve of growth; according to Worrall and Wilson this is the only independent evidence for the existence of small scale turbulent motion in stellar atmospheres. Their statements on this point are strong: “ … There are no independent observations even suggesting that such small-scale, non-thermal motion exists, much less defining its amplitude. . . . ”. Worrall and Wilson suggest that the level of the flat part of the curve of growth is determined by non-local thermodynamic equilibrium (LTE) effects. I show here that other observations, supporting the concept of microturbulence, do exist.

On the Turbulence in the Protoplanetary Cloud

The problem of turbulence in the protoplanetary cloud is of importance for planetary cosmogony. Chaotic macroscopic motions probably existed in the cloud during its formation. Further evolution of the cloud depended to a great extent upon whether these original motions damped in a short time, or turbulence supported by some source of energy existed during planet formation. According to Kuiper and Fessenkov's hypotheses, massive protoplanets formed as a result of gravitational instability and turned into planets after the dissipation of light elements. Large-scale turbulent motions with mean velocities exceeding the thermal velocities of atoms and molecules would prevent, however, gravitational instability in the cloud, even if its mass was of the order of the mass of the sun. According to Edgeworth and to Gurevitch and Lebedinsky the planets grew gradually from small condensations formed in a flattened dust disk with a mass equal to that of the present planetary system. But even small scale turbulent motions would prevent extreme flattening of the disk necessary in this case for gravitational instability. The problem of turbulence is also connected with the problem of present distribution of angular momentum between the sun and planets, as large-scale turbulence produces redistribution of matter and of angular momentum in the cloud.

On the Turbulence in the Protoplanetary Cloud

The problem of turbulence in the protoplanetary cloud is of importance for planetary cosmogony. Chaotic macroscopic motions probably existed in the cloud during its formation. Further evolution of the cloud depended to a great extent upon whether these original motions damped in a short time, or turbulence supported by some source of energy existed during planet formation. According to Kuiper and Fessenkov's hypotheses, massive protoplanets formed as a result of gravitational instability and turned into planets after the dissipation of light elements. Large-scale turbulent motions with mean velocities exceeding the thermal velocities of atoms and molecules would prevent, however, gravitational instability in the cloud, even if its mass was of the order of the mass of the sun. According to Edgeworth and to Gurevitch and Lebedinsky the planets grew gradually from small condensations formed in a flattened dust disk with a mass equal to that of the present planetary system. But even small scale turbulent motions would prevent extreme flattening of the disk necessary in this case for gravitational instability. The problem of turbulence is also connected with the problem of present distribution of angular momentum between the sun and planets, as large-scale turbulence produces redistribution of matter and of angular momentum in the cloud.

A Study of Line Profiles: the Spectrum of Rho Leonis.

The broad absorption lines of the B0 I supergiant p Leonis have been compared with several theoretical line profiles computed for different kinds of mass motion. The observed profiles agree with the rotational profiles (or perhaps with profiles broadened by vertical convection with an assumed distribution of velocities according to a step function). A simple method of determining the velocity of mass motion has been developed. When this method is applied to the medium and weak lines in p Leonis, a mean rotational velocity of 61.8 km/sec, with a probable error of 5.8 km/sec, is obtained. If the broadening of lines in p Leonis is due to convection mstead of rotation, the value thus determined can be interpreted as the maximum velocity (in the step- function distribution) of the convection motion. Because of the observational uncertainties as well as the theoretical complications, we cannot be certain which of the two possibilities is the correct one. The original lines, before being broadened by 61.8 km/sec of rotation (or of convection), have large widths and shallow depths, suggesting the presence of other kinds of large-scale motion. We have estimated from the curve of line-width correlation that such a large-scale motion has a velocity of about 18 km/sec, while the small-scale turbulent motion and the thermal motion combined have a velocity of 10 km/sec. The stronger lines do ot show appreciable rotation (or convection). They are perhaps broadened by other kinds of mass motion, possibly by large-scale turbulence.

The General Circulation of the Atmosphere

ON May 18 a meeting of the Royal Meteorological Society was held to discuss the problem of the changing pattern of lergescale flow in the atmosphere, usually known as the ‘geberak circulation'. In opening the discussion, Dr. E. T. Eady pointed out that even on a large scale, when the motion has been smoothed of such small-scale and transient irregularities as traielling depressions and anticyclones, fronts, etc., we were not concerned with a problem of steady motion ; 5-day mean charts smooth out most of the travelling disturbances (including the ‘long waves’ which travel, on the average, nearly a complete wave-length during this period), but differ very considerably among themselves even for the same time of year. Only when we take means over a long period does the mean flow approximate to that shown on climatological charts. The general behaviour is reminiscent of small-scale turbulent motion (friction-ally induced) in aerodynamics, means over longer and longer periods bringing out disturbances of longer and longer wave-length, finally yielding a quasi-steady mean flow. Although the mechanism by which large turbulent disturbances in the atmosphere are continually regenerated (to make up for frictional dissipation) differs from that by which small-scale aerodynamic turbulence is maintained, there is a broad similarity between the two types of turbulence. Just as in aerodynamics, we cannot divorce the study of the mean motion from that of the turbulent disturbances, since these are mutually determining.