Turbulence‐driven angular momentum transport in modulated Kepler flows

The velocity fluctuations in a spherical shell arising from sinusoidal perturbations of a Keplerian shear flow with a free amplitude parameter ε are studied numerically by means of fully 3D nonlinear simulations. The investigations are performed at high Reynolds numbers, i.e. 3000 < Re < 5000. We find Taylor‐Proudman columns of large eddies parallel to the rotation axis for sufficiently strong perturbations. An instability sets in at critical amplitudes with ε_crit ∝ Re^—1. The whole flow turns out to be almost axisymmetric and nonturbulent exhibiting, however, a very rich radial and latitudinal structure. The Reynolds stress 〈u′_ru′_ϕ〉 is positive in the entire computational domain, from its Gaussian radial profile a positive viscosity‐alpha of about 10^—4 is derived. The kinetic energy of the turbulent state is dominated by the azimuthal component 〈u^′2_ϕ whereas the other components are smaller by two orders of magnitude. Our simulations reveal, however, that these structures disappear as soon as the perturbations are switched off. We did not find an “effective” perturbation whose amplitude is such that the disturbance is sustained for large times (cf. Dauchot & Daviaud 1995) which is due to the effective violation of the Rayleigh stability criterion. The fluctuations rapidly smooth the original profile towards to pure Kepler flow which, therefore, proves to be stable in that sense.     

Scattering of radiowaves from cosmic sources in the solar corona

The scattering of radiowaves in the outer solar corona is discussed. Results are given of the decametric wave observations. In the theoretical analysis both regular refraction and the gradients in the electron density fluctuations are considered. The theory is in satisfactory agreement with the experimental data. From their comparison the ratio n=(l _r /l _t ) is deduced of the correlation scales in the radial (l _r )and transverse directions. This value is not equal to the ratio of the observed distribution dimensions. The frequency dependence of the angular spectrum rms width is not λ² at longer wavelengths. At small separations from the Sun, however, the rms angular size cannot serve as the only characteristic of the spectrum, the latter being non-Gaussian. Referred to in the paper as the Ukr. IRE.     

Internal rotation of the Sun as inferred from GONG observations

Helioseismology is a direct and most informative method of studying the structure and dynamics of the Sun. Determining the internal differential rotation of the Sun requires that the frequencies of its eigentones be estimated with a high accuracy, which is possible only on the basis of continuous long-term observations. The longest quasi-continuous series of data have been obtained by the Global Oscillation Network Group (GONG). The parameters of each individual mode of solar acoustic oscillations with low spherical degrees l=0, 1, 2, 3, 4, 5, 6 are determined by using 1260-day-long series of GONG observations. The mean frequency splitting by rotation for the modes of each radial order n is calculated by using all possible combinations between the eigenfrequencies in multiplets. As a result, it has become possible to statistically estimate the splitting and its measurement errors for the modes of each radial order. The mean splitting for each given degree l=1–6 is presented under the assumption of its independence of oscillation frequency, which holds for the achieved accuracy. The frequencies and splittings for the modes with low spherical degrees l, together with the MDI group results for higher degrees l, are used to invert the radial profile of solar angular velocity. Using the SOLA method to solve the inverse problem of restoring the rotation profile has yielded solutions sensitive to the deepest stellar interiors. Our results indicate that the solar core rotates faster than the surface, and there may be a local minimum in angular velocity at its boundary.     

Structure of the 5-minute solar oscillations 1976–1980

The discrete structure in the 5 min velocity oscillations of the solar surface has been confirmed by a re-analysis of data obtained between 1976 and 1979, and in addition a preliminary analysis of 1980 data show excellent consistency of the determined frequencies over the five year period. It is further shown that atmospheric transparency, as measured by the power in the solar intensity fluctuations, shows no correlation with the measured amplitude of the velocity fluctuations, over 2 orders of magnitude.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

An attempt to identify low l - low n solar acoustic modes

The low l solar acoustic spectrum has been measured with great accuracy (v/v 10^–4), for intermediate radial order modes, 11 n 34 (Jiménez et al., 1986; Grec, Fossat, and Pomerantz, 1983; Pallé et al., 1986). The measurement of the frequencies of modes of lower n, up to the fundamental one, are very important as they depart from asymptotic behaviour and, therefore, put more severe constraints on solar models. However, their amplitudes are very low (under 2 cm s^–1) and when compared to the solar velocity background noise (Jiménez et al., 1986), a S/N 1 is obtained. Taking advantage of the fact that lifetimes seem to be higher at lower frequencies (lower n values) (Jefferies et al., 1988; Elsworth et al., 1990), very long Doppler velocity measurements, obtained at Teide Observatory, have been used to increase S/N, therefore, providing the possibility to detect such modes. The frequencies observed are compared to those predicted by a solar model (Christensen-Dalsgaard, Däppen, and Lebreton, 1988), using the best equation of state yet computed (Mihalas, Däppen, and Hummer, 1988).     

Velocities of beam-plasma structures at their propagation in the solar corona

It was found recently that fast electrons travel through the plasma of the solar corona in the form of beam-plasma structure (BPS), which consists of electrons and Langmuir waves. In this paper the influence of scattering BPS Langmuir waves off plasma ions (l+i=l+i) on BPS velocity is studied. We show that the maximum BPS velocity equals 0.35c, which is close to the velocity of Type III bursts sources.     

Solar oscillations: Past,present, and future

Observation of global oscillations of the Sun constitutes a primitive seismology of the solar interior. The frequencies, if correctly identified with definite normal modes of vibration, provide a measure of the average velocity of sound in the interior and thereby of its composition and temperature. Fine structure in the frequencies of nonradial modes may provide information on their character (multiplicity) and on the rotation of the solar interior. Study of the amplitudes and phase fluctuations of the vibrations may clarify the excitation and damping of the vibrations.After a brief historical review emphasizing global velocity spectroscopy an account is given of the present status of the observations of global oscillations in the range of periods of 3 to 160 min.Finally the future capabilities of the observational techniques and their resultant potential is discussed.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Preliminary Results on the Solar Photospheric Dynamics Observed with Vamos

The intensity and velocity fluctuations, observed simultaneously, are a powerful diagnostic tool of the dynamics of the solar atmosphere. The phase relation between the fluctuations can improve our knowledge of the solar background, its relation with the acoustic sources, and its interaction with the solar acoustic oscillations. Furthermore, the opposite asymmetries observed along the p-mode line profiles in the intensity and velocity power spectra contain information about the source of the solar acoustic oscillations. For these reasons, it is relevant to study the height dependence of the asymmetries and phases in the solar atmosphere. In this paper, we present the results from the analysis of observations performed by the VAMOS instrument in the potassium 769.9 nm line and Na i D lines, and compare the measured phases with those obtained at different layers in the solar atmosphere by different instruments, spanning from the base of the photosphere to the low chromosphere.     

Large density fluctuations in the martian ionosphere as observed by the Mars Express radar sounder

The MARSIS (Mars Advanced Radar for Subsurface and Ionosphere Sounding) instrument on the Mars Express spacecraft provides both local and remote measurements of electron densities and measurements of magnetic fields in the martian ionosphere. The density measurements show a persistent level of large fluctuations, sometimes as much as a factor of three or more at high altitudes. Large magnetic field fluctuations are also observed in the same region. The power spectrums of both the density and magnetic field fluctuations have slopes on a log-log plot that are consistent with the Kolmogorov spectrum for isotropic fluid turbulence. The fractional density fluctuation, Δn_e/n_e, of the turbulence increases with altitude, and reaches saturation, Δn_e/n_e ∼ 1, at an altitude of about 400 km, near the nominal boundary between the ionosphere and the magnetosheath. The fluctuations are usually so large that a well-defined ionopause-like boundary between the ionosphere and the solar wind is seldom observed. Of mechanisms that could be generating this turbulence, we believe that the most likely are (1) solar wind pressure perturbations, (2) an instability in the magnetosheath plasma, such as the mirror-mode instability, or (3) the Kelvin-Helmholtz instability driven by velocity shear between the rapidly flowing magnetosheath and the ionosphere.     

Inhomogeneities in the solar atmosphere from the CaII infra-red lines

From a time sequence of high dispersion spectra taken by Evans, the solar fine structures are studied in the Caii infra-red triplet. The Doppler shifts and the intensity fluctuations in different points of the profiles are converted into fluctuations of the model atmosphere. A weighting function method is worked out in that purpose. The theoretical line profiles are computed in non LTE from a program written by Dumont. The results are arranged in two parts:

1. Low temporal frequencies. A three-column model describes the steady field of temperature, microturbulence and radial velocities fluctuations in the photosphere-chromosphere transition zone.
2. Oscillations. The propagation of waves is considered in the three above-mentioned columns. The oscillation amplitudes seem statistically larger in the hot column. The vertical phase velocity is very large, even for frequencies higher than the cut-off frequency of acoustic waves. Velocity and temperature fluctuations are connected by different curves of phase-lags and amplitude ratios suggesting a short relaxation time of the temperature fluctuations in the low chromosphere.

     

Quenching of the beam-plasma instability by large-scale density fluctuations in 3 dimensions

A model is presented to explain the highly variable yet low level of Langmuir waves measured in situ by spacecraft when electron beams associated with type III solar bursts are passing by; the low level of excited waves allows the propagation of such streams from the Sun to well past 1 AU without catastrophic energy losses. The model is based, first, on the existence of large-scale density fluctuations that are able to efficiently diffuse small-k beam-unstable Langmuir waves in phase space, and, second, on the presence of a significant isotropic non-thermal tail in the distribution function of the background electron population, which is capable of stabilizing larger k modes. The strength of the model lies in its ability to predict various levels of Langmuir waves depending on the parameters. This feature is consistent with the high variability actually observed in the measurements. The calculations indicate that, for realistic parameters, the most unstable, small k modes are fully stabilized while some oblique mode with higher k and lower growth rate might remain unstable; thus a very broad range of levels of Langmuir waves is possible from levels of the order of enhanced spontaneous emission to the threshold level for nonlinear processes. On the other hand, from in situ measurements of the density fluctuations spectrum by ISEE-1 and 2 in the vicinity of the Earth, it is shown that measured 100 km scale fluctuations may be too effective in quenching the instability. If such strong density fluctuations are common in the solar wind, we show they must be highly anisotropic in order to allow the build-up of Langmuir waves to the observed mV m^–1 range. Moreover, the anisotropy must be such that the strongest variations of density occur in a plane perpendicular to the magnetic field.     

Low-l 5-min oscillation observations

Medium resolution CCD-spectrograph observations have been obtained that are suitable for studying long spatial wavelength 5-min oscillations. We find evidence that at wavelengths of order one solar radius the oscillation field is not isotropic. It is also not well described by modes of uniform excitation. The velocity power density per spherical harmonic increases with decreasing l to 1.1 × 10³ cm² s^–2 per 3.5 × 10^–4 Hz angular frequency bandwidth at l = 4. These results are inconsistent with the data of Fossat and Ricort (1975) as analyzed by Christensen-Dalsgaard and Gough (1982), who found a substantially constant modal amplitude at intermediate l values. It is interesting that other calculations have seen a similar dependence at small l in the growth rate of p-modes due to the -mechanism.Visiting Astronomer, Sacramento Peak Observatory.     

IN-FLIGHT PERFORMANCE OF THE VIRGO LUMINOSITY OSCILLATIONS IMAGER ABOARD SOHO

The Luminosity Oscillations Imager (LOI) is a part of the VIRGO instrument aboard the Solar and Heliospheric Observatory (SOHO). The scientific objective of the LOI experiment is to identify and characterize pressure and internal gravity oscillations of the Sun by observing the radiance variations. The LOI is a low-resolution imager with 12 pixels, for the measurement of the radiance distribution over the solar disk at 500 nm. The low resolution capability of the instrument allows the identification of individual azimuthal orders for l = 0 to 7, without suffering the mixing that affects integrated solar disk instruments. The performance, calibrations and instrumental effects of the LOI are described together with the procedures for extracting the solar p modes.     

The radial evolution of the IMF fluctuations: A comparison with theoretical models

We conducted an analysis of the radial evolution of the wave phenomena observed in the inner solar system and associated with the high velocity solar wind stream pattern. The combined interplanetary magnetic field observations performed by Helios-1 and Helios-2 spacecraft allow to draw the following conclusions: (a) The compressive contribution to field fluctuations with periods less than 6 hr is observed to increase with the increasing heliocentric distance and the total variance of the field components decreases appreciably faster than r ^–3. (b) When compared with theoretical models, Helios observations confirm a better agreement with wave modes which saturate at a constant value of the ratio between the wave energy density and the ambient field energy density.Also at Istituto per il Plasma nello Spazio, CNR, Frascati, Italy.     

Frequencies of low-degree solar acoustic oscillations and the phase of the solar cycle

A study of the solar total irradiance data of the Active Cavity Radiometer Irradiance Monitor (ACRIM) on the Solar Maximum Mission (SMM) satellite shows a small but formally significant shift in the frequencies of solar acoustic (p-mode) oscillations between the epochs of maximum and minimum solar activity. Specifically, the mean frequency of the strongest p-mode resonances of low spherical-harmonic degree (l = 0–2) is approximately 1.3 parts in 10⁴ higher in 1980, near the time of sunspot maximum, than in 1985, near sunspot minimum. The observed frequency shift may be an 11-yr effect but the precise mechanism is not clear.     

Amplitude distributions of solar photospheric fluctuations

Amplitude distributions, which are nearly Gaussian, have been calculated for radial velocity, continuum brightness, spectral line equivalent width and spectral line central residual intensity fluctuations measured from high-dispersion high-resolution spectrograms taken at the center of the solar disk. The RMS and skewness S for each distribution have been calculated in a manner which allows testing of the homogeneity of the granulation pattern (i.e. variations in its statistics across the solar disk and with time). Pattern inhomogeneity across the disk is strongly indicated, and further evidence suggesting appreciable pattern persistence over time intervals 15 minutes is presented. The possibilities for investigations of S and its associated bi-spectrum are discussed. The qualitative values of S obtained are shown not to be due to unusually bright, rising granules (though a statistical tendency towards such granules is possible). An attempt to explain S for continuum brightness fluctuations in terms of the nonlinear effects of Planckian emission and opacity fluctuations in a stratified photosphere, leads to contradiction with the measured amplitude distributions, a contradiction which is probably due to an oversimplified treatment of radiative transfer in an inhomogeneous photosphere.     

Dynamics of a cloud of fast electrons travelling through the plasma

A simulation of normal type III radio bursts has been made in a whole frequency range of about 200 MHz to 30 kHz by the usage of the semi-analytical method as developed in previous papers for the plasma waves excited by a cloud of fast electrons. Three-dimensional plasma waves are computed, though the velocities of fast electrons are assumed to be one-dimensional. Many basic problems about type III radio bursts and associated solar electrons have been solved showing the following striking or unexpected results.Induced scattering of plasma waves, by thermal ions, into the plasma waves with opposite wave vectors is efficient even for a solar electron cloud of rather low number density. Therefore, the second harmonic radio emission as attributed to the coalescence of two plasma waves predominates in a whole range from meter waves to km waves. Fundamental radio emission as ascribed to the scattering of plasma waves by thermal ions is negligibly small almost in the whole range. On the other hand, third harmonic radio emission can be strong enough to be observed in a limited frequency range.If, however, the time integral of electron flux is, for example, 2 × 10¹³ cm^–2 (>5 keV) or more at the height of 4.3 × 10¹⁰ cm ( _p = 40 MHz) above the photosphere, the fundamental may be comparable with or greater than the second harmonic, but an effective area of cross-section of the electron beam is required to be very small, 10¹⁷ cm² or less, and hence much larger sizes of the observed radio sources must be attributed to the scattering alone of radio waves.The radio flux density expected at the Earth for the second harmonic can increase with decreasing frequencies giving high flux densities at low frequencies as observed, if x-dependence of the cross-sectional area of the electron beam is x ^1.5 or less instead of x ², at least at x 2 × 10¹² cm.The second harmonic radio waves are emitted predominantly into forward direction at first, but the direction of emission may reverse a few times in a course of a single burst showing a greater backward emission at the low frequencies.In a standard low frequency model, a total number of solar electrons above 18 keV arriving at the Earth orbit reduces to 12% of the initial value due mainly to the collisional decay of plasma waves before the waves are reabsorbed by the beam electrons arriving later. However, no deceleration of the apparent velocity of exciter appears. A change in the apparent velocity, if any, results from a change in growth rate of the plasma waves instead of the deceleration of individual electrons.Near the Earth, the peak of second harmonic radio flux as emitted from the local plasma appears well after the passage of a whole solar electron cloud through this layer. This is ascribed to the secondary and the third plasma waves as caused in non-resonant regions by the induced scattering of primary plasma waves in a resonant region.     

Periodicities of Jovian broad-band kilometric radiation observed by Ulysses

Observations of the Unified Radio and Plasma Wave (URAP) instrument onboard the Ulysses spacecraft have been used to analyze periods inherent in the Jovian broad-banded kilometric radio emission (bKOM) between 29 and 47 kHz. It is demonstrated, by using power spectrum analysis and linear prediction time filtering that the long-term fluctuations of the bKOM signal are triggered by the solar wind, particularly by the solar wind density, while no association was found with the solar wind velocity. In addition, there seem to be some inherent periodicities in the bKOM events which cannot be fully attributed to the influence of solar wind plasma quantities by these techniques.     

Periods and stability of solar g-modes

We consider the rotation independent (m = 0) frequencies of Hill and Gu (1988) and Henning and Scherrer (1988). Comparison with Cox, Guzik, and Kidman (CGK) frequencies shows that CGK are systematically 5.7 ± 0.7% larger. This effect may be due to the larger central density in this model (162 g cm^–3) compared to the real Sun. A known systematic error of about one percent in the pressure calculated by the Iben (1965) procedure can account for the higher CGK central helium and density. A check of this increase of g-mode frequency with central density is made by calculating g-mode frequencies for a WIMP model with a central density of 210 g cm^–3. This 30% density increase gives a 17% frequency increase, and implies a law with frequency increasing with the 17/30 power of the central density. Thus the 5.7% decrease of frequencies from the model to the real Sun indicates a central density decrease of about 9.7% to about 147 g cm^–3. Comparison with the recent van der Raay g-mode frequencies shows that the CGK model frequencies are about 14% larger, as one would expect for these observed frequencies with a large P ₀ of 41.2 min.Destabilizing mechanisms of the normal -effect at the top of the convection zone and convection blocking at the bottom of the convection zone for low order and low-l g-modes produces pulsation driving that does not seem to be damped by radiation and convection effects at the surface. Since the surface motions are very small, photospheric damping does not stabilize these modes at it does for the 5-min p-modes. For higher-order and degree modes, deep damping by radiation flow across nodes overwhelms the destabilization and any small effect.     

A large-eddy simulation of turbulent compressible convection: differential rotation in the solar convection zone

We present the results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shell. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong meridional circulation, which traverses the entire depth. The second simulation has isorotation contours about mid-way between cylinders and cones, and a weak meridional circulation, concentrated in the uppermost part of the shell.
We show that the solar differential rotation is directly related to a latitudinal entropy gradient, which pervades into the deep layers of the convection zone. We also offer an explanation of the angular velocity shear found at low latitudes near the top. A non-zero correlation between radial and zonal velocity fluctuations produces a significant Reynolds stress in that region. This constitutes a net transport of angular momentum inwards, which causes a slight modification of the overall structure of the differential rotation near the top. In essence, the thermodynamics controls the dynamics through the Taylor–Proudman momentum balance . The Reynolds stresses only become significant in the surface layers, where they generate a weak meridional circulation and an angular velocity 'bump'.