Differential rotation and meridional flow in the solar supergranulation layer: Measuring the eddy viscosity

We measure the eddy viscosity in the outermost layers of the solar convection zone by comparing the rotation law computed with the Reynolds stress resulting from f-plane simulations of the angular momentum transport in rotating convection with the observed differential rotation pattern. The simulations lead to a negative vertical and a positive horizontal angular momentum transport. The consequence is a subrotation of the outermost layers, as it is indeed indicated both by helioseismology and the observed rotation rates of sunspots. In order to reproduce the observed gradient of the rotation rate a value of about 1.5 x 10^{13} cm/s for the eddy viscosity is necessary. Comparison with the magnetic eddy diffusivity derived from the sunspot decay yields a surprisingly large magnetic Prandtl number of 150 for the supergranulation layer. The negative gradient of the rotation rate also drives a surface meridional flow towards the poles, in agreement with the results from Doppler measurements. The successful reproduction of the abnormally positive horizontal cross correlation (on the northern hemisphere) observed for bipolar groups then provides an independent test for the resulting eddy viscosity.Comment: 6 pages, 8 figures, Astronomy and Astrophysics (subm.

Observation and Modeling of the Solar-Cycle Variation of the Meridional Flow

We present independent observations of the solar-cycle variation of flows near the solar surface and at a depth of about 60 Mm, in the latitude range $\pm45^\circ$. We show that the time-varying components of the meridional flow at these two depths have opposite sign, while the time-varying components of the zonal flow are in phase. This is in agreement with previous results. We then investigate whether the observations are consistent with a theoretical model of solar-cycle dependent meridional circulation based on a flux-transport dynamo combined with a geostrophic flow caused by increased radiative loss in the active region belt (the only existing quantitative model). We find that the model and the data are in qualitative agreement, although the amplitude of the solar-cycle variation of the meridional flow at 60 Mm is underestimated by the model.Comment: To be published in Solar Physcis Topical Issue "Helioseismology, Asteroseismology, and MHD Connections

Solar-cycle variation of the sound-speed asphericity from GONG and MDI data 1995-2000

We study the variation of the frequency splitting coefficients describing the solar asphericity in both GONG and MDI data, and use these data to investigate temporal sound-speed variations as a function of both depth and latitude during the period from 1995-2000 and a little beyond. The temporal variations in even splitting coefficients are found to be correlated to the corresponding component of magnetic flux at the solar surface. We confirm that the sound-speed variations associated with the surface magnetic field are superficial. Temporally averaged results show a significant excess in sound speed around 0.92 solar radii and latitude of 60 degrees.Comment: To be published in MNRAS, accepted July 200

Time series of high resolution photospheric spectra in a quiet region of the Sun. I. Analysis of global and spatial variations of line parameters

A 50 min time series of one-dimensional slit-spectrograms, taken in quiet sun at disk center, observed at the German Vacuum Tower Telescope (Observatorio del Teide), was used to study the global and spatial variations of different line parameters. In order to determine the vertical structure of the photosphere two lines with well separated formation heights have been considered. The data have been filtered of p-modes to isolate the pure convective phenomenon. From our studies of global correlation coefficients and coherence and phase shift analyzes between the several line parameters, the following results can be reported. The convective velocity pattern preserves structures larger than 1.0" up to the highest layers of the photosphere (~ 435 km). However, at these layers, in the intensity pattern only structures larger than 2.0" are still connected with those at the continuum level although showing inverted brightness contrast. This confirms an inversion of temperature that we have found at a height of ~140 km. A possible evidence of gravity waves superimposed to the convective motions is derived from the phase shift analysis. We interpret the behavior of the full width at half maximum and the equivalent width as a function of the distance to the granular borders, as a consequence of enhanced turbulence and/or strong velocity gradients in the intergranular lanes.Comment: 16 pages, 15 figures, 5 tables; Astronomy & Astrophysics, Volume 408, p.363-378, 200

Deeply penetrating banded zonal flows in the solar convection zone

Helioseismic observations have detected small temporal variations of the rotation rate below the solar surface corresponding to the so-called `torsional oscillations' known from Doppler measurements of the surface. These appear as bands of slower and faster than average rotation moving equatorward. Here we establish, using complementary helioseismic observations over four years from the GONG network and from the MDI instrument on board SOHO, that the banded flows are not merely a near-surface phenomenon: rather they extend downward at least 60 Mm (some 8% of the total solar radius) and thus are evident over a significant fraction of the nearly 200 Mm depth of the solar convection zone.Comment: 4 pages, 4 figures To be published in ApJ Letters (accepted 3/3/2000

Midterm Results After Subtrochanteric End-to-Side Valgization Osteotomy in Severe Infantile Coxa Vara

Background: For the treatment of the severe infantile coxa vara it is mandatory for the orthopaedic surgeon to observe the mechanobiology of the growing hip before and after the surgical intervention. We hereby would like to present our experiences with the subtrochanteric end-to-side valgization osteotomy and to compare the procedure with the alternatively used Y-shaped osteotomy as described by Pauwels. Methods: Thirteen patients (20 hips) who had undergone subtrochanteric end-to-side valgization were followed for a mean 6.2 years (range, 0.8 to 12.8 y). At the time of surgery the mean age was 7.1 years (range, 2.0 to 13.3 y), last follow-up examination was performed at a mean of 13.4 years of age (range, 5.1 to 18.3 y). The deformities were etiologically based on 5 entities: congenital coxa vara (n = 1), osteochondrodysplasias (n = 12), postosteomyelitic coxa vara (n = 5), and avascular femoral head necrosis in the course of congenital dysplasia of the hip (n = 2). The follow-up rate was 100%. In addition, we analyzed a total of 93 pelvic radiographies with a total of 139 hip joints. Thirty angles and distances were assessed according to parameters described in the literature. Results: Although preoperatively 12 patients presented with a positive Trendelenburg's sign, it was only present postoperatively in 2 patients. Duchenne's limp reduced from 10 to 1. All of the 15 preoperatively apparent nonunions could be healed by means of surgery. Two hips redeveloped pathologically lowered collodiaphyseal angles postoperatively, one of which had to undergo revision surgery. Preoperatively 15 out of 20 patients (75%) showed nonunions all of which healed after surgery. No recurrence could be seen at the time of the last follow-up. The following angles were assessed on plain radiographies of the pelvis preoperatively and directly postoperatively as well as on the last follow-up at a mean of 85 months: CCD-angle 98 degrees/156 degrees/144 degrees, EY-angle 55 degrees/5 degrees/15.7 degrees, AY-angle 32 degrees/75 degrees/66 degrees, CE-angle 20 degrees/25 degrees/18 degrees, AC-angle 20 degrees/18 degrees/20 degrees. The articulotrochanteric distance was 5 mm/26 mm/14 mm. Conclusions: The subtrochanteric end-to-side valgization osteotomy showed to be highly effective in the management of the infantile coxa vara, improving the clinical impairment of the patients postoperatively. All of the preoperatively present nonunions showed osseous consolidation at follow-up examination. Only minor revarization tendencies could be found. The procedure is technically less demanding, safer and more efficient regarding the lengthening of the affected limb in comparison to the Y-shaped intertrochanteric osteotomy as described by Pauwels. Level of Evidence: Case-control study (EBM-level III)

Online Multi-Coloring with Advice

We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.Comment: IMADA-preprint-c