Turbulent convection in protoplanetary discs and its role in angular momentum transfer

We present a model for the transport of anisotropic turbulence in an accretion disc. The model uses the Reynolds stress tensor approach in the mean field approximation. To study the role of convection in a protoplanetary disc, we combine the turbulence model with a radiative transfer calculation, and also include convection using the mixing length approximation. We find that the turbulence generated by convection causes the angular momentum of the accretion disc to be directed outwards. We also confirm the conclusions of other authors that turbulent convection is unable to provide the observed disc accretion rates as well as a heat source sufficient for the convection to be self-sustaining. The reasons for the latter are the strong anisotropy of the turbulence together with the low efficiency of the energy transfer from the background velocity shear to the turbulent stress tensor.Comment: MNRAS accepted | 15 pages, 8 figure

An approximation of matrix exponential by a truncated Laguerre series

The Laguerre functions $l_{n,\tau}^\alpha$, $n=0,1,\dots$, are constructed from generalized Laguerre polynomials. The functions $l_{n,\tau}^\alpha$ depend on two parameters: scale $\tau>0$ and order of generalization $\alpha>-1$, and form an orthogonal basis in $L_2[0,\infty)$. Let the spectrum of a square matrix $A$ lie in the open left half-plane. Then the matrix exponential $H_A(t)=e^{At}$, $t>0$, belongs to $L_2[0,\infty)$. Hence the matrix exponential $H_A$ can be expanded in a series $H_A=\sum_{n=0}^\infty S_{n,\tau,\alpha,A}\,l_{n,\tau}^\alpha$. An estimate of the norm $\Bigl\lVert H_A-\sum_{n=0}^N S_{n,\tau,\alpha,A}\,l_{n,\tau}^\alpha\Bigr\rVert_{L_2[0,\infty)}$ is proposed. Finding the minimum of this estimate over $\tau$ and $\alpha$ is discussed. Numerical examples show that the optimal $\alpha$ is often almost 0, which essentially simplifies the problem.Comment: 20 pages, 4 figure

Sulfur Isotopic Measurements from a West Antarctic Ice Core: Implications for Sulfate Source and Transport

Measurements of delta(34)S covering the years 1935-76 and including the 1963 Agung (Indonesia) eruption were made on a West Antarctic firn core, RIDSA (78.73 degrees S, 116.33 degrees W; 1740m a.s.l.), and results are used to unravel potential source functions in the sulfur cycle over West Antarctica. The delta(34)S values Of SO42- range from 3.1 parts per thousand to 9.9 parts per thousand. These values are lower than those reported for central Antarctica, from near South Pole station, of 9.3-18.1 parts per thousand (Patris and others, 2000). While the Agung period is isotopically distinct at South Pole, it is not in the RIDSA dataset, suggesting differences in the source associations for the sulfur cycle between these two regions. Given the relatively large input of marine aerosols at RIDSA (determined from Na+ data and the seasonal SO42- cycle), there is likely a large marine biogenic SO42- influence. The delta(34)S values indicate, however, that this marine biogenic SO42-, with a well-established delta(34)S of 18 parts per thousand, is mixing with SO42- that has extremely negative delta(34)S values to produce the measured isotope values in the RIDSA core. We suggest that the transport and deposition of stratospheric SO42- in West Antarctica, combined with local volcanic input, accounts for the observed variance in delta(34)S values