Reynolds stress and heat flux in spherical shell convection

Context. Turbulent fluxes of angular momentum and heat due to rotationally affected convection play a key role in determining differential rotation of stars. Aims. We compute turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. Methods. We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong 'banana cells'. Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance.

Ajan sisäkkäiset tilat. Arkkitehtuuri, valokuva ja menneisyyden esittäminen W. G. Sebaldin romaanissa Austerlitz

In her thesis, Kaisa Kaakinen analyzes how the German emigrant author W. G. Sebald (1944-2001) uses architecture and photography in his last novel "Austerlitz" to represent time, history and remembering. Sebald describes time in spatial terms: it is like a building, the rooms and chambers of which are connected to each other. The poetics of spatial time manifests itself on multiple levels of the text. Kaakinen traces it in architectural representations, photographic images, intertextuality, as well as in the form of the text, using the concept of spatial form by Joseph Frank. Architectural and photographic representations serve as meeting points for different aspects and angles of the novel and illustrate the idea of a layered present that has multiple connections to the past. The novel tells a story of Jacques Austerlitz, who as a small child was sent from Prague to Britain in one of the so-called Kindertransports that saved children from Central Europe occupied by the National Socialists. Only gradually he remembers his Jewish parents, who have most likely perished in Nazi concentration camps. The novel brings the problematic of writing about another person's past to the fore by the fact that Austerlitz's story is told by an anonymous narrator, Austerlitz's interlocutor, who listens to and writes down Austerlitz's story. Kaakinen devotes the final part of her thesis to study the demands of representing a historical trauma, drawing on authors such as Dominick LaCapra and Michael Rothberg. Through the analysis of architectural and photographic representations in the novel, she demonstrates how Austerlitz highlights the sense of singularity and inaccessibility of memories of an individual, while also stressing the necessity - and therefore a certain kind of possibility - of passing these memories to another person. The coexistence of traumatic narrowness and of the infinity of history is reflected in ambivalent buildings. Some buildings in the novel resemble reversible figures: they can be perceived simultaneously as ruins and as construction sites. Buildings are also shown to be able to both cover and preserve memories - an idea that also is repeated in the use of photography, which tends to both replace memories and cause an experience of the presence of an absent thing. Commenting and critisizing some recent studies on Sebald, the author develops a reading which stresses the ambivalence inherent in Sebald's view on history and historiography. Austerlitz shows the need to recognize the inevitable absence of the past as well as the distance from the experiences of others. Equally important, however, is the refusal to give up narrating the past: Sebald's novel stresses the necessity to preserve the sites of the past, which carry silent traces of vanished life. The poetics of Austerlitz reflects the paradox of the simultaneous impossibility and indispensability of writing history.

Local numerical modelling of magnetoconvection and turbulence - implications for mean-field theories

During the last decades mean-field models, in which large-scale magnetic fields and differential rotation arise due to the interaction of rotation and small-scale turbulence, have been enormously successful in reproducing many of the observed features of the Sun. In the meantime, new observational techniques, most prominently helioseismology, have yielded invaluable information about the interior of the Sun. This new information, however, imposes strict conditions on mean-field models. Moreover, most of the present mean-field models depend on knowledge of the small-scale turbulent effects that give rise to the large-scale phenomena. In many mean-field models these effects are prescribed in ad hoc fashion due to the lack of this knowledge. With large enough computers it would be possible to solve the MHD equations numerically under stellar conditions. However, the problem is too large by several orders of magnitude for the present day and any foreseeable computers. In our view, a combination of mean-field modelling and local 3D calculations is a more fruitful approach. The large-scale structures are well described by global mean-field models, provided that the small-scale turbulent effects are adequately parameterized. The latter can be achieved by performing local calculations which allow a much higher spatial resolution than what can be achieved in direct global calculations. In the present dissertation three aspects of mean-field theories and models of stars are studied. Firstly, the basic assumptions of different mean-field theories are tested with calculations of isotropic turbulence and hydrodynamic, as well as magnetohydrodynamic, convection. Secondly, even if the mean-field theory is unable to give the required transport coefficients from first principles, it is in some cases possible to compute these coefficients from 3D numerical models in a parameter range that can be considered to describe the main physical effects in an adequately realistic manner. In the present study, the Reynolds stresses and turbulent heat transport, responsible for the generation of differential rotation, were determined along the mixing length relations describing convection in stellar structure models. Furthermore, the alpha-effect and magnetic pumping due to turbulent convection in the rapid rotation regime were studied. The third area of the present study is to apply the local results in mean-field models, which task we start to undertake by applying the results concerning the alpha-effect and turbulent pumping in mean-field models describing the solar dynamo.