Transition in inclined internally heated fluid layers

Non-linear solutions and studies of their stability are presented for flows in a homogeneously heated fluid layer under the influence of a constant pressure gradient or when the mass flux across any lateral cross-section of the channel is required to vanish. The critical Grashof number is determined by a linear stability analysis of the basic state which depends only on the z-coordinate perpendicular to the boundary. Bifurcating longitudinal rolls as well as secondary solutions depending on the streamwise x-coordinate are investigated and their amplitudes are determined as functions of the supercritical Grashof number for various Prandtl numbers and angles of inclination of the layer. Solutions that emerge from a Hopf bifurcation assume the form of propagating waves and can thus be considered as steady flows relative to an appropriately moving frame of reference. The stability of these solutions with respect to three-dimensional disturbances is also analyzed in order to identify possible bifurcation points for evolving tertiary flows.

Pattern competition in homogeneously heated fluid layers

Simulations examining pattern competition have been performed on a horizontal homogeneously heated layer that is bounded by an isothermal plane above an adiabatic plane. Several different circulation patterns arose as the heating regime applied to the horizontal layer was modified. The sequence of the patterns formed as the Grashof number was increased had the following order: laminar, z-axis rolls, squares, hexagons and pentagons, pentagons and then two different square modes of differing orientations. Fourier analysis was used to determine how the key modes interact in the presence of different patterns.

Range of validity of weakly non-linear theory in Rayleigh-Bénard convection

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

Europäische Nachbarschaftspolitik:Entstehung, Effektivität, Herausforderungen

„Ich wünsche mir einen Ring von Freunden um die Europäische Union und ihre engsten Nachbarn herum, von Marokko bis Russland und zum Schwarzen Meer“, formulierte Kommissionspräsident Romano Prodi bereits im Jahr 2002. Für die Gestaltung kooperativer Beziehungen zu diesem Ring von Freunden ist die Europäische Nachbarschaftspolitik (ENP) das jüngste Instrument der Europäischen Union. Die Kooperationen erfolgen in einer Reihe verschiedener Politikfelder und sollen dazu dienen, Stabilität, Sicherheit und Wohlstand an den Außengrenzen der EU zu sichern. Ziel dieses Beitrags ist es, einen Überblick über die Europäische Nachbarschaftspolitik (ENP) zu geben, insbesondere über ihre Gründung und Entwicklung, ihre zentralen Institutionen und Entscheidungsprozesse sowie die Debatte um ihre Wirksamkeit. Der Beitrag schließt mit einem Überblick über Forschungslücken und offene Fragen, die weitere Forschungsarbeiten zur ENP anregen sollen.