Rayleigh-Bénard konvektion.

Sammanfattning: Abstract Consider a 　uid being heated from below. The heating leads to an upward convective force that is counteracted by the viscous forces of the 　uid. If the convective force is large enough in comparison to the viscous forces the 　uid will be put in an unstable state. This means that a small disturbance will give rise to a 　ow driven by a temperature gradient. This 　ow is characterised by a pattern of convection cells. The phenomenon is called Rayleigh-Bénard convection. An example of this can be seen when heating a pot of oil from below. A part of the contribution to the formation of these cells is attributed to the variation of surface tension due to heating. This contribution is of less signicance when the 　uid layer is thicker. In this report the studied 　ow eld lies between two plates where the convective force drives the motion. The in　uence of surface tension is eliminated since the 　uid lacks a free surface in this problem. The boundary between stability and instability is investigated both theoretically, using simplied Navier-Stokes equations, and by simulation using a DNS-code with the program Simson(Chevalier et al., 2007). The simulation also makes it possible to see the shape of the convection cells. The results is presented in stability diagrams that describe how the stability boundary is aected by the wavelength, related to the wave number K, of the applied disturbance and the dimensionless Rayleigh number, Ra. The critical value for the two parameters is found to be Ra= 1708whenK= 3:12 Finally the similarity between the simplied theory and the more realistic simulation is discussed.