System size determines turbulent state transition
Researchers of the Foundation for Fundamental Research on Matter (FOM), University of Twente, Eindhoven University of Technology and the University of California in Santa Barbara (United States) have shown that the sharp transition between different turbulent regimes is the result of the limited size of the system. They had previously shown that there are two different forms of turbulence. This was major news, because scientists had always thought that there was only one state of fully developed turbulence. The researchers published their latest findings in the renowned journal Physical Review Letters last Friday.
Rayleigh-Bénard convection
Fluids between two horizontal plates, with the lower plate at a higher temperature than the top plate, show convection behaviour when there is a large enough temperature difference between the plates. The fluid near the lower plate is warmer and therefore lighter than the fluid above, which results in it flowing upwards. The reverse happens near the top plate. This phenomenon is called Rayleigh-Bénard convection. To investigate the effect of rotation on this heat transport, the system is rotated around its vertical axis. 'The effect of rotation is relevant to an improved understanding of many astrophysical and geophysical phenomena, such as convection in the oceans, the earth's mantle, on the inside of large gas planets and in the outermost layer of the sun because rotation also plays an important role there,' explains researcher Richard Stevens.
Two turbulent states
Since Kolmogorov's pioneering work in 1941, scientists have always thought that there was only one state of fully developed turbulence. The researchers have used experiments and numerical simulations of rotating Rayleigh-Bénard convection to show that there are two distinct forms of turbulence: one weakly rotating state dominated by a large-scale convection roll in the entire cell and one strongly rotating state dominated by local vortices. An illustration of the two states, based on the results of simulations performed as part of a DEISA project in the Huygens Cluster of SARA, is shown in Figure 1.
The researchers' latest findings demonstrate that the transition between the two states is the result of the finite size of the system. These results build on the bifurcation theory for low-dimensional chaos.
Theory and practice
The regime dominated by the convection roll does not exist for infinitely large systems with an infinite speed of rotation. Kolmogorov's theorem only holds in this – ideal – scenario. Real-life effects caused by the finite size of a system are unavoidable for real turbulence and so there are different states of fully developed turbulence with a sharp transition between these regimes.
Further information
Contact Richard Stevens +31 (0)53 489 2487 or Detlef Lohse +31 (0)53 489 8076.
Reference
Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh-Bénard convection, Stephan Weiss, Richard J.A.M Stevens, Jin-Qiang Zhong, Herman J.H Clercx, Detlef Lohse, Guenter Ahlers, Phys. Rev. Lett. (2010).
Link: http://link.aps.org/doi/10.1103/PhysRevLett.105.224501