Department of Physics & Astronomy, Dartmouth College
April 28, 2005
Foothills Laboratory, Room 1001
Two-dimensional turbulence with material wall boundaries
Most theoretically-oriented studies of turbulence in both two and three dimensions have been done either for infinite systems or with rectangular periodic boundary conditions enforced. However, many if not most turbulent fluids are turbulent because of what is done to them at their boundaries, where periodic boundary conditions are a poor representation.
The present work represents an effort to ask what changes occur in two-dimensional turbulence when there are material wall boundaries at which either no-slip or stress-free boundary conditions apply. In particular, circular and rectangular boundary conditions have been investigated, including some laboratory experiments on stratified quasi-two dimensional fluids. Several new features arise, such as the importance of net angular momentum (not well-defined for periodic boundaries) and the phenomenon of "spontaneous spin-up."
The work also highlights some long-unresolved mathematical issues, such as pressure determinations in incompressible, multi-dimensional,wall-bounded flows.
Z. Yin et al, Phys. Fluids 15, 1937 (2003).
S. Li et al, Phys. Lett. A 218, 281 (1996).
S. Li et al, Theor. & Comp. Fluid Dyn. 9, 167 (1997).
S.R. Maassen et al, Europhysics Letters 46, 339 (1999).
H.J.H. Clercx et al, Phys. Rev. Lett. 80, 5129 (1998).
B.T. Kress et al, J. Plasma Phys. 64, 371 (2000).