Hjh. Clercx et al., Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries, PHYS FLUIDS, 11(3), 1999, pp. 611-626
We report results of direct numerical simulations of decaying two-dimension
al (2D) turbulence inside a square container with rigid boundaries. It is s
hown that the type of boundary condition (no-slip or stress-free) determine
s the flow evolution essentially. During the initial (0 less than or equal
to t less than or equal to 0.2 root Re) and intermediate (0.2 root Re less
than or equal to t less than or equal to 3 root Re) stages of decaying 2D t
urbulence (t congruent to 1 is comparable with an eddy turnover time, Re is
the Reynolds number of the flow), the decay scenario for simulations with
no-slip boundary conditions can be understood from turbulent spectral trans
fer and selective decay. A third mechanism can be recognized for t greater
than or equal to 3 root Re: A decay stage where diffusion dominates over no
nlinear advection, i.e., spectral transfer is then absent in favor of self-
similar decay. The present results show that at presently accessible Reynol
ds numbers and computation times, laboratory experiments cannot be accurate
ly compared with quasi-stationary states from ideal maximum-entropy theorie
s or with computed solutions of flows in containers with stress-free bounda
ries. The decay which results in rectangular containers with no-slip bounda
ries does not yet yield anything that is meaningfully comparable with these
formulations. The evolution of the number of vortices V, the average vorte
x radius a, the ratio of enstrophy Omega over energy E, and the extremum of
vorticity (normalized by root E) have been computed based on ensemble aver
aging of the no-slip runs. An algebraic regime has been observed with V(t)s
imilar to t(-0.90), a(t) similar to t(0.31), Omega(t)/E(t)similar to t(- 0.
63), and omega(ext)(t)/ root E(t)similar to t(-0 30). Finally, quantities s
uch as a measure of the viscous stresses near the boundaries have been comp
uted in order to analyze the decay of 2D turbulence in containers with rigi
d boundaries. (C) 1999 American Institute of Physics. [S1070-6631(99)01403-
8].