- Access by Xinjiang University
Scalar gradient fields by geometric measure theory
Phys. Rev. E 69, 047301 – Published 9 April, 2004
DOI: https://doi.org/10.1103/PhysRevE.69.047301
Abstract
Upper bounds of the Hausdorff volume of scalar gradient field graphs are derived by means of geometric measure theory. The approach reproduces that scalar gradient fields along a mean imposed scalar gradient become space filling for sufficiently high values of Schmidt numbers The bounds are consistent with findings from recent high-resolution numerical experiments for but too rough when compared with numerical simulations. A Reynolds number dependence of the bounds is found due to the additional scalar gradient stretching term in the equation of motion.
References (15)
- P.K. Yeung et al., Phys. Fluids 14, 4178 (2002).
- G. Brethouwer et al., J. Fluid Mech. 474, 193 (2003).
- Z. Warhaft, Annu. Rev. Fluid Mech. 32, 203 (2000).
- J. Schumacher et al., Phys. Rev. Lett. 91, 174501 (2003).
- F. Morgan, Geometric Measure Theory, a Beginners Guide (Academic, Boston, 1988).
- P. Constantin et al., Phys. Rev. Lett. 67, 1739 (1991).
- P. Constantin and I. Procaccia, Phys. Rev. E 47, 3307 (1993).
- S. Grossmann and D. Lohse, Europhys. Lett. 27, 347 (1994); B. Eckhardt and J. Schumacher, Phys. Rev. E 60, 4185 (1999).
- G.K. Batchelor, J. Fluid Mech. 5, 113 (1959).
- K.J. Falconer, The Geometry of Fractal Sets (Cambridge University Press, Cambridge, 1985).
- S.B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000).
- P. Mattila, Ann. Acad. Sci. Fenn., Ser. A1, 227 (1975).
- J. Schumacher and B. Eckhardt, Europhys. Lett. 52, 627 (2000); J. Schumacher, J. Fluid Mech. 441, 109 (2001).
- K.R. Sreenivasan et al., Phys. Rev. A 38, 6287 (1988).
- R.R. Prasad et al., Phys. Rev. Lett. 61, 74 (1988).