Physica A 288 (2000) 265–279 www.elsevier.com/locate/physa The eects of nite lifetime of passive scalars and vorticity on their power spectra Keeyeol Nam a , Thomas M. Antonsen Jr. a; b , Parvez N. Guzdar a , Edward Ott a; b; ∗ a Department of Physics, Institute for Plasma Research, University of Maryland, College Park, MD 20742, USA b Department of Electrical Engineering, Institute for Plasma Research, University of Maryland, College Park, MD 20742, USA Abstract The power law exponent for the wavenumber power spectrum of a passive scalar eld with nite lifetime in Lagrangian chaotic ows and the enstrophy spectrum of two-dimensional Navier–Stokes turbulence with drag are investigated. The power law exponents are related to the distribution of nite-time Lyapunov exponents and the nite lifetime (or the drag coecient). c 2000 Published by Elsevier Science B.V. All rights reserved. PACS: 47.27.-i; 05.45.-a; 47.20.-k 1. Introduction The advection of passive scalars by uid ows is of interest due to its relevance to many situations, such as industrial chemical mixing processes and various mixing phenomena of chemicals, pollutants, and temperature in the atmosphere and oceans. If a passive scalar is injected into a chaotic ow, the passive scalar eld is advected, stretched, and folded due to the chaotic nature of the ow. This repeated stretching and folding results in the development of ner and ner structures in the passive scalar eld until the ne scales are removed by diusive smoothening. In particular, even in the absence of high wavenumber velocity eld structures, it is known that a weakly diusing passive scalar still shows the development of high wavenumber structures as * Corresponding author. Fax: +1 301 405 1678. E-mail addresses: antonsen@glue.umd.edu (T.M. Antonsen), guzdar@ipr.umd.edu (P.N. Guzdar), eo4@umail.umd.edu (E. Ott). 0378-4371/00/$ - see front matter c 2000 Published by Elsevier Science B.V. All rights reserved. PII: S0378-4371(00)00426-X