Anomalous scaling for a passive scalar near the Batchelor limit

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 3, 1998, Pages 2965-2977

  Shraiman, Boris I ^a   Siggia, Eric D ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 9744284781     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.2965     Document Type: Article

References (27)

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22. The dissipation operator could be made Hermitian by adding the term 2εΛ. Although this would appear in the leading order calculation, it is nonsingular and represents but a trivial modification of the calculation. Since there is no physical requirement of Hermiticity for the evolution operator we chose to work with the marginally simpler non-Hermitian form.
23. It is natural to require the solution to be smooth along w=0 as long as no two points in the configuration do not coincide. The smoothness for noncoincident configurations can be satisfied even in the absence of molecular diffusion. Indeed, since the molecular diffusion operator is τ(R)κ∑i∂→i2 it is small compared to LD as long as κ<εR4/3.
24. The matching of the O(εlnw) is not required to the leading order, but can be done by letting ν=12+O(ε).
25. Authors are indebted to A. Pumir who found that an earlier version of this analysis was in error and collaborated in producing the present, corrected, version.
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