Anomalous diffusion in bounded temporally irregular flows

Shankar C. Venkataramani; Thomas M. Antonsen; Edward Ott

doi:10.1016/S0167-2789(97)00184-X

Anomalous diffusion in bounded temporally irregular flows

Shankar C. Venkataramani, Thomas M. Antonsen, Edward Ott

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We investigate the longitudinal dispersion of passive tracers in a transversely bounded shear flow. The flow is assumed to be temporally irregular, but to possess smooth large scale spatial structure without significant small spatial scale motions. We show that the existence of a region where the longitudinal velocity goes to zero linearly with distance from the wall causes the tracers to "stick" to the walls. This results in a superdiffusive dispersion of the tracer. We analyze the growth of the variance and show that σ²(t) ∼ t^v with v = 3/2. We verify this result by numerical simulation and compare the results from this model with experimental observations.

Original language	English (US)
Pages (from-to)	412-440
Number of pages	29
Journal	Physica D: Nonlinear Phenomena
Volume	112
Issue number	3-4
DOIs	https://doi.org/10.1016/S0167-2789(97)00184-X
State	Published - 1998
Externally published	Yes

Keywords

Anomalous diffusion
Hamiltonian systems
Levy flights
Passive tracer transport

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/S0167-2789(97)00184-X

Cite this

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title = "Anomalous diffusion in bounded temporally irregular flows",

abstract = "We investigate the longitudinal dispersion of passive tracers in a transversely bounded shear flow. The flow is assumed to be temporally irregular, but to possess smooth large scale spatial structure without significant small spatial scale motions. We show that the existence of a region where the longitudinal velocity goes to zero linearly with distance from the wall causes the tracers to {"}stick{"} to the walls. This results in a superdiffusive dispersion of the tracer. We analyze the growth of the variance and show that σ2(t) ∼ tv with v = 3/2. We verify this result by numerical simulation and compare the results from this model with experimental observations.",

keywords = "Anomalous diffusion, Hamiltonian systems, Levy flights, Passive tracer transport",

author = "Venkataramani, {Shankar C.} and Antonsen, {Thomas M.} and Edward Ott",

note = "Funding Information: We would like to thank Eric Weeks and Harry Swinney for useful discussions and for providing us with a prepublication copy of their paper \[23\]T. his research was supported by the Office of Naval Research. The numerical computations reported in this paper were made possible by a grant from the W.M. Keck foundation.",

year = "1998",

doi = "10.1016/S0167-2789(97)00184-X",

language = "English (US)",

volume = "112",

pages = "412--440",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier B.V.",

number = "3-4",

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TY - JOUR

T1 - Anomalous diffusion in bounded temporally irregular flows

AU - Venkataramani, Shankar C.

AU - Antonsen, Thomas M.

AU - Ott, Edward

N1 - Funding Information: We would like to thank Eric Weeks and Harry Swinney for useful discussions and for providing us with a prepublication copy of their paper \[23\]T. his research was supported by the Office of Naval Research. The numerical computations reported in this paper were made possible by a grant from the W.M. Keck foundation.

PY - 1998

Y1 - 1998

N2 - We investigate the longitudinal dispersion of passive tracers in a transversely bounded shear flow. The flow is assumed to be temporally irregular, but to possess smooth large scale spatial structure without significant small spatial scale motions. We show that the existence of a region where the longitudinal velocity goes to zero linearly with distance from the wall causes the tracers to "stick" to the walls. This results in a superdiffusive dispersion of the tracer. We analyze the growth of the variance and show that σ2(t) ∼ tv with v = 3/2. We verify this result by numerical simulation and compare the results from this model with experimental observations.

AB - We investigate the longitudinal dispersion of passive tracers in a transversely bounded shear flow. The flow is assumed to be temporally irregular, but to possess smooth large scale spatial structure without significant small spatial scale motions. We show that the existence of a region where the longitudinal velocity goes to zero linearly with distance from the wall causes the tracers to "stick" to the walls. This results in a superdiffusive dispersion of the tracer. We analyze the growth of the variance and show that σ2(t) ∼ tv with v = 3/2. We verify this result by numerical simulation and compare the results from this model with experimental observations.

KW - Anomalous diffusion

KW - Hamiltonian systems

KW - Levy flights

KW - Passive tracer transport

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U2 - 10.1016/S0167-2789(97)00184-X

DO - 10.1016/S0167-2789(97)00184-X

M3 - Article

AN - SCOPUS:1842652382

SN - 0167-2789

VL - 112

SP - 412

EP - 440

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 3-4

ER -

Anomalous diffusion in bounded temporally irregular flows

Abstract

Keywords

ASJC Scopus subject areas

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