Abstract
Stretching fields and their statistical properties are studied experimentally for four distinct two-dimensional time-periodic confined fluid flows exhibiting chaotic advection: a random vortex array for two different Reynolds numbers, a set of parallel shear layers, and a vortex lattice. The flows are driven electromagnetically, and they are studied by means of precise particle velocimetry. We find that for a given flow, the probability distributions of log S (where S is the local stretching in N cycles) can be nearly superimposed for different N when log S is rescaled using the geometrical mean of the stretching distribution. The rescaled stretching fields for a given flow at various N are highly correlated spatially when N is large. Finally, the scaled distributions for different flows are similar, though there are some differences connected to the degree of spatial symmetry and time-reversibility of the flows.
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References
RT. Pierrehumbert (1991) ArticleTitleLarge-scale horizontal mixing in planetary atmospheres Phys. Fluids A 3 1250–1260 Occurrence Handle10.1063/1.858053 Occurrence Handle1991PhFl....3.1250P
T. Akira RA. Rogers PE. Hydon JP. Butler (2002) ArticleTitleChaotic mixing deep in the lung, Proc Natl. Acad. Sci. 99 10173–10178
GK. Batchelor (1952) ArticleTitleThe effect of homogeneous turbulence on material lines and surfaces Proc. R. Soc. London Ser. A 213 349–368 Occurrence Handle1952RSPSA.213..349B Occurrence Handle0046.42201 Occurrence Handle14,698a
H. Aref (1984) ArticleTitleStirring by chaotic advection J. Fluid Mech. 143 1–21 Occurrence Handle1984JFM...143....1A Occurrence Handle0559.76085 Occurrence Handle86g:76011
JM. Ottino FJ. Muzzio M. Tjahjadi JG. Franjione S.C Jana HA. Kusch (1992) ArticleTitleChaos, symmetry, and self-similarity: Exploiting order and disorder in mixing processes Science 257 754–760 Occurrence Handle1992Sci...257..754O
X.Z. Tang AH. Boozer (1996) ArticleTitleFinite time Lyapunov exponent and advection–diffusion equation Physica D 95 283–305 Occurrence Handle10.1016/0167-2789(96)00064-4 Occurrence Handle97g:35141
GA. Voth G. Haller JP. Gollub (2002) ArticleTitleExperimental measurements of stretching fields in fluid mixing Phys. Rev. Lett. 88 254501 Occurrence Handle2002PhRvL..88y4501V
Ottino JM. The Kinematics of Mixing: Stretching, Chaos, and Transport. (Cambridge University Press, 1989)
GA. Voth TC. Saint G. Dobler JP. Gollub (2003) ArticleTitleMixing rates and symmetry breaking in two-dimensional chaotic flow Phys Fluids 15 2560–2566 Occurrence Handle10.1063/1.1596915 Occurrence Handle2003PhFl...15.2560V Occurrence Handle2060062
E. Ott TM. Antonsen (1989) ArticleTitleFractal measures of passively convected vector fields and scalar gradients in chaotic fluid flows Phys. Rev. A 39 3660–3671 Occurrence Handle1989PhRvA..39.3660O
F. Varosi TM. Antonsen E. Ott (1991) ArticleTitleThe spectrum of fractal dimensions of passively convected scalar gradients in chaotic fluid flows Phys. Fluids A 3 1017–1028 Occurrence Handle1991PhFl....3.1017V Occurrence Handle93k:76065
FJ. Muzzio PD. Swanson JM. Ottino (1991) ArticleTitleThe statistics of stretching and stirring in chaotic flows Phys. Fluids 3 822–834 Occurrence Handle1991PhFl....3..822M Occurrence Handle1205474
MA. Sepulveda R. Badii E. Pollak (1989) ArticleTitleSpectral analysis of conservative dynamical systems Phys. Rev. Lett. 63 1226–1229 Occurrence Handle1989PhRvL..63.1226S
RT. Pierrehumbert (2002) ArticleTitleDecay of passive scalars under the action of single scale smooth velocity fields in bounded two-dimensional domains: From non-self-similar probability distribution functions to self-similar eigenmodes Phys. Rev. E. 66 056302 Occurrence Handle2002PhRvE..66e6302S Occurrence Handle1948579
E.R. Abraham MM. Bowen (2002) ArticleTitleChaotic stirring by a mesoscale surface ocean-flow Chaos 12 373–381 Occurrence Handle2002Chaos..12..373A Occurrence Handle1907649
A. Prasad R. Ramaswamy (1999) ArticleTitleCharacteristic distributions of finite-time Lyapunov exponents Phys. Rev. E. 60 2761–2766 Occurrence Handle10.1103/PhysRevE.60.2761 Occurrence Handle1999PhRvE..60.2761P
VI. Oseledec (1968) ArticleTitleA multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems Trans. Moscow Math. Soc. 19 197–231 Occurrence Handle0236.93034 Occurrence Handle39 #1629
A. Androver M. Giona (1998) ArticleTitleLong-range correlation properties of area-preserving chaotic systems Physica A 253 143–153
D. Beigie A. Leonard S. Wiggins (1991) ArticleTitleA global study of enhanced stretching and diffusion in chaotic tangles Phys. Fluids A 3 1039–1050 Occurrence Handle10.1063/1.858084 Occurrence Handle1991PhFl....3.1039B Occurrence Handle93k:76063
FJ. Muzzio C. Meneveau PD. Swanson JM. Ottino (1992) ArticleTitleScaling and multifractal properties of mixing in chaotic flows Phys. Fluids A 4 1439–1456 Occurrence Handle10.1063/1.858419 Occurrence Handle1992PhFl....4.1439M Occurrence Handle93a:76055
J.G. Franjione JM. Ottino (1992) ArticleTitleSymmetry concepts for the geometric analysis of mixing flows Phil. Trans. R. Soc Lond. A 338 301–323 Occurrence Handle1992RSPTA.338..301F
RS. Ellis (1985) Entropy, Large Deviations, and Statistical Mechanics Springer-Verlag New York
T. Horita H. Hata H. Mori (1990) ArticleTitleLong-time correlations and expansion-rate spectra of chaos in Hamiltonian systems Prog Theor. Phys. 83 1065–1070 Occurrence Handle10.1143/PTP.83.1065 Occurrence Handle1990PThPh..83.1065H Occurrence Handle91f:58060
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Arratia, P.E., Gollub, J.P. Statistics of Stretching Fields in Experimental Fluid Flows Exhibiting Chaotic Advection. J Stat Phys 121, 805–822 (2005). https://doi.org/10.1007/s10955-005-8664-8
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DOI: https://doi.org/10.1007/s10955-005-8664-8