DOI: 10.1063/1.868599. On the determination of solenoidal or compressible velocity fields from measurements of passive or reactive scalars

On the determination of solenoidal or compressible velocity fields from measurements of passive or reactive scalars

10.1063/1.868599

Crossref journal-article

AIP Publishing

Physics of Fluids (317)

Abstract

Several techniques have been proposed for determining two- or three-dimensional velocity fields from measurements of one passive scalar. It is shown that measurements of one scalar and knowledge of the equation governing its transport determine a velocity field, only up to an additive vector field locally perpendicular to the gradient of the scalar field but otherwise arbitrary. Three previously proposed procedures for selecting a unique velocity field from among the uncountable infinity consistent with the scalar transport data and equation are then discussed, and it is shown that a recent ‘‘iterative inversion’’ procedure for ‘‘solution’’ of a singular linear equation system (obtained using only measurements of one scalar and the equation governing its transport) cannot converge as claimed. A method for determining the correct n-dimensional (n=2 or 3) divergence-free velocity field from measurements of n−1 passive or reactive scalars is then developed. Finally, it is shown how the velocity field in an n-dimensional compressible flow can be determined from measurements of density and n−1 passive or reactive scalars.

Bibliography

Pearlstein, A. J., & Carpenter, B. N. (1995). On the determination of solenoidal or compressible velocity fields from measurements of passive or reactive scalars. Physics of Fluids, 7(4), 754â763.

Authors 2

Arne J. Pearlstein (first)
Bonnie N. Carpenter (additional)

References 26 Referenced 15

10.2514/3.61127 / AIAA J. / Flying-hot-wire study of flow past an NACA 4412 airfoil at maximum lift (1979)
10.1063/1.866111 / Phys. Fluids / Scanning laser anemometer measurements of a forced cylinder wake (1987)
10.1146/annurev.fl.23.010191.001401 / Annu. Rev. Fluid Mech. / Particle imaging techniques for experimental fluid mechanics (1991)
10.1007/BF00190388 / Exp. Fluids / Digital particle image velocimetry (1991)
{'key': '2024020618332304200_r5', 'first-page': '706', 'article-title': 'Measurement of two-dimensional fluid dynamic quantities using a photochromic grid tracing technique', 'volume': '814', 'year': '1987', 'journal-title': 'Proc. SPIE'} / Proc. SPIE / Measurement of two-dimensional fluid dynamic quantities using a photochromic grid tracing technique (1987)
10.2514/3.11350 / AIAA J. / Fundamental turbulence measurements by relief flow tagging (1993)
10.1007/BF00189883 / Exp. Fluids / Limitation and improvement of PIV, Part I: Limitation of conventional techniques due to deformation of particle image patterns (1993)
{'key': '2024020618332304200_r8', 'first-page': '1263', 'article-title': 'Limitation and improvement of PIV, Part II: Particle image distortion, a novel technique', 'volume': '15', 'year': '1993', 'journal-title': 'Exp. Fluids'} / Exp. Fluids / Limitation and improvement of PIV, Part II: Particle image distortion, a novel technique (1993)
{'key': '2024020618332304200_r9'}
10.1007/BF00261322 / Exp. Fluids / Flow visualization of a recirculating flow by rheoscopic liquid and liquid crystal techniques (1984)
10.1364/OL.18.000161 / Opt. Lett. / Subresolution measurements of unmixed fluid using electronic quenching of NOA2Σ+ (1993)
10.1063/1.858461 / Phys. Fluids A / A scalar imaging velocimetry technique for fully resolved four-dimensional vector velocity field measurements in turbulent flows (1992)
{'key': '2024020618332304200_r13'}
{'key': '2024020618332304200_r14'}
{'key': '2024020618332304200_r15'}
{'key': '2024020618332304200_r16'}
{'key': '2024020618332304200_r17', 'first-page': '2255', 'article-title': 'Micromeasurements of fluid turbulence', 'volume': '38', 'year': '1993', 'journal-title': 'Bull. Am. Phys. Soc.'} / Bull. Am. Phys. Soc. / Micromeasurements of fluid turbulence (1993)
{'key': '2024020618332304200_r18', 'first-page': '2286', 'article-title': 'Scalar imaging velocimetry measurements of the dissipative scales of turbulent flows', 'volume': '38', 'year': '1993', 'journal-title': 'Bull. Am. Phys. Soc.'} / Bull. Am. Phys. Soc. / Scalar imaging velocimetry measurements of the dissipative scales of turbulent flows (1993)
{'key': '2024020618332304200_r19'}
10.1080/14786441308635022 / Philos. Mag. / On the motion of a viscous fluid (1913)
{'key': '2024020618332304200_r21', 'first-page': '452', 'article-title': 'Direct measurement of the density field using high speed differential interferometry', 'volume': '15', 'year': '1994', 'journal-title': 'Exp. Fluids'} / Exp. Fluids / Direct measurement of the density field using high speed differential interferometry (1994)
10.1063/1.866513 / Phys. Fluids / Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence (1987)
{'key': '2024020618332304200_r23', 'first-page': '349', 'article-title': 'The effect of homogeneous turbulence on material lines and surfaces', 'volume': '213', 'year': '1951', 'journal-title': 'Proc. R. Soc. London Ser. A'} / Proc. R. Soc. London Ser. A / The effect of homogeneous turbulence on material lines and surfaces (1951)
10.1017/S002211205900009X / J. Fluid Mech. / Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity (1959)
10.1098/rspa.1951.0216 / Proc. R. Soc. London Ser. A / The diffusion of heat spots in isotropic turbulence (1951)
10.1017/S0022112085001136 / J. Fluid Mech. / Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence (1985)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:09 a.m.)
Deposited	1 year, 6 months ago (Feb. 6, 2024, 6:06 p.m.)
Indexed	1 year, 5 months ago (March 9, 2024, 5:30 a.m.)
Issued	30 years, 4 months ago (April 1, 1995)
Published	30 years, 4 months ago (April 1, 1995)
Published Print	30 years, 4 months ago (April 1, 1995)

Funders 0

None

BibTeX

@article{Pearlstein_1995, title={On the determination of solenoidal or compressible velocity fields from measurements of passive or reactive scalars}, volume={7}, ISSN={1089-7666}, url={http://dx.doi.org/10.1063/1.868599}, DOI={10.1063/1.868599}, number={4}, journal={Physics of Fluids}, publisher={AIP Publishing}, author={Pearlstein, Arne J. and Carpenter, Bonnie N.}, year={1995}, month=apr, pages={754–763} }

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