V. K. Horváth, R. Crassman, W. I. Goldburg, X.-L. Wu, “Hysteresis at low Reynolds number: onset of two-dimensional vortex shedding,” Phys. Rev. E 61, R4702–4705 (2000).

[CrossRef]

K. R. Sreenivasan, “Fluid turbulence,” Rev. Mod. Phys. 71, S383–395 (1999).

[CrossRef]

Y. Du, B. J. Ackerson, P. Tong, “Velocity difference measurement with a fiber-optic coupler,” J. Opt. Soc. Am. A 15, 2433–2439 (1998).

[CrossRef]

W. I. Goldburg, A. Belmonte, X.-L. Wu, I. Zusman, “Flowing soap films: a laboratory for studying two-dimensional hydrodynamics,” Physica A 254, 231–247 (1998).

[CrossRef]

T. Narayanan, C. Cheung, P. Tong, W. I. Goldburg, X.-L. Wu, “Measurement of the velocity difference by photon correlation spectroscopy: an improved scheme,” Appl. Opt. 36, 7639–7644 (1997).

[CrossRef]

M. A. Rutgers, X.-L. Wu, R. Bagavatula, A. A. Peterson, W. I. Goldburg, “Two-dimensional velocity profiles and laminar boundary layers in flowing soap films,” Phys. Fluids 8, 2847 (1997).

[CrossRef]

H. Kellay, X.-L. Wu, W. I. Goldburg, “Experiments with turbulent soap films,” Phys. Rev. Lett. 74, 3975–3978 (1995).

[CrossRef]
[PubMed]

P. Tong, K.-Q. Xia, B. J. Ackerson, “Incoherent cross-correlation spectroscopy,” J. Chem. Phys. 98, 9256–9264 (1993).

[CrossRef]

H. K. Pak, W. I. Goldburg, A. Sirivat, “Measuring the probability distribution of the relative velocities in grid-generated turbulence,” Phys. Rev. Lett. 68, 938–941 (1992).

[CrossRef]
[PubMed]

P. Tong, Y. Shen, “Relative velocity fluctuations in turbulent Rayleigh–Bénard convection,” Phys. Rev. Lett. 69, 2066–2069 (1992).

[CrossRef]
[PubMed]

J. D. Scargle, “Studies in astronomical time series analysis III,” Astrophys. J. 343, 874–887 (1989).

[CrossRef]

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).

[CrossRef]
[PubMed]

F. Durst, J. H. Whitelaw, “Optimization of optical anemometers,” Proc. R. Soc. London Ser. A 324, 157–181 (1971).

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. London Ser. A 164, 476–490 (1938).

[CrossRef]

Y. Du, B. J. Ackerson, P. Tong, “Velocity difference measurement with a fiber-optic coupler,” J. Opt. Soc. Am. A 15, 2433–2439 (1998).

[CrossRef]

P. Tong, K.-Q. Xia, B. J. Ackerson, “Incoherent cross-correlation spectroscopy,” J. Chem. Phys. 98, 9256–9264 (1993).

[CrossRef]

S. H. Yao, P. Tong, B. J. Ackerson, “Instantaneous vorticity measurements using fiber-optic couplers,” manuscript available from the authors, c/o P. Tong at Oklahoma State University, Physics Department, Stillwater, Okla. 74078-3072.

M. A. Rutgers, X.-L. Wu, R. Bagavatula, A. A. Peterson, W. I. Goldburg, “Two-dimensional velocity profiles and laminar boundary layers in flowing soap films,” Phys. Fluids 8, 2847 (1997).

[CrossRef]

W. I. Goldburg, A. Belmonte, X.-L. Wu, I. Zusman, “Flowing soap films: a laboratory for studying two-dimensional hydrodynamics,” Physica A 254, 231–247 (1998).

[CrossRef]

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).

[CrossRef]
[PubMed]

V. K. Horváth, R. Crassman, W. I. Goldburg, X.-L. Wu, “Hysteresis at low Reynolds number: onset of two-dimensional vortex shedding,” Phys. Rev. E 61, R4702–4705 (2000).

[CrossRef]

J. W. Daily, D. R. F. Harleman, Fluid Dynamics (Addison–Wesley, Reading, Mass., 1966), p. 421.

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

F. Durst, J. H. Whitelaw, “Optimization of optical anemometers,” Proc. R. Soc. London Ser. A 324, 157–181 (1971).

See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, 2nd ed. (Cambridge U. Press, UK, 1992).

U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge U. Press, Cambridge, UK, 1995).

V. K. Horváth, R. Crassman, W. I. Goldburg, X.-L. Wu, “Hysteresis at low Reynolds number: onset of two-dimensional vortex shedding,” Phys. Rev. E 61, R4702–4705 (2000).

[CrossRef]

W. I. Goldburg, A. Belmonte, X.-L. Wu, I. Zusman, “Flowing soap films: a laboratory for studying two-dimensional hydrodynamics,” Physica A 254, 231–247 (1998).

[CrossRef]

T. Narayanan, C. Cheung, P. Tong, W. I. Goldburg, X.-L. Wu, “Measurement of the velocity difference by photon correlation spectroscopy: an improved scheme,” Appl. Opt. 36, 7639–7644 (1997).

[CrossRef]

M. A. Rutgers, X.-L. Wu, R. Bagavatula, A. A. Peterson, W. I. Goldburg, “Two-dimensional velocity profiles and laminar boundary layers in flowing soap films,” Phys. Fluids 8, 2847 (1997).

[CrossRef]

H. Kellay, X.-L. Wu, W. I. Goldburg, “Experiments with turbulent soap films,” Phys. Rev. Lett. 74, 3975–3978 (1995).

[CrossRef]
[PubMed]

H. K. Pak, W. I. Goldburg, A. Sirivat, “Measuring the probability distribution of the relative velocities in grid-generated turbulence,” Phys. Rev. Lett. 68, 938–941 (1992).

[CrossRef]
[PubMed]

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).

[CrossRef]
[PubMed]

J. W. Daily, D. R. F. Harleman, Fluid Dynamics (Addison–Wesley, Reading, Mass., 1966), p. 421.

V. K. Horváth, R. Crassman, W. I. Goldburg, X.-L. Wu, “Hysteresis at low Reynolds number: onset of two-dimensional vortex shedding,” Phys. Rev. E 61, R4702–4705 (2000).

[CrossRef]

H. Kellay, X.-L. Wu, W. I. Goldburg, “Experiments with turbulent soap films,” Phys. Rev. Lett. 74, 3975–3978 (1995).

[CrossRef]
[PubMed]

H. K. Pak, W. I. Goldburg, A. Sirivat, “Measuring the probability distribution of the relative velocities in grid-generated turbulence,” Phys. Rev. Lett. 68, 938–941 (1992).

[CrossRef]
[PubMed]

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

M. A. Rutgers, X.-L. Wu, R. Bagavatula, A. A. Peterson, W. I. Goldburg, “Two-dimensional velocity profiles and laminar boundary layers in flowing soap films,” Phys. Fluids 8, 2847 (1997).

[CrossRef]

See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, 2nd ed. (Cambridge U. Press, UK, 1992).

M. A. Rutgers, X.-L. Wu, R. Bagavatula, A. A. Peterson, W. I. Goldburg, “Two-dimensional velocity profiles and laminar boundary layers in flowing soap films,” Phys. Fluids 8, 2847 (1997).

[CrossRef]

J. D. Scargle, “Studies in astronomical time series analysis III,” Astrophys. J. 343, 874–887 (1989).

[CrossRef]

P. Tong, Y. Shen, “Relative velocity fluctuations in turbulent Rayleigh–Bénard convection,” Phys. Rev. Lett. 69, 2066–2069 (1992).

[CrossRef]
[PubMed]

H. K. Pak, W. I. Goldburg, A. Sirivat, “Measuring the probability distribution of the relative velocities in grid-generated turbulence,” Phys. Rev. Lett. 68, 938–941 (1992).

[CrossRef]
[PubMed]

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).

[CrossRef]
[PubMed]

K. R. Sreenivasan, “Fluid turbulence,” Rev. Mod. Phys. 71, S383–395 (1999).

[CrossRef]

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. London Ser. A 164, 476–490 (1938).

[CrossRef]

See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, 2nd ed. (Cambridge U. Press, UK, 1992).

Y. Du, B. J. Ackerson, P. Tong, “Velocity difference measurement with a fiber-optic coupler,” J. Opt. Soc. Am. A 15, 2433–2439 (1998).

[CrossRef]

T. Narayanan, C. Cheung, P. Tong, W. I. Goldburg, X.-L. Wu, “Measurement of the velocity difference by photon correlation spectroscopy: an improved scheme,” Appl. Opt. 36, 7639–7644 (1997).

[CrossRef]

P. Tong, K.-Q. Xia, B. J. Ackerson, “Incoherent cross-correlation spectroscopy,” J. Chem. Phys. 98, 9256–9264 (1993).

[CrossRef]

P. Tong, Y. Shen, “Relative velocity fluctuations in turbulent Rayleigh–Bénard convection,” Phys. Rev. Lett. 69, 2066–2069 (1992).

[CrossRef]
[PubMed]

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).

[CrossRef]
[PubMed]

S. H. Yao, P. Tong, B. J. Ackerson, “Instantaneous vorticity measurements using fiber-optic couplers,” manuscript available from the authors, c/o P. Tong at Oklahoma State University, Physics Department, Stillwater, Okla. 74078-3072.

See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, 2nd ed. (Cambridge U. Press, UK, 1992).

F. M. White, Viscous Fluid Flow, (McGraw-Hill, New York, 1991), p. 470.

F. Durst, J. H. Whitelaw, “Optimization of optical anemometers,” Proc. R. Soc. London Ser. A 324, 157–181 (1971).

V. K. Horváth, R. Crassman, W. I. Goldburg, X.-L. Wu, “Hysteresis at low Reynolds number: onset of two-dimensional vortex shedding,” Phys. Rev. E 61, R4702–4705 (2000).

[CrossRef]

W. I. Goldburg, A. Belmonte, X.-L. Wu, I. Zusman, “Flowing soap films: a laboratory for studying two-dimensional hydrodynamics,” Physica A 254, 231–247 (1998).

[CrossRef]

T. Narayanan, C. Cheung, P. Tong, W. I. Goldburg, X.-L. Wu, “Measurement of the velocity difference by photon correlation spectroscopy: an improved scheme,” Appl. Opt. 36, 7639–7644 (1997).

[CrossRef]

M. A. Rutgers, X.-L. Wu, R. Bagavatula, A. A. Peterson, W. I. Goldburg, “Two-dimensional velocity profiles and laminar boundary layers in flowing soap films,” Phys. Fluids 8, 2847 (1997).

[CrossRef]

H. Kellay, X.-L. Wu, W. I. Goldburg, “Experiments with turbulent soap films,” Phys. Rev. Lett. 74, 3975–3978 (1995).

[CrossRef]
[PubMed]

P. Tong, K.-Q. Xia, B. J. Ackerson, “Incoherent cross-correlation spectroscopy,” J. Chem. Phys. 98, 9256–9264 (1993).

[CrossRef]

S. H. Yao, P. Tong, B. J. Ackerson, “Instantaneous vorticity measurements using fiber-optic couplers,” manuscript available from the authors, c/o P. Tong at Oklahoma State University, Physics Department, Stillwater, Okla. 74078-3072.

W. I. Goldburg, A. Belmonte, X.-L. Wu, I. Zusman, “Flowing soap films: a laboratory for studying two-dimensional hydrodynamics,” Physica A 254, 231–247 (1998).

[CrossRef]

J. D. Scargle, “Studies in astronomical time series analysis III,” Astrophys. J. 343, 874–887 (1989).

[CrossRef]

P. Tong, K.-Q. Xia, B. J. Ackerson, “Incoherent cross-correlation spectroscopy,” J. Chem. Phys. 98, 9256–9264 (1993).

[CrossRef]

M. A. Rutgers, X.-L. Wu, R. Bagavatula, A. A. Peterson, W. I. Goldburg, “Two-dimensional velocity profiles and laminar boundary layers in flowing soap films,” Phys. Fluids 8, 2847 (1997).

[CrossRef]

P. Tong, W. I. Goldburg, C. K. Chan, A. Sirivat, “Turbulent transition by photon correlation spectroscopy,” Phys. Rev. A 37, 2125–2133 (1988).

[CrossRef]
[PubMed]

V. K. Horváth, R. Crassman, W. I. Goldburg, X.-L. Wu, “Hysteresis at low Reynolds number: onset of two-dimensional vortex shedding,” Phys. Rev. E 61, R4702–4705 (2000).

[CrossRef]

H. K. Pak, W. I. Goldburg, A. Sirivat, “Measuring the probability distribution of the relative velocities in grid-generated turbulence,” Phys. Rev. Lett. 68, 938–941 (1992).

[CrossRef]
[PubMed]

P. Tong, Y. Shen, “Relative velocity fluctuations in turbulent Rayleigh–Bénard convection,” Phys. Rev. Lett. 69, 2066–2069 (1992).

[CrossRef]
[PubMed]

H. Kellay, X.-L. Wu, W. I. Goldburg, “Experiments with turbulent soap films,” Phys. Rev. Lett. 74, 3975–3978 (1995).

[CrossRef]
[PubMed]

W. I. Goldburg, A. Belmonte, X.-L. Wu, I. Zusman, “Flowing soap films: a laboratory for studying two-dimensional hydrodynamics,” Physica A 254, 231–247 (1998).

[CrossRef]

F. Durst, J. H. Whitelaw, “Optimization of optical anemometers,” Proc. R. Soc. London Ser. A 324, 157–181 (1971).

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. London Ser. A 164, 476–490 (1938).

[CrossRef]

K. R. Sreenivasan, “Fluid turbulence,” Rev. Mod. Phys. 71, S383–395 (1999).

[CrossRef]

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

S. H. Yao, P. Tong, B. J. Ackerson, “Instantaneous vorticity measurements using fiber-optic couplers,” manuscript available from the authors, c/o P. Tong at Oklahoma State University, Physics Department, Stillwater, Okla. 74078-3072.

U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge U. Press, Cambridge, UK, 1995).

For a full description of the correlator board, see http://karman.phyast.pitt.edu/horvath/corr/ . The total cost for the correlator board is less than $100. The device can be duplicated for nonprofit applications without permission.

See, e.g., W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, 2nd ed. (Cambridge U. Press, UK, 1992).

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

J. W. Daily, D. R. F. Harleman, Fluid Dynamics (Addison–Wesley, Reading, Mass., 1966), p. 421.

F. M. White, Viscous Fluid Flow, (McGraw-Hill, New York, 1991), p. 470.

Oz Optics Ltd, 219 Westbrook Road, Carp, Ontario, Canada, K0A 1LO ( http://ozoptics.com ).