Abstract

It is possible to devise an experiment in which the local vorticity of a flow can be estimated by probing the fluid with Laguerre–Gauss (LG) beams, i.e., optical beams that show an azimuthal phase variation that is the origin of its characteristic nonzero orbital angular momentum. The key point is to make use of the transversal Doppler effect of the returned signal that depends only on the azimuthal component of the flow velocity along the ring-shaped observation beam. We found from a detailed analysis of the experimental method that probing the fluid with LG beams is an effective and simple sensing technique that is able to produce accurate estimates of flow vorticity.

© 2015 Optical Society of America

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References

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    [Crossref]
  3. R. Loudon, Phys. Rev. A 68, 013806 (2003).
    [Crossref]
  4. A. Belmonte and J. P. Torres, Opt. Lett. 36, 4437 (2011).
    [Crossref]
  5. M. P. J. Lavery, F. C. Speirits, S. M. Barnet, and M. J. Padgett, Science 341, 537 (2013).
    [Crossref]
  6. C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 36, 2815 (2013).
  7. R. J. Adrian, Annu. Rev. Fluid Mech. 23, 261 (1991).
    [Crossref]
  8. R. J. Adrian and J. Westerweel, Particle Image Velocimetry (Cambridge University, 2011).
  9. S. Yao, P. Tong, and B. J. Ackerson, Appl. Opt. 40, 4022 (2001).
    [Crossref]
  10. Y. Yeh and H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
    [Crossref]
  11. F. Durst, A. Melling, and J. Whitelaw, Principles and Practices of Lase Doppler Anemometry (Academic, 1981).
  12. M. Frish and W. Webb, J. Fluid Mech. 107, 173 (1981).
    [Crossref]
  13. T. Fujii and T. Fukuchi, eds., Laser Remote Sensing (CRC Press, 2005).

2013 (2)

M. P. J. Lavery, F. C. Speirits, S. M. Barnet, and M. J. Padgett, Science 341, 537 (2013).
[Crossref]

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 36, 2815 (2013).

2011 (1)

2003 (1)

R. Loudon, Phys. Rev. A 68, 013806 (2003).
[Crossref]

2001 (1)

1995 (1)

J. M. Wallace and J. F. Foss, Annu. Rev. Fluid Mech. 27, 469 (1995).
[Crossref]

1991 (1)

R. J. Adrian, Annu. Rev. Fluid Mech. 23, 261 (1991).
[Crossref]

1981 (1)

M. Frish and W. Webb, J. Fluid Mech. 107, 173 (1981).
[Crossref]

1964 (1)

Y. Yeh and H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[Crossref]

Ackerson, B. J.

Adrian, R. J.

R. J. Adrian, Annu. Rev. Fluid Mech. 23, 261 (1991).
[Crossref]

R. J. Adrian and J. Westerweel, Particle Image Velocimetry (Cambridge University, 2011).

Barnet, S. M.

M. P. J. Lavery, F. C. Speirits, S. M. Barnet, and M. J. Padgett, Science 341, 537 (2013).
[Crossref]

Batchelor, G. K.

G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University, 2000).

Belmonte, A.

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 36, 2815 (2013).

A. Belmonte and J. P. Torres, Opt. Lett. 36, 4437 (2011).
[Crossref]

Cummins, H. Z.

Y. Yeh and H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[Crossref]

Durst, F.

F. Durst, A. Melling, and J. Whitelaw, Principles and Practices of Lase Doppler Anemometry (Academic, 1981).

Foss, J. F.

J. M. Wallace and J. F. Foss, Annu. Rev. Fluid Mech. 27, 469 (1995).
[Crossref]

Frish, M.

M. Frish and W. Webb, J. Fluid Mech. 107, 173 (1981).
[Crossref]

Hermosa, N.

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 36, 2815 (2013).

Lavery, M. P. J.

M. P. J. Lavery, F. C. Speirits, S. M. Barnet, and M. J. Padgett, Science 341, 537 (2013).
[Crossref]

Loudon, R.

R. Loudon, Phys. Rev. A 68, 013806 (2003).
[Crossref]

Melling, A.

F. Durst, A. Melling, and J. Whitelaw, Principles and Practices of Lase Doppler Anemometry (Academic, 1981).

Padgett, M. J.

M. P. J. Lavery, F. C. Speirits, S. M. Barnet, and M. J. Padgett, Science 341, 537 (2013).
[Crossref]

Rosales-Guzmán, C.

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 36, 2815 (2013).

Speirits, F. C.

M. P. J. Lavery, F. C. Speirits, S. M. Barnet, and M. J. Padgett, Science 341, 537 (2013).
[Crossref]

Tong, P.

Torres, J. P.

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 36, 2815 (2013).

A. Belmonte and J. P. Torres, Opt. Lett. 36, 4437 (2011).
[Crossref]

Wallace, J. M.

J. M. Wallace and J. F. Foss, Annu. Rev. Fluid Mech. 27, 469 (1995).
[Crossref]

Webb, W.

M. Frish and W. Webb, J. Fluid Mech. 107, 173 (1981).
[Crossref]

Westerweel, J.

R. J. Adrian and J. Westerweel, Particle Image Velocimetry (Cambridge University, 2011).

Whitelaw, J.

F. Durst, A. Melling, and J. Whitelaw, Principles and Practices of Lase Doppler Anemometry (Academic, 1981).

Yao, S.

Yeh, Y.

Y. Yeh and H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[Crossref]

Annu. Rev. Fluid Mech. (2)

J. M. Wallace and J. F. Foss, Annu. Rev. Fluid Mech. 27, 469 (1995).
[Crossref]

R. J. Adrian, Annu. Rev. Fluid Mech. 23, 261 (1991).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y. Yeh and H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[Crossref]

J. Fluid Mech. (1)

M. Frish and W. Webb, J. Fluid Mech. 107, 173 (1981).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (1)

R. Loudon, Phys. Rev. A 68, 013806 (2003).
[Crossref]

Sci. Rep. (1)

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, Sci. Rep. 36, 2815 (2013).

Science (1)

M. P. J. Lavery, F. C. Speirits, S. M. Barnet, and M. J. Padgett, Science 341, 537 (2013).
[Crossref]

Other (4)

G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University, 2000).

F. Durst, A. Melling, and J. Whitelaw, Principles and Practices of Lase Doppler Anemometry (Academic, 1981).

R. J. Adrian and J. Westerweel, Particle Image Velocimetry (Cambridge University, 2011).

T. Fujii and T. Fukuchi, eds., Laser Remote Sensing (CRC Press, 2005).

Supplementary Material (2)

NameDescription
» Supplement 1: PDF (1124 KB)      LG beam
» Visualization 1: MPG (5634 KB)      Parabolic Flow Visualization

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Figures (3)

Fig. 1.
Fig. 1. Measure of vorticity in a flow. (a) Here we show the schematic of an experiment in which the local vorticity of a flow can be estimated by probing the fluid with LG beams. The proposed measurement technique considers an incident LG laser beam whose phase depends only on the azimuthal angle, and the intensity distribution describes a bright ring of light over the flow. When a set of independent scatterers, moving with the flow, passes the ring-like observation region, it generates a burst of optical echoes (scattered glow) that contributes to the received optical signal. (b) The inset depicts the illumination beam on the center of the flow channel with a spatially varying phase gradient (as indicated by color scales). The key point is to make use of the transversal Doppler effect of the returned signal that depends only on the azimuthal component Uϕ of the flow velocity U⃗ along the ring-shaped observation beam.
Fig. 2.
Fig. 2. Numerical experiments on the measurement of flow vorticity. (a) The parabolic profile of velocities (red line, right axis) in a laminar flow gives a linear vorticity profile (blue line, left axis). The measurements with LG beams (triangular markers) reproduce very closely the expected vorticity values. As an illustrative example, we present (inset, right) the frequency signal spectra corresponding to measurements S1 and S2 in the plot. (b) Vorticity in a complex flow created by the unsteady separation of fluid around a cylindrical object located upstream (not shown in the graph). The flow is pictured with a set of streamlines (white curves) that are tangent to the flow velocity vector. Left: a measure of flow vorticity with LG beams (triangles) and the corresponding theoretical expectations (solid line). In the simulation, the measurement is realized across the flow (transversal dashed line in the right graph), downstream from the cylindrical object.
Fig. 3.
Fig. 3. Laboratory experiments on the measurement of flow vorticity. (a) In the experimental setup, a collimated Gaussian beam is divided by a polarized beam splitter (PBS1) into a reference beam (red line) and a probe beam (green line). The probe beam acquires the desired phase profile after impinging onto a computer-controlled SLM. This structured light (green line) is filtered and made to shine onto a DMD. The DMD is controlled with a PC to generate on-demand particle flows with different velocity profiles. Light reflected by the particles (blue line) is made to interfere with the reference beam using a beam splitter (BS). The interference signal is captured using two photodetectors (PD1 and PD2) connected to an oscilloscope. A phase shifter is used to shift our detected signal to 1 KHz. (b) Over a laminar boundary layer flow characterized by a parabolic profile of velocities, a least-squares approach in a regression analysis of the measurements (triangles) produce a linear vorticity profile (blue, solid lines). (c) As before, but now the laminar boundary layer flow is characterized by a linear profile of velocities.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

ω=1/πρ0202πUϕ(ρ0,ϕ)ρ0dϕ·
E(ρ⃗,t)=E0(ρ)exp{i[2πftΦ(ρ⃗)]}·
f(ρ0,ϕ)=m/2πUϕ(ρ0,ϕ)/ρ0·
ω=2/m02πf(ρ0,ϕ)dϕ·
f1/2π02πf(ρ0,ϕ)dϕ,
ω=(4π/m)f.

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