Abstract

We report measurements by a heterodyne-detection technique of density fluctuations in a free air jet by collective scattering of a 10-W cw CO2 laser beam. Above a certain threshold of the flow velocity we observe a well-defined signal in the lower-frequency side of the spectrum, which can be simply interpreted as resulting from negative flow velocities inside the jet (eventually associated with the formation of vortices). For increasing values of the flow velocities the negative frequency peak breaks into a sequence of equally spaced peaks that are characteristic of a quasi-periodic state before developing into a broadband spectrum (turbulent nonperiodic regime). A measured bifurcation diagram is presented and discussed in detail.

© 1996 Optical Society of America

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  1. H. L. Swinney, J. P. Gollub, Phys. Today 31(8), 41 (1978).
    [Crossref]
  2. N. R. Panchapakesan, J. L. Lumley, J. Fluid Mech. 246, 197 (1993).
    [Crossref]
  3. C. M. Surko, R. E. Slusher, D. R. Moler, M. Porkolab, Phys. Rev. Lett. 29, 81 (1972).
    [Crossref]
  4. R. E. Slusher, C. M. Surko, Phys. Fluids 23, 472 (1980).
    [Crossref]
  5. E. Holzhauer, J. H. Massig, Plasma Phys. 20, 867 (1978).
    [Crossref]
  6. D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
    [Crossref]
  7. D. Grésillon, M. S. Mohamed-Benkadda, Phys. Fluids 31, 1904 (1988).
  8. J. P. Bonnet, D. Grésillon, B. Cabrit, V. Frolov, Meas. Sci. Technol. 6, 1 (1995).
    [Crossref]
  9. C. Stern, D. Grésillon, J. Phys. (Paris) 44, 1325 (1983).
    [Crossref]
  10. J. P. Gollub, H. L. Swinney, Phys. Rev. Lett. 35, 927 (1975).
    [Crossref]
  11. J. P. Gollub, S. V. Benson, J. Fluid Mech. 100, 449 (1980).
    [Crossref]
  12. D. Ruelle, F. Takens, Commun. Math. Phys. 20, 167 (1971).
    [Crossref]

1995 (1)

J. P. Bonnet, D. Grésillon, B. Cabrit, V. Frolov, Meas. Sci. Technol. 6, 1 (1995).
[Crossref]

1993 (1)

N. R. Panchapakesan, J. L. Lumley, J. Fluid Mech. 246, 197 (1993).
[Crossref]

1988 (1)

D. Grésillon, M. S. Mohamed-Benkadda, Phys. Fluids 31, 1904 (1988).

1983 (1)

C. Stern, D. Grésillon, J. Phys. (Paris) 44, 1325 (1983).
[Crossref]

1982 (1)

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

1980 (2)

R. E. Slusher, C. M. Surko, Phys. Fluids 23, 472 (1980).
[Crossref]

J. P. Gollub, S. V. Benson, J. Fluid Mech. 100, 449 (1980).
[Crossref]

1978 (2)

E. Holzhauer, J. H. Massig, Plasma Phys. 20, 867 (1978).
[Crossref]

H. L. Swinney, J. P. Gollub, Phys. Today 31(8), 41 (1978).
[Crossref]

1975 (1)

J. P. Gollub, H. L. Swinney, Phys. Rev. Lett. 35, 927 (1975).
[Crossref]

1972 (1)

C. M. Surko, R. E. Slusher, D. R. Moler, M. Porkolab, Phys. Rev. Lett. 29, 81 (1972).
[Crossref]

1971 (1)

D. Ruelle, F. Takens, Commun. Math. Phys. 20, 167 (1971).
[Crossref]

Benson, S. V.

J. P. Gollub, S. V. Benson, J. Fluid Mech. 100, 449 (1980).
[Crossref]

Bonnet, J. P.

J. P. Bonnet, D. Grésillon, B. Cabrit, V. Frolov, Meas. Sci. Technol. 6, 1 (1995).
[Crossref]

Cabrit, B.

J. P. Bonnet, D. Grésillon, B. Cabrit, V. Frolov, Meas. Sci. Technol. 6, 1 (1995).
[Crossref]

Frolov, V.

J. P. Bonnet, D. Grésillon, B. Cabrit, V. Frolov, Meas. Sci. Technol. 6, 1 (1995).
[Crossref]

Gervais, F.

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

Gollub, J. P.

J. P. Gollub, S. V. Benson, J. Fluid Mech. 100, 449 (1980).
[Crossref]

H. L. Swinney, J. P. Gollub, Phys. Today 31(8), 41 (1978).
[Crossref]

J. P. Gollub, H. L. Swinney, Phys. Rev. Lett. 35, 927 (1975).
[Crossref]

Grésillon, D.

J. P. Bonnet, D. Grésillon, B. Cabrit, V. Frolov, Meas. Sci. Technol. 6, 1 (1995).
[Crossref]

D. Grésillon, M. S. Mohamed-Benkadda, Phys. Fluids 31, 1904 (1988).

C. Stern, D. Grésillon, J. Phys. (Paris) 44, 1325 (1983).
[Crossref]

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

Hémon, A.

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

Holzhauer, E.

E. Holzhauer, J. H. Massig, Plasma Phys. 20, 867 (1978).
[Crossref]

Lapierre, Y.

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

Lehner, T.

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

Lumley, J. L.

N. R. Panchapakesan, J. L. Lumley, J. Fluid Mech. 246, 197 (1993).
[Crossref]

Massig, J. H.

E. Holzhauer, J. H. Massig, Plasma Phys. 20, 867 (1978).
[Crossref]

Mohamed-Benkadda, M. S.

D. Grésillon, M. S. Mohamed-Benkadda, Phys. Fluids 31, 1904 (1988).

Moler, D. R.

C. M. Surko, R. E. Slusher, D. R. Moler, M. Porkolab, Phys. Rev. Lett. 29, 81 (1972).
[Crossref]

Olivain, J.

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

Panchapakesan, N. R.

N. R. Panchapakesan, J. L. Lumley, J. Fluid Mech. 246, 197 (1993).
[Crossref]

Porkolab, M.

C. M. Surko, R. E. Slusher, D. R. Moler, M. Porkolab, Phys. Rev. Lett. 29, 81 (1972).
[Crossref]

Quéméneur, A.

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

Ruelle, D.

D. Ruelle, F. Takens, Commun. Math. Phys. 20, 167 (1971).
[Crossref]

Slusher, R. E.

R. E. Slusher, C. M. Surko, Phys. Fluids 23, 472 (1980).
[Crossref]

C. M. Surko, R. E. Slusher, D. R. Moler, M. Porkolab, Phys. Rev. Lett. 29, 81 (1972).
[Crossref]

Stern, C.

C. Stern, D. Grésillon, J. Phys. (Paris) 44, 1325 (1983).
[Crossref]

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

Surko, C. M.

R. E. Slusher, C. M. Surko, Phys. Fluids 23, 472 (1980).
[Crossref]

C. M. Surko, R. E. Slusher, D. R. Moler, M. Porkolab, Phys. Rev. Lett. 29, 81 (1972).
[Crossref]

Swinney, H. L.

H. L. Swinney, J. P. Gollub, Phys. Today 31(8), 41 (1978).
[Crossref]

J. P. Gollub, H. L. Swinney, Phys. Rev. Lett. 35, 927 (1975).
[Crossref]

Takens, F.

D. Ruelle, F. Takens, Commun. Math. Phys. 20, 167 (1971).
[Crossref]

Truc, A.

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

Commun. Math. Phys. (1)

D. Ruelle, F. Takens, Commun. Math. Phys. 20, 167 (1971).
[Crossref]

J. Fluid Mech. (2)

J. P. Gollub, S. V. Benson, J. Fluid Mech. 100, 449 (1980).
[Crossref]

N. R. Panchapakesan, J. L. Lumley, J. Fluid Mech. 246, 197 (1993).
[Crossref]

J. Phys. (1)

C. Stern, D. Grésillon, J. Phys. (Paris) 44, 1325 (1983).
[Crossref]

Meas. Sci. Technol. (1)

J. P. Bonnet, D. Grésillon, B. Cabrit, V. Frolov, Meas. Sci. Technol. 6, 1 (1995).
[Crossref]

Phys. Fluids (2)

D. Grésillon, M. S. Mohamed-Benkadda, Phys. Fluids 31, 1904 (1988).

R. E. Slusher, C. M. Surko, Phys. Fluids 23, 472 (1980).
[Crossref]

Phys. Rev. Lett. (2)

C. M. Surko, R. E. Slusher, D. R. Moler, M. Porkolab, Phys. Rev. Lett. 29, 81 (1972).
[Crossref]

J. P. Gollub, H. L. Swinney, Phys. Rev. Lett. 35, 927 (1975).
[Crossref]

Phys. Scr. (1)

D. Grésillon, C. Stern, A. Hémon, A. Truc, T. Lehner, J. Olivain, A. Quéméneur, F. Gervais, Y. Lapierre, Phys. Scr. T2/2, 459 (1982).
[Crossref]

Phys. Today (1)

H. L. Swinney, J. P. Gollub, Phys. Today 31(8), 41 (1978).
[Crossref]

Plasma Phys. (1)

E. Holzhauer, J. H. Massig, Plasma Phys. 20, 867 (1978).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the CO2 laser scattering experiment.

Fig. 2
Fig. 2

Scattered-light signal for increasing values of nozzle pressure. The sequence consists of (a) no counterpropagating flow at low pressure, p = 0.05 bars; (b) a periodic state with a single peak in the counterpropagating side of the spectrum, p = 0.5 bars; (c) a quasi-periodic state with several equally spaced peaks, p = 0.78 bar; (d) a nonperiodic state with some peaks above turbulent noise, p = 0.95 bars; (e) a turbulent flow with no sharp peaks and only a broadband noise, p = 1.04 bars. The symbols fn are a shorthand notation of fn(p), with n = 1, 2, . . . , 5.

Fig. 3
Fig. 3

Experimental bifurcation diagram: filled squares, the measured main velocity of the jet with a fitted curve (solid curve); open circles, measured first oscillation of the counterpropagating flow; open squares, upward-pointing triangles, downward-pointing triangles, and diamonds, the second, third, fourth, and fifth oscillations (measured peaks) of the counterpropagating flow, respectively; dashed lines, the evolution of each oscillation as the pressure increases; hatched zone, the completely turbulent counterflow.

Equations (2)

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E s ( r , t ) exp ( - i ω 0 t ) V d r 3 n ( r , t ) exp ( - ik · r ) ,
f n ( p ) = f 1 ( p ) + ( n - 1 ) f 2

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