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On the origin of streamwise vortices in a turbulent boundary layer. (English) Zbl 0624.76069
Several experiments have suggested that streamwise vortices, with their accompanying low-momentum streaks in a turbulent boundary layer have a characteristic spanwise wavelength of approximately \(\lambda_ z^+=100\). Here a mechanism is proposed which selects a comparable spanwise wavelength and produces counter-rotating streamwise vortices in a turbulent boundary layer. Examining the equations which describe the deviation of the velocity field from its time-average, it is found that a resonance is associated with the mean-velocity profile. As an integral part of this resonance, there is a mean secondary flow which has a spanwise wavelength \(\lambda^+_ z=90\) and whose velocities exhibit a streamwise vortex structure similar to those observed.

MSC:
76F99 Turbulence
76M99 Basic methods in fluid mechanics
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[1] DOI: 10.1017/S0022112077001402 · doi:10.1017/S0022112077001402
[2] DOI: 10.1017/S0022112067000941 · Zbl 0152.45403 · doi:10.1017/S0022112067000941
[3] DOI: 10.1146/annurev.fl.13.010181.002325 · doi:10.1146/annurev.fl.13.010181.002325
[4] DOI: 10.1017/S0022112076003145 · doi:10.1017/S0022112076003145
[5] DOI: 10.1063/1.864047 · doi:10.1063/1.864047
[6] Benney, Stud. Appl. Math. 64 pp 185– (1981) · Zbl 0481.76048 · doi:10.1002/sapm1981643185
[7] Benney, Stud. Appl. Math. 70 pp 1– (1984) · Zbl 0566.76046 · doi:10.1002/sapm19847011
[8] DOI: 10.1017/S0022112061000196 · Zbl 0096.21201 · doi:10.1017/S0022112061000196
[9] DOI: 10.1017/S0022112075001991 · doi:10.1017/S0022112075001991
[10] DOI: 10.1017/S0022112072000679 · doi:10.1017/S0022112072000679
[11] DOI: 10.1017/S002211207500208X · doi:10.1017/S002211207500208X
[12] DOI: 10.1017/S0022112069002072 · doi:10.1017/S0022112069002072
[13] DOI: 10.1017/S002211207600147X · Zbl 0339.76030 · doi:10.1017/S002211207600147X
[14] Lin, Am. Math. Soc., Proc. Symp. Appl. Math. 13 pp 1– (1962) · doi:10.1090/psapm/013/0137413
[15] DOI: 10.1017/S0022112067000953 · Zbl 0147.46005 · doi:10.1017/S0022112067000953
[16] DOI: 10.1017/S0022112067001740 · doi:10.1017/S0022112067001740
[17] DOI: 10.1017/S0022112062000014 · Zbl 0131.41901 · doi:10.1017/S0022112062000014
[18] DOI: 10.1063/1.864413 · Zbl 0522.76058 · doi:10.1063/1.864413
[19] DOI: 10.1017/S0022112069000395 · doi:10.1017/S0022112069000395
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