# zbMATH — the first resource for mathematics

Structures in turbulent boundary layers subjected to adverse pressure gradients. (English) Zbl 1183.76767
Summary: The effects of adverse pressure gradients on turbulent structures were investigated by carrying out direct numerical simulations of turbulent boundary layers subjected to adverse and zero pressure gradients. The equilibrium adverse pressure gradient flows were established by using a power law free-stream distribution $$U_{\infty } \sim x^{m}$$. Two-point correlations of velocity fluctuations were used to show that the spanwise spacing between near-wall streaks is affected significantly by a strong adverse pressure gradient. Low-momentum regions are dominant in the middle of the boundary layer as well as in the log layer. Linear stochastic estimation was used to provide evidence for the presence of low-momentum regions and to determine their statistical properties. The mean width of such large-scale structures is closely associated with the size of the hairpin-like vortices in the outer layer. The conditionally averaged flow fields around events producing Reynolds stress show that hairpin-like vortices are the structures associated with the production of outer turbulence. The shapes of the vortices beyond the log layer were found to be similar when their length scales were normalized according to the boundary layer thickness. Estimates of the conditionally averaged velocity fields associated with the spanwise vortical motion were obtained by using linear stochastic estimation. These results confirm that the outer region of the adverse pressure gradient boundary layer is populated with streamwise-aligned vortex organizations, which are similar to those of the vortex packet model proposed by Adrian, Meinhart & Tomkins (J. Fluid Mech., vol. 422, 2000, pp. 1-54). The adverse pressure gradient augments the inclination angles of the packets and the mean streamwise spacing of the vortex heads in the packets.

##### MSC:
 76F40 Turbulent boundary layers
Full Text:
##### References:
 [1] Theodorsen, Proceedings of the Second Midwestern Conference on Fluid Mechanics pp 1– (1952) [2] DOI: 10.1017/S0022112003005251 · Zbl 1063.76514 · doi:10.1017/S0022112003005251 [3] DOI: 10.1017/S0022112001003512 · Zbl 1008.76029 · doi:10.1017/S0022112001003512 [4] DOI: 10.1017/S0022112083000634 · doi:10.1017/S0022112083000634 [5] Bogard, J. Fluid Mech. 76 pp 89– (1986) [6] DOI: 10.1023/A:1009934906108 · Zbl 0949.76044 · doi:10.1023/A:1009934906108 [7] DOI: 10.1063/1.862928 · doi:10.1063/1.862928 [8] DOI: 10.1017/S0022112088001818 · Zbl 0643.76066 · doi:10.1017/S0022112088001818 [9] DOI: 10.1017/S0022112002002173 · Zbl 1026.76029 · doi:10.1017/S0022112002002173 [10] DOI: 10.1017/S0022112088001442 · Zbl 0642.76070 · doi:10.1017/S0022112088001442 [11] DOI: 10.1017/S0022112094004489 · doi:10.1017/S0022112094004489 [12] DOI: 10.1017/S0022112000001580 · Zbl 0959.76503 · doi:10.1017/S0022112000001580 [13] DOI: 10.1146/annurev.fl.23.010191.003125 · doi:10.1146/annurev.fl.23.010191.003125 [14] DOI: 10.1063/1.857411 · doi:10.1063/1.857411 [15] DOI: 10.1017/S0022112095003351 · Zbl 0849.76030 · doi:10.1017/S0022112095003351 [16] DOI: 10.1063/1.2717527 · Zbl 1146.76307 · doi:10.1063/1.2717527 [17] DOI: 10.1017/S002211208600304X · Zbl 0597.76052 · doi:10.1017/S002211208600304X [18] DOI: 10.1017/S0022112087000284 · doi:10.1017/S0022112087000284 [19] Nagano, Turbulent Shear Flows 8 pp 7– (1993) · doi:10.1007/978-3-642-77674-8_2 [20] DOI: 10.1017/S0022112098003218 · Zbl 1083.76526 · doi:10.1017/S0022112098003218 [21] Moin, Proceedings of the Sixth Turbulent Shear Flow Symposium pp 16.9.1– (1987) [22] DOI: 10.1017/S0022112066000612 · doi:10.1017/S0022112066000612 [23] DOI: 10.1063/1.1343480 · Zbl 1184.76351 · doi:10.1063/1.1343480 [24] DOI: 10.1017/S0022112095003363 · doi:10.1017/S0022112095003363 [25] DOI: 10.1006/jcph.1998.5882 · Zbl 0936.76026 · doi:10.1006/jcph.1998.5882 [26] DOI: 10.1016/j.ijheatfluidflow.2008.01.016 · doi:10.1016/j.ijheatfluidflow.2008.01.016 [27] DOI: 10.1063/1.868513 · doi:10.1063/1.868513 [28] Kline, Near Wall Turbulence pp 218– (1989) [29] DOI: 10.1017/S0022112067001740 · doi:10.1017/S0022112067001740 [30] DOI: 10.1063/1.3001797 · Zbl 1182.76375 · doi:10.1063/1.3001797 [31] DOI: 10.1017/S0022112087000892 · Zbl 0616.76071 · doi:10.1017/S0022112087000892 [32] DOI: 10.1002/fld.205 · Zbl 1059.76046 · doi:10.1002/fld.205 [33] Jeong, J. Fluid Mech. 332 pp 185– (1997) [34] DOI: 10.1017/S0022112005005872 · Zbl 1119.76304 · doi:10.1017/S0022112005005872 [35] DOI: 10.1016/S0142-727X(00)00014-X · doi:10.1016/S0142-727X(00)00014-X [36] DOI: 10.1017/S0022112081001791 · doi:10.1017/S0022112081001791 [37] DOI: 10.1017/S0022112002003270 · Zbl 1032.76500 · doi:10.1017/S0022112002003270 [38] DOI: 10.1017/S002211209900467X · Zbl 0946.76030 · doi:10.1017/S002211209900467X [39] DOI: 10.1002/aic.690340402 · doi:10.1002/aic.690340402 [40] DOI: 10.1063/1.868838 · Zbl 1027.76589 · doi:10.1063/1.868838 [41] DOI: 10.1017/S0022112000001713 · Zbl 0958.76509 · doi:10.1017/S0022112000001713 [42] DOI: 10.1017/S0022112061000883 · Zbl 0127.42602 · doi:10.1017/S0022112061000883 [43] DOI: 10.1098/rsta.1991.0070 · Zbl 0731.76033 · doi:10.1098/rsta.1991.0070
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.