Turbulent fluctuations above the buffer layer of wall-bounded flows

Abstract

The behaviour of the velocity and pressure fluctuations in the logarithmic and outer layers of turbulent flows is analysed using spectral information and probability density functions from channel simulations at Re τ 6 2000. Comparisons are made with experimental data at higher Reynolds numbers. It is found, in agreement with previous investigations, that the intensity profiles of the streamwise and spanwise velocity components have logarithmic ranges that are traced to the widening spectral range of scales as the wall is approached. The same is true for the pressure, both theoretically and observationally, but not for the normal velocity or for the tangential stress cospectrum, although even those two quantities have structures with lengths of the order of several hundred times the wall distance. Because the logarithmic range grows longer as the Reynolds number increases, variables which are 'attached' in this sense scale in the buffer layer in mixed units. These results give strong support to the attached-eddy scenario proposed by Townsend (1976), but they are not linked to any particular eddy model. The scaling of the outer modes is also examined. The intensity of the streamwise velocity at fixed y/ h increases with the Reynolds number. This is traced to the large-scale modes, and to an increased intensity of the ejections but not of the sweeps. Several differences are found between the outer structures of different flows. The outer modes of the spanwise and wall-normal velocities in boundary layers are stronger than in internal flows, and their streamwise velocities penetrate closer to the wall. As a consequence, their logarithmic layers are thinner, and some of their logarithmic slopes are different. The channel statistics are available electronically at

How linear is wall-bounded turbulence?

“…The lower total acceleration of u 1 in Figure 7(a) can only be due to weaker streamwise gradients of that velocity component, even if the intensity of u 1 is the highest of the three. 51 That is consistent with the longer streamwise dimensions of the u 1 spectra, 52,56,58 but implies that part of the streamwise velocity is not only "inactive," in the Townsend 59 sense of not carrying Reynolds stresses, but "passive" in the sense of evolving much more slowly than the other two velocity components.…”

“…In particular, the effect of the linearized "fast" pressure is found to be weak with respect to the total pressure, in agreement with the relative magnitudes of the two pressure components. 41,56 However, we have shown by a simple example that the Orr mechanism is not necessarily linear. It occurs whenever a vortical structure, whether weak or strong, overtakes another at a lower level of a shear flow, and their cross-shear velocities reinforce each other.…”

“…Both in the linear and in the nonlinear case, the residual accelerations are much weaker than those in Figure 7 are therefore consistent with the known result that the pressure terms dominate the viscous ones in the Lagrangian accelerations in isotropic turbulence, 55 and also with the observation that the fast pressure p L is a relatively small part of the total one. 41,56 However, the magnitude of the terms in which the acceleration can be decomposed is not additive, because the terms are not necessarily uncorrelated. Thus, while it can be concluded from the previous discussion that the much smaller viscous term is not an important part of N , the only reason why N and L can be claimed from Figure 7(a) to be almost equal is that the magnitude of their difference is independently checked to be small.…”

Wall-based identification of coherent structures in wall-bounded turbulence

“…The choice is also motivated by previous works on the scaling of the spectra of the pressure fluctuations at the wall (p w ), which suggests that different frequency content on p w might be related to turbulent sources at different wall-normal locations [15,16]. Since then, several other authors have analysed the spectrum of the pressure fluctuations, using DNS using numerical [17,18] or experimental data [19,20], corroborating the scaling arguments mentioned above. Also, models for the wall-pressure have been formulated using structures based on Townsend's attached eddy hypothesis [21], and some authors have linked specific features of the pressure fluctuations at the wall to coherent structures in the flow [22,23].…”

Reynolds stress scaling in pipe flow turbulence—first results from CICLoPE

“…The Re-independent plateau for the wall-normal variance has previously been documented for R + > 1 × 10 3 [16,60], while the logarithmic scaling for the spanwise component has been observed only at Re that are assessable by DNS [20,61], contrary to its streamwise counterpart. When it comes to high Re pipe-flow experiments, only the wall-normal components have been measured before in the Superpipe, leading to B 2,v = 1.15 2 (= 1.32) [62], which, despite its excessively long wire length (of up to L + = 1226), appears to agree with other studies at lower Re.…”