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Coherent structures and wall pressure fluctuations
As pointed out above, it is possible to establish a connection between the wall pressure wavenumber spectra and physical quantities describing the turbulent boundary layer. In particular, the high wavenumber components should be attributed to fluid dynamic structures in the near wall region while the low wavenumber domain is influenced by the large scale structures in the outer layer. However, the detailed features of organized events that occur in the boundary layer are lost by the unconditional averaging techniques used in obtaining spectral estimates of the pressure field. This is an important issue from the practical viewpoint since a deeper knowledge of the fluid dynamic structures underlying the observed pressure properties may be helpful to address suitable control strategies aimed at manipulating the flow structures and modifying the wall pressure behavior.
Numerical simulations of simplified configurations attempted to clarify the connection between wall pressure fields and near wall vortical structures whose topology was selected a-priori according to classical conceptual models of the turbulent boundary layer. For example, Dhanak & Dowling (1995) and Dhanak, Dowling & Si (1997), following the conceptual model of the boundary layer proposed by Orlandi & Jimenez (1994), were able to clarify the effect of near wall quasi-streamwise structures upon the wall pressure field. More recently, Ahn, Graham & Rizzi (2004) and Ahn, Graham & Rizzi (2010) reproduced correlations and spectra at the wall. In order to estimate the wall pressure distribution, they reproduced hairpin vortex dynamics on the basis of the so called attached eddy model proposed by Perry & Chong (1982).
Only a few experiments have been focused on these aspects, since the correlation between wall pressure and coherent structures is rather difficult to interpret due to the chaotic nature of the pressure field. Among the existing studies, the work by Johansson, Her & Haritonidis (1987) can be mentioned: they carried out simultaneous pressure-velocity measurements and suggested physical mechanisms for the underlying generation of positive or negative pressure peaks at the wall. However, they did not clarify the connection between the educed structures and the wall pressure spectral quantities.
In a recent paper, Camussi, Robert & Jacob (2008) applied non conventional time-frequency post-processing tools to analyze wall pressure experimental data. The application of multi-variate wavelet transform permitted them to establish a connection between sweep/ejections events and large pressure coherence. More specifically, using a conditional sampling technique, they observed that averaged pressure signatures due to hydrodynamic effects were composed of a large negative pressure drop coupled to a weaker positive bump. This behavior was ascribed to accelerated-decelerated motions within the turbulent boundary layer.
The presence of a positive pressure bump coupled with a stronger negative pressure drop was also observed by Dhanak & Dowling (1995) who simulated numerically the pressure field induced at the wall by streamwise vortices. Similarly, in an experiment performed by Johansson, Her & Hari – tonidis (1987) negative-positive pressure jumps were also observed and were identified as burst — sweep events. The conditional results of Johansson, Her & Haritonidis (1987) were obtained by correlating pressure negative peaks with velocity events found in the buffer region of the boundary layer through the so-called VITA technique [see e. g. Blackwelder & Kaplan (1976)].
Analogous conclusions were driven by Jayasundera, Casarella & Russell (1996) through the investigation of experimental wall pressure and inflow velocity data and the application of coherent structures identification techniques. They showed that the organized structures present within the turbulent boundary layer contain both ejection and sweep motions inducing positive and negative pressure events respectively.
More recently, Kim, Choi & Sung (2002) attempted to correlate the wall pressure fluctuations with the streamwise vortices of a numerically simulated turbulent boundary layer. They suggest that the high negative wall pressure fluctuations are due to outward motion in the vicinity of the wall correlated to the presence of streamwise vortices.
