Destabilization of the Type-II eigenmode in boundary layers over compliant rotating disks was predicted theoretically by Cooper and Carpenter ͓J. Fluid Mech. 350, 231 ͑1997͔͒. Their results showed that for relatively low levels of compliance the Type-II eigenmode was destabilized, to be stabilized and ultimately eliminated for higher levels of compliance. The goal of the present study was to obtain the first experimental verification of the prediction that the Type-II mode can be destabilized at low levels of compliance. To this end a new type of rotating-disk apparatus was designed and a new type of material was used to produce suitable compliant walls for the experiments. Background noise in the new facility is substantially reduced in comparison with that in facilities used in related previous studies. This enabled the detection of substantially cleaner hot-film signals. Although the mean base flow remained unchanged, noise characteristics have been improved and turbulence intensities are significantly reduced. The measurements reveal not only the comparatively strong signals from the Type-I ͑cross-flow vortices͒ instability mode but also clear evidence of the Type-II eigenmode. In agreement with the theory of Cooper and Carpenter the data analysis shows that relatively low levels of wall compliance destabilize the Type-II mode.
Boundary-layer transition over a disk spinning under water is investigated. Transitional Reynolds numbers, Rec, and associated boundary-layer velocity profiles are determined from flow-visualizations and hot-film measurements, respectively. The value of Rec and the velocity profiles are studied as a function of the disk’s surface roughness. It is found that transition over rough disks occurs in a similar fashion to that over smooth disks, i.e., abruptly and axisymmetrically at well-defined radii. Wall roughness has little effect on Rec until a threshold relative roughness is reached. Above the threshold Rec decreases sharply. The decrease is consistent with the drop one expects for our flow for the absolute instability discovered by Lingwood [J. Fluid Mech. 299, 17 (1995); 314, 373 (1996); 331, 405 (1997)]. This indicates that the Lingwood absolute instability may continue to play a major role in the transition process even for large relative roughness.
We present a relatively simple, deterministic, theoretical model for the sublayer streaks in a turbulent boundary layer based on an analogy with Klebanoff modes. Our approach is to generate the streamwise vortices found in the buffer layer by means of a vorticity source in the form of a fictitious body force. It is found that the strongest streaks correspond to a spanwise wavelength that lies within the range of the experimentally observed values for the statistical mean streak spacing. We also present results showing the effect of streamwise pressure gradient, Reynolds number and wall compliance on the sublayer streaks. The theoretical predictions for the effects of wall compliance on the streak characteristics agree well with experimental data. Our proposed theoretical model for the quasi-periodic bursting cycle is also described, which places the streak modelling in context. The proposed bursting process is as follows: (i) streamwise vortices generate sublayer streaks and other vortical elements generate propagating plane waves, (ii) when the streaks reach a sufficient amplitude, they interact nonlinearly with the plane waves to produce oblique waves that exhibit transient growth, and (iii) the oblique waves interact nonlinearly with the plane wave to generate streamwise vortices; these in turn generate the sublayer streaks and so the cycle is renewed.
Torsional Couette flow between a rotating disk and a stationary wall is studied experimentally. The surface of the disk is either rigid or covered with a compliant coating. The influence of wall compliance on characteristic flow instabilities and on the laminar-turbulent flow transition is investigated. Data obtained from analysing flow visualizations are discussed. It is found that wall compliance favours two of the three characteristic wave patterns associated with the transition process and broadens the parameter regime in which these patterns are observed. The results for the effects of wall compliance on the third pattern are inconclusive. However, the experiments indicate that the third pattern is not a primary constituent of the laminar-turbulent transition process of torsional Couette flow. IntroductionThe concept of developing compliant coatings as a technique for laminar-flow control and, hence, for drag reduction has become widely known following the seminal publications of Kramer (1957Kramer ( , 1960Kramer ( , 1962Kramer ( , 1965. However, after the publication of his experimental results, dispute arose concerning the nature of compliant-wall/fluid-flow interactions and the feasibility of the suggested technique (Carpenter, Davies & Lucey 2000).Over the last twenty years it has been clearly established through experiments and theory that wall compliance can suppress the growth of Tollmien-Schlichting waves, leading to substantial delays in the onset of laminar-turbulent transition (see reviews by Riley, Gad-el-Hak & Metcalfe 1988;Carpenter 1990;Carpenter et al. 2000;Carpenter, Lucey & Davies 2001and Gad-el-Hak 1996, 2003. However, this favourable evidence really only applies to low-noise flow environments, similar to the flat-plate boundary layer, where amplification of Tollmien-Schlichting waves is the primary route to transition. In many applications, other, quite different and much more powerful instabilities may be dominant and result in transition. An important example is the cross-flow vortices that develop near the leading edge of a swept wing. These also develop in the three-dimensional boundary layer over a rotating disk. This is one of the reasons why flow instability and transition in the rotating-disk flow has been widely investigated in the past.
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