Experiments in Transient Growth and Roughness-Induced Bypass Transition

Abstract

SummaryThe work reported here is a series of wind-tunnel experiments that establishes the basic behavior of roughness-induced disturbances that undergo transient algebraic growth in a laminar boundary layer. The experiments explore three aspects of these disturbances' behavior: their fundamental response to various configurations of surface roughness, their receptivity, and their behavior when the surface roughness amplitude is large. The experiments consist of hotwire measurements of the steady and unsteady disturbances created by isolated 3D roughness elements, spanwise arrays of 3D elements and patches of random, distributed roughness. Spanwise roughness arrays are used most extensively as these are found to produce disturbances best-suited for comparison with theoretical predictions.The results establish that surface roughness does create disturbances that undergo transient growth and that it does so in a manner consistent with the physical picture known as Landahl's lift-up mechanism. The observed growth is qualitatively similar to what is predicted by optimal-disturbance theory. However, theoretical predictions tend to overestimate the length over which disturbances grow and are thought to overestimate the total amount of transient growth.The difference between what is predicted by optimal disturbance theories and what is observed in the experiments is linked to receptivity. Receptivity is found to play two roles in the transient growth phenomenon: it determines initial disturbance amplitude and also distributes energy among the modes of the continuous disturbance spectrum. This second effect is associated with the initial-value-problem formulation of the transient growth problem and explains why some disturbances grow and decay in a manner very similar to what is predicted by optimal-disturbance theory while others only decay and others undergo a significant decay and then a weak phase of transient growth. Regardless of whether certain disturbances undergo transient growth or not, all of the roughness-induced disturbances studied in this experiment have energies that scale approximately as the square of roughness-based Reynolds number across a wide range of Reynolds numbers. At high values of the roughness-based Reynolds number (above approximately 250) transition occurs just aft of the arrays of 3D roughness elements. This transition does not appear to be connected with transient growth. Rather, it occurs because the element's wakes are unstable to a high-frequency Kelvin-Helmoholtz type instability mechanism. Transient growth of steady disturbances only occurs if this rapid transition connected with the unsteady disturbances does not occur.

Mechanisms of flow tripping by discrete roughness elements in a swept-wing boundary layer

“…A series of experiments aimed at the understanding of roughness-induced transient growth was conducted by, e.g. White & Ergin (2003), Ergin & White (2005, Denissen & White (2008); the major findings are compiled in White (2005). White & Ergin (2003) observed that the energy associated with transiently amplified disturbances scales with Re 2 kk for roughness elements.…”