On a turbulent ‘spot’ in a laminar boundary layer

Abstract

Artificially initiated turbulent spots in a Blasius boundary layer were investi- gated experimentally using hot-wire anemometers. Electrical discharges generated the spots, which grew in all directions rn they were swept downstream by the mean flow. A typical lateral spread angle of the spots is 10° to each side of t.he plane of symmetry. Conditional sampling methods were used to form ensemble-averaged data yielding the average shape of a spot and the mean flow field in its vicinity. Far downstream a spot exhibits conical similarity and all quantities measured seem to be independent of the type of disturbance which generated the spot in the first place.

In plan view, the spot has an arrowhead shape whose leading interface is convected downstream somewhat more slowly than the free-stream velocity near the plane of symmetry and at approximately half the free-stream velocity at the extreme spanwise location. The trailing interface is convected at a constant velocity throughout (U_TE = 0·5 U∞). In this way the spot entrains laminar fluid through both interfaces, resulting in its elongation it proceeds downstream. The flow near the surface accelerates abruptly as the leading interface passes by, however the acceleration continues within the spot and the velocity attains a maximum near the trailing interface. There is therefore a continuous increase in skin friction towards the trailing interface. Further away from the surface the passage of the spot is marked by deceleration followed by acceleration after the ridge of the spot passes the measuring station. All changes in velocity occur monotonically without causing inflexions or kinks in the ensemble-averaged velocity profiles. Although the displacement and momentum thicknesses change quite rapidly within the spot, the shape factor is practically constant in the interior region (H = 1·5); and the velocity profiles may be very well represented by the universal logarithmic distribution. The spanwise velocity component W is everywhere directed outwards (i.e. away from the plane of symmetry) and increases with increasing z. The component of velocity normal to the surface is directed towards the plate near the leading interface and away from it in the remaining part of the spot.

Two-point velocity correlation measurements suggest that the spot may be represented by an arrowhead vortex tube which is convected downstream with a velocity equal to 65 yo of the free-stream velocity. Pluid which is entrained near the plane of symmetry acquires a helical motion towards the extremities of the spot. This motion helps to explain the lateral as well as the longitudinal spread of the spot.