Structure and entrainment in the plane of symmetry of a turbulent spot

Publisher Website
Google Scholar
Abstract
Laser-Doppler velocity measurements in water are reported for the flow in the plane of symmetry of a turbulent spot. The unsteady mean flow, defined as an ensemble average, is fitted to a conical growth law by using data at three streamwise stations to determine the virtual origin in x and t. The two-dimensional unsteady stream function is expressed as in conical similarity co-ordinates ζ = x/U∞t and η = y/U∞t. In these co-ordinates, the equations for the unsteady particle displacements reduce to an autonomous system. This system is integrated graphically to obtain particle trajectories in invariant form. Strong entrainment is found to occur along the outer part of the rear interface and also in front of the spot near the wall. The outer part of the forward interface is passive. In terms of particle trajectories in conical co-ordinates, the main vortex in the spot appears as a stable focus with celerity 0·77U∞. A second stable focus with celerity 0·64U∞ also appears near the wall at the rear of the spot.Some results obtained by flow visualization with a dense, nearly opaque suspension of aluminium flakes are also reported. Photographs of the sublayer flow viewed through a glass wall show the expected longitudinal streaks. These are tentatively interpreted as longitudinal vortices caused by an instability of Taylor-Görtler type in the sublayer.