Tributes & Remembrances

From a memorial service held in memory of Charles Price, Professor Emeritus of Art History, at Harkness Chapel, Connecticut College, April 13, 2004. With tributes written by Barbara Zabel, Christopher London, Brian Rogers, Cynthia Willauer, Maureen McCabe and John H. B. Knowlton. Illustrations by Charles Price

The three-dimensional evolution of a plane mixing layer. Part 1: The Kelvin-Helmholtz roll-up

The Kelvin Helmholtz roll up of three dimensional, temporally evolving, plane mixing layers were simulated numerically. All simulations were begun from a few low wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity profile. The spanwise disturbance wavelength was taken to be less than or equal to the streamwise wavelength associated with the Kelvin Helmholtz roll up. A standard set of clean structures develop in most of the simulations. The spanwise vorticity rolls up into a corrugated spanwise roller, with vortex stretching creating strong spanwise vorticity in a cup shaped region at the vends of the roller. Predominantly streamwise rib vortices develop in the braid region between the rollers. For sufficiently strong initial three dimensional disturbances, these ribs collapse into compact axisymmetric vortices. The rib vortex lines connect to neighboring ribs and are kinked in the opposite direction of the roller vortex lines. Because of this, these two sets of vortex lines remain distinct. For certain initial conditions, persistent ribs do not develop. In such cases the development of significant three dimensionality is delayed. When the initial three dimensional disturbance energy is about equal to, or less than, the two dimensional fundamental disturbance energy, the evolution of the three dimensional disturbance is nearly linear (with respect to the mean and the two dimensional disturbances), at least until the first Kelvin Helmholtz roll up is completed

Coherent structures in a simulated turbulent mixing layer

A direct numerical simulation of a plane turbulent mixing layer has been performed. The simulation was initialized using two turbulent velocity fields obtained from direct numerical simulation of a turbulent boundary layer at momentum thickness Reynolds number 300 (Spalart, 1988). The mixing layer is allowed to evolve long enough for self-similar linear growth to occur, with the visual thickness Reynolds number reaching 14,000. The simulated flow is examined for evidence of the coherent structures expected in a mixing layer (rollers and rib vortices). Before the onset of self-similar growth, such structures are present with properties similar to the corresponding laminar or transitional structures. In the self-similar growth regime, however, only the rollers are present with no indication of rib vortices and no indication of conventional pairing. This results in a reduction of mixing and layer growth

The three-dimensional evolution of a plane mixing layer. Part 2: Pairing and transition to turbulence

The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings was simulated numerically. Initial conditions for all simulations consisted of a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found both to inhibit the growth of infinitesimal three-dimensional disturbances and to trigger the transition to turbulence in highly three dimensional flows. The mechanisms responsible for the growth of three-dimensionality as well as the initial phases of the transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of span wise vorticity, which undergo a secondary roll up. Transition also produces an increase in the degree of scalar mixing, in agreement with experimental observations of mixing transition. Simulations were also conducted to investigate changes in span wise length scale that may occur in response to the change in stream wise length scale during a pairing. The linear mechanism for this process was found to be very slow, requiring roughly three pairings to complete a doubling of the span wise scale. Stronger three-dimensionality can produce more rapid scale changes but is also likely to trigger transition to turbulence. No evidence was found for a change from an organized array of rib vortices at one span wise scale to a similar array at a larger span wise scale