Robert E. Breidenthal

A simple model of mixing and chemical reaction in a turbulent shear layer

Arguments are presented to show that the concept of gradient diffusion is inapplicable to mixing in turbulent shear layers. A new model is proposed for treating molecular mixing and chemical reaction in such flows at high Reynolds number. It is based upon the experimental observations that revealed the presence of coherent structures and that showed that fluid elements from the two streams are distributed unmixed throughout the layer by large-scale inviscid motions. The model incorporates features of the strained flame model and makes use of the Kolmogorov cascade in scales. Several model predictions differ markedly from those of diffusion models and suggest experiments for testing the two approaches.

Structure and mixing of a transverse jet in incompressible flow

The flow field induced by a jet in incompressible cross-flow is analysed and the results compared with those obtained in a reacting water-jet experiment. It is argued that the axial vortex pair in the flow arises from the jet momentum normal to the free stream, the momentum flux being equivalent to a normal force, i.e. to a lift.

Structure, Penetration, and Mixing of Pulsed Jets in Crossflow

Effects of periodic disturbances on the structure and mixing of a transverse jet have been investigated through chemically reactive laser-induced fluorescence experiments in a water model. Flow visualization experiments with a steady, round jet in crossflow revealed a distinct vortex loop merging pattern among the vortices that make up the curved shear layer around the jet. As the vortex loops are stretched and distorted, certain parts of the neighboring loops with the opposite or the same sign of vorticity merge, resulting in cancellation or intensification of the vorticity in the corresponding regions of the jet. When the flow rate of this jet was periodically modulated by a square wave, however, distinct vortex rings were created whose spacing and strength were dictated by the pulsing frequency for a given jet and crossflow combination. At low pulsing rates, these rings penetrated into the crossflow significantly deeper than the steady jet. An optimum pulsing frequency was found at which closely spaced vortex rings were observed, which penetrated as discrete vortices into the crossflow in the near field. Strong interactions among neighboring rings were observed farther downstream

Response of plane shear layers and wakes to strong three‐dimensional disturbances

Shear layers and wakes formed downstream of a splitter plate whose trailing edge has spanwise variations were briefly explored using the reacting flow visualization technique. A fundamental difference in behavior was observed between the two types of flows. The shear layer (which has only one sign of mean vorticity) rapidly forms its characteristic two‐dimensional vortex structures, whereas, in contrast, the wake (which has both signs of mean vorticity) forms closed vortex loops. These loops do not grow appreciably in the spanwise direction over the test section length, even though the transverse growth is comparable to the two‐dimensional wake behavior. The global structure of the shear layer quickly forgets the initial perturbations, while the wake remembers them. The results strongly suggest that the presence of only one or both signs of mean vorticity in these plane turbulent flows has a fundamental bearing on the spanwise structure and stability of the vorticity field.

Sonic Eddy—A Model for Compressible Turbulence

A new model is proposed for entrainment in supersonic turbulence. The central assumption is that only those eddies whose rotational Mach number is unity directly engulf fluid. With the additional assumption that a Kolmogorov spectrum of eddy scales exists for all subsonic eddies, the theoretical effect of the sonic eddy on entrainment and structure is compared to observation in shear layers and wakes

Laboratory experiments on the cloud-top entrainment instability

The stability of stratocumulus clouds with strong evaporative cooling effects is explored in laboratory simulations. Two fluids, initially separated by a thin horizontal plate, contain mixtures of water, alcohol and glycol which have a strongly nonlinear density as a function of mixture ratio. Initially, the fluid below the plate is more dense than that above the plate. When the plate is suddenly withdrawn, the turbulence in its wake mixes the two fluids together, producing mixtures with densities greater than that of either initial fluid. It is found that the system is unstable to strong perturbations only in cases of relatively large buoyancy reversal. The system is stable to strong perturbations if the buoyancy reversal is comparable to or less than the initial stratification. A simple model is presented to explain the results.

The turbulent exponential jet

A new, self‐similar, turbulent jet flow is postulated in which the global vorticity Ω is a constant following any vortex. In contrast, conventional self‐similar flows all exhibit Ω inversely proportional to the vortex age. In order for the new, postulated flow to exist, the nozzle exit speed must increase exponentially with time. It is shown that this circumstance may strongly inhibit the entrainment of ambient fluid into the jet.

TURBULENCE INSIDE A VORTEX

Following Bradshaw’s analogy between rotating and stratified flows, the turbulence within a vortex is analyzed using a new model for stratified entrainment. At the vortex radius where the tangential velocity is a maximum, the model predicts that the flow is so strongly “stratified” that even the smallest turbulent eddies are incapable of transporting fluid there. The growth of the vortex is thus limited by molecular viscosity, even though the vortex Reynolds number is large. The model prediction is compared to experiments in the literature of wingtip vortices. The result is consistent with the remarkable observations of laminar-like growth of this turbulent flow.

Non‐stationary entrainment and tunneling eruptions: A dynamic link between eruption processes and magma mixing

The products of many intermediate arc volcanoes and batholiths manifest compositional complexity with mafic and mixed material occurring early and through-out a period of eruption and pluton assembly. We present a vesiculation model suggesting that the progressive and repeated vesiculation of volatile-rich magmas yields a super-linear buoyancy acceleration. This style of non-stationary entrainment provides a mechanism for compositional reversal, the intimate co-occurrence of mixed and un-mixed magmas, and rapid, chaotic crystal and melt dispersal. Under some circumstances, entrainment can cease entirely, producing eruptions with compositional tunneling where nearly unmixed mafic, or newly intruded silicic magma, exits first.

A model of stratified entrainment using vortex persistence

A new model is proposed for the entrainment rate by vortices across stratified interfaces. In the model, different entrainment regimes are distinguished by the conventional parameters Richardson, Reynolds, and Schmidt number as well as a new parameter, the “vortex persistence”. Vortex persistence is defined as the number of rotations a vortex makes during the time it moves its own diameter with respect to the interface. It is further proposed that the concept of vortex persistence is important whenever a vortex is near any kind of surface, either stratified or solid. The model is in accord with most field and laboratory observations in a variety of stratified and bounded flows, including measurements of wall heat transfer and vortex formation in starting jets.