ALBERT

Description: Experimental evidence suggests that in the turbulent mixing layer the fundamental mechanism of growth is two-dimensional and little affected by the presence of vigorous three-dimensional motion. To quantify this apparent property and study the growth of streamwise vorticity, we write for the velocity field V(x, t) = U(x, z, t) + u(x, y, z, t), where U is two-dimensional and u is three-dimensional. In a first version of the problem U is independent of u, while in the second U is the spanwise average of V. In both cases the equation for u is linearized around U. The equations for U and u are solved simultaneously by a finite-difference calculation starting with a slightly disturbed parallel shear layer. The solutions provide a detailed description of the growth of the three-dimensional motion. They show that its characteristics are dictated by the distribution of spanwise vorticity which results from roll-up and pairing. Pairing inhibits its growth. The solutions also demonstrate that even when the three-dimensional flow attains large amplitudes it has a negligible effect on the interaction of spanwise vortices and thus on the growth of the layer. © 1984, Archives Européenes de Sociology. All rights reserved.

Description: … in hydrodynamic turbulence … the fate of vortices extending in the direction of motion is of great importance (J. M. Burgers 1948).We examine an elementary model of the dynamics of streamwise vorticity in a plane mixing layer. We assume that the vorticity is unidirectional and subjected to a two-dimensional spatially uniform strain, positive along the direction of vorticity. The equations of motion are solved numerically with initial conditions corresponding to a strain-viscous-diffusion balance for a layer with a sinusoidal variation of vorticity. The numerical results are interpreted physically and compared to those of an asymptotic analysis of the same problem by Neu. It is found that strained vortex sheets are fundamentally unstable unless their local strength nowhere exceeds a constant (somewhat larger than 2) times the square root of the product of strain and viscosity. The instability manifests itself by the spanwise redistribution of the vorticity towards the regions of maximum strength. This is accompanied by the local rotation of the layer and the intensification of the vorticity. The end result of this evolution is a set of discrete round vortices whose structure is well approximated by that of axially symmetric vortices in an axially symmetric strain. The phenomenon can proceed (possibly simultaneously) on two separate lengthscales and with two correspondingly different timescales. The first lengthscale is the initial spanwise extent of vorticity of a given sign. The second, relevant to initially thin and spanwise slowly varying vortex layers, is proportional to the layer thickness. The two types of vorticity focusing or collapse are studied separately. The effect of the first on the diffusion rate of a scalar across the layer is calculated. The second is examined in detail for a spanwise-uniform layer: First we solve the eigenvalue problem for infinitesimal perturbations and then use the eigenfunctions as initial conditions for a numerical finite-differences solution. We find that the initial instability is similar to that of unstrained layers, in that roll-up and pairings also follow. However, at each stage a strain-diffusion balance eventually imposes the same cross-sectional lengthscale and each of these events leads to an intensification of the local value of the vorticity.The parameters upon which collapse and its timescale depend are related to those which are known to govern a mixing layer. The results suggest that the conditions for collapse of strained vortex sheets into concentrated round vortices are easily met in a mixing layer, even at low Reynolds numbers, so that these structures whose size is the Taylor microscale are far more plausibly typical than are vortex sheets on that scale. We found that they raise significantly the diffusion rate of scalar attributes by enhancing the rate of growth of material surfaces across which diffusion takes place. Finally, experimental methods that rely on the visualization of the gradient of scalar concentration are shown to be unable to reveal the presence of streamwise vorticity unless that vorticity has already gathered into concentrated vortex tubes.

Description: Procedure for computing subsonic, turbulent flow in turbofan lobe mixers was extended to allow consideration of flow fields in which a swirl component of velocity may be present. Additional, an optional k-lambda turbulence model was added to the procedure. The method of specifying the initial flow field was also modified, allowing parametric specification or radial secondary flow velocities, and making it possible to consider initial flow fields which have significant inlet secondary flow vorticity. A series of example calculations was performed which demonstrate the various capabilities of the modified code. These calculations demonstrate the effects of initial secondary flows of various magnitudes, the effects of swirl, and the effects of turbulence model on the mixing process. The results of these calculations indicate that the initial secondary flows, presumed to be generated within the lobes, play a dominant role in the mixing process, and that the predicted results are relatively insensitive to the turbulence model used.

Description: This study investigates the influence of stable and convective latent heat release on synoptic-scale vertical motions and the corresponding evolution of an extratropical cyclone during a 48 h period of strong development. The cyclone's early evolution was dominated by dry dynamical processes. By midway through the period, however, forcing by latent heat release accounted for over 50 percent of the upward vertical motions, with the convective component dominating. The cyclone's development was most intense during the second 24 h, despite a decrease in latent heat release. During the latter period, the reduced direct latent heat influence may have been augmented by an indirect influence, in which pre-existing dry dynamical forcing was enhanced by diabatic intensification of vorticity and thermal gradients.