The mixing layer: deterministic models of a turbulent flow. Part 1. Introduction and the two-dimensional flow

1984 ◽  
Vol 139 ◽  
pp. 29-65 ◽  
Author(s):  
G. M. Corcos ◽  
F. S. Sherman

The prevalence in a turbulent mixing layer of dynamical events with a coherent history over substantial times suggests that it is profitable to study in detail entirely deterministic versions of this flow and to attempt to use a simplified synthesis of these solutions as the fundamental representation in a stochastic treatment of the layer. It is proposed that the deterministic representation of the flow be achieved by the embedding of a short hierarchy of motions which are studied in detail, though not exhaustively, in Parts 1, 2 and 3. Part 1 deals with the fundamental or first-order motion, which is the evolution of a layer constrained to be purely two-dimensional.

1984 ◽  
Vol 139 ◽  
pp. 67-95 ◽  
Author(s):  
G. M. Corcos ◽  
S. J. Lin

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 \[ {\boldmath V}(x, t) = {\boldmath U}(x, z, t) + {\boldmath u}(x, y, z, t), \] 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.


2007 ◽  
Vol 589 ◽  
pp. 479-507 ◽  
Author(s):  
E. KIT ◽  
I. WYGNANSKI ◽  
D. FRIEDMAN ◽  
O. KRIVONOSOVA ◽  
D. ZHILENKO

The flow in a turbulent mixing layer resulting from two parallel different velocity streams, that were brought together downstream of a jagged partition was investigated experimentally. The trailing edge of the partition had a short triangular ‘chevron’ shape that could also oscillate up and down at a prescribed frequency, because it was hinged to the stationary part of the partition to form a flap (fliperon). The results obtained from this excitation were compared to the traditional results obtained by oscillating a two-dimensional fliperon. Detailed measurements of the mean flow and the coherent structures, in the periodically excited and spatially developing mixing layer, and its random constituents were carried out using hot-wire anemometry and stereo particle image velocimetry.The prescribed spanwise wavelength of the chevron trailing edge generated coherent streamwise vortices while the periodic oscillation of this fliperon locked in-phase the large spanwise Kelvin–Helmholtz (K-H) rolls, therefore enabling the study of the inter- action between the two. The two-dimensional periodic excitation increases the strength of the spanwise rolls by increasing their size and their circulation, which depends on the input amplitude and frequency. The streamwise vortices generated by the jagged trailing edge distort and bend the primary K-H rolls. The present investigation endeavours to study the distortions of each mode as a consequence of their mutual interaction. Even the mean flow provides evidence for the local bulging of the large spanwise rolls because the integral width (the momentum thickness, θ), undulates along the span. The lateral location of the centre of the ensuing mixing layer (the location where the mean velocity is the arithmetic average of the two streams,y0), also suggests that these vortices are bent. Phase-locked and ensemble-averaged measurements provide more detailed information about the bending and bulging of the large eddies that ensue downstream of the oscillating chevron fliperon. The experiments were carried out at low speeds, but at sufficiently high Reynolds number to ensure naturally turbulent flow.


1990 ◽  
Vol 56 (528) ◽  
pp. 2189-2197 ◽  
Author(s):  
Akito ANDO ◽  
Hiroaki SADATA ◽  
Koichi HISHIDA ◽  
Masanobu MAEDA

2007 ◽  
Vol 178 (3) ◽  
pp. 151-165 ◽  
Author(s):  
Xiaogang Yang ◽  
Chris Rielly ◽  
Li Li ◽  
Guang Li ◽  
Bin Chen ◽  
...  

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