NONLINEAR SPATIAL EVOLUTION OF HELICAL DISTURBANCES TO AN AXIAL JET

被引:19
作者
CHURILOV, SM
SHUKHMAN, IG
机构
[1] Institute of Solar-Terrestrial Physics, Irkutsk, 664033
关键词
D O I
10.1017/S0022112094003150
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
We investigate the weakly nonlinear spatial evolution of helical disturbances of an axisymmetrical jet which are the analogue of three-dimensional disturbances, such as a single oblique wave (the wave vector is directed at an angle to the main flow velocity) in plane-parallel flows. It is shown that when a supercriticality is large enough, the perturbation amplitude A grows in the streamwise direction (along z) explosively: A similar to (z(0)-z)(-5/2), though more slowly than in the case of essentially three-dimensional disturbances in the form of a pair of oblique waves (A similar to (z(0) - z)(-3); Goldstein and Choi 1989). The nonlinearity needed for such a growth, is due equally to the cylindricity of shear layer and to the spatial character of the evolution (in the temporal problem the 'evolution' contribution is absent). At a smaller supercriticality, the evolution equation has a non-local (integral in z) nonlinearity, unusual for the regime of a viscous critical layer. Scenarios of disturbance development for different levels of supercriticality are studied, with proper account taken of viscous broadening of the flow.
引用
收藏
页码:371 / 402
页数:32
相关论文
共 21 条
[1]   NONLINEAR STABILITY OF A STRATIFIED SHEAR-FLOW IN THE REGIME WITH AN UNSTEADY CRITICAL LAYER [J].
CHURILOV, SM ;
SHUKHMAN, IG .
JOURNAL OF FLUID MECHANICS, 1988, 194 :187-216
[2]   THE NONLINEAR DEVELOPMENT OF DISTURBANCES IN A ZONAL SHEAR-FLOW [J].
CHURILOV, SM ;
SHUKHMAN, IG .
GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS, 1987, 38 (03) :145-175
[3]  
CHURILOV SM, IN PRESS IZV RAN FIZ
[4]  
CHURILOV SM, 1993, ISTP493 PREPR
[5]  
CHURILOV SM, 18TH INT C THEOR APP, P39
[6]   THE EVOLUTION OF INSTABILITIES IN THE AXISYMMETRICAL JET .1. THE LINEAR GROWTH OF DISTURBANCES NEAR THE NOZZLE [J].
COHEN, J ;
WYGNANSKI, I .
JOURNAL OF FLUID MECHANICS, 1987, 176 :191-219
[7]   THE EVOLUTION OF INSTABILITIES IN THE AXISYMMETRICAL JET .2. THE FLOW RESULTING FROM THE INTERACTION BETWEEN 2 WAVES [J].
COHEN, J ;
WYGNANSKI, I .
JOURNAL OF FLUID MECHANICS, 1987, 176 :221-235
[8]   NONLINEAR SPATIAL EVOLUTION OF AN EXTERNALLY EXCITED INSTABILITY WAVE IN A FREE SHEAR-LAYER [J].
GOLDSTEIN, ME ;
HULTGREN, LS .
JOURNAL OF FLUID MECHANICS, 1988, 197 :295-330
[9]   NONLINEAR EVOLUTION OF INTERACTING OBLIQUE WAVES ON TWO-DIMENSIONAL SHEAR LAYERS [J].
GOLDSTEIN, ME ;
CHOI, SW .
JOURNAL OF FLUID MECHANICS, 1989, 207 :97-120
[10]   NONLINEAR EVOLUTION OF OBLIQUE WAVES ON COMPRESSIBLE SHEAR LAYERS [J].
GOLDSTEIN, ME ;
LEIB, SJ .
JOURNAL OF FLUID MECHANICS, 1989, 207 :73-96