Nonlinear stability of a stratified shear flow in the regime with an unsteady critical layer. Part 2. Arbitrary stratification of asymmetric flow

Author:

CHURILOV S. M.

Abstract

A weakly nonlinear analysis of the downstream evolution of weakly unstable disturbances in a stably stratified mixing layer with a large Reynolds number is carried out. No other requirements are imposed upon velocity and density profiles, thus making it possible to overcome the restrictions placed in earlier studies (Brown & Stewartson 1978; Brown et al. 1981; Churilov & Shukhman 1987, 1988) by a particular choice of weakly supercritical flow models assuming symmetry. For each of the two critical layer regimes possible here, viscous and unsteady, evolution equations are obtained, their solutions and competition between nonlinearities in the course of instability development are analysed, and evolution scenarios for unstable disturbances are constructed for different levels of their supercriticality. It is established that the regime with a nonlinear critical layer does not arise in an evolutionary manner, except for the previously studied case of a weak stratification (Shukhman & Churilov 1997). It is shown that while in the viscous critical layer regime the relaxation of assumptions of the symmetry and weak supercriticality of the flow produces no fundamental changes in the theory, in the unsteady critical layer regime a new (non-dissipative cubic) nonlinearity appears which governs the instability development on equal terms with two already known nonlinearities. Results are illustrated by calculations for two families of flow models with a controlled degree of asymmetry.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3