دورية أكاديمية
ON THE NONLINEAR EVOLUTION OF INSTABILITY MODES IN UNSTEADY SHEAR LAYERS: THE STOKES LAYER AS A PARADIGM
| العنوان: | ON THE NONLINEAR EVOLUTION OF INSTABILITY MODES IN UNSTEADY SHEAR LAYERS: THE STOKES LAYER AS A PARADIGM |
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| المؤلفون: | WU, XUESONG, COWLEY, STEPHEN J. |
| بيانات النشر: | Oxford University Press |
| سنة النشر: | 1995 |
| المجموعة: | HighWire Press (Stanford University) |
| مصطلحات موضوعية: | Articles |
| الوصف: | The Stokes layer generated by a flat plate oscillating sinusoidally in an infinite fluid is an important prototype of unsteady flows. It is known to be susceptible to high-frequency instabilities at large Reynolds numbers. Linear theory shows that small disturbances can grow exponentially over part of a period, before becoming neutral at a later time. We show that at times when a disturbance is almost neutral, it can evolve through a weakly nonlinear stage. Our approach is a simple extension of previous non-equilibrium critical-layer theories developed for quasi-parallel flows. For any inviscidly unstable, unsteady shear layer, we present a unified explanation of the asymptotic scalings required to describe three distinct types of small disturbance. We then specialize to weakly nonlinear two-dimensional disturbances, and show that when the critical layer is ‘singular’ the amplitude equation is of Hickernell's ( 1 ) integro-differential type. Solutions to this equation develop finitetime singularities if viscous effects are not too large. For the particular case of a Stokes layer, we find that for a class of disturbances with normalized wavenumbers in the range [0, 0–6] or [1–29, 1–43], the singularity can be eliminated by sufficiently large viscous effects; the instability wave then evolves to an equilibrium state. However, for wavenumbers in the range [0–6, 1–29], a finite-time singularity occurs no matter how large the scaled viscosity parameter is. This nonlinear explosive amplification may be related to the rapid growth of high-frequency disturbances observed as bursts in experiments. |
| نوع الوثيقة: | text |
| وصف الملف: | text/html |
| اللغة: | English |
| العلاقة: | http://qjmam.oxfordjournals.org/cgi/content/short/48/2/159Test; http://dx.doi.org/10.1093/qjmam/48.2.159Test |
| DOI: | 10.1093/qjmam/48.2.159 |
| الإتاحة: | https://doi.org/10.1093/qjmam/48.2.159Test http://qjmam.oxfordjournals.org/cgi/content/short/48/2/159Test |
| حقوق: | Copyright (C) 1995, Oxford University Press |
| رقم الانضمام: | edsbas.798AFD87 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1093/qjmam/48.2.159 |
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