dorsal/arxiv
View SchemaPhysics of Flow Instability and Turbulent Transition in Shear Flows
| Authors | Hua-Shu Dou |
|---|---|
| Categories | |
| ArXiv ID | physics/0607004 |
| URL | https://arxiv.org/abs/physics/0607004 |
| Journal | International Journal of Physical Science, 6(6), March 2011, 1411-1425 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model derived strictly from physics is proposed to show that the flow instability under finite amplitude disturbance leads to turbulent transition. The proposed model is named as "energy gradient method." It is demonstrated that it is the transverse energy gradient that leads to the disturbance amplification while the disturbance is damped by the energy loss due to viscosity along the streamline. It is also shown that the threshold of disturbance amplitude obtained is scaled with the Reynolds number by an exponent of -1, which exactly explains the recent modern experimental results by Hof et al. for pipe flow. The mechanism for velocity inflection and hairpin vortex formation are explained with reference to analytical results. Following from this analysis, it can be demonstrated that the critical value of the so called energy gradient parameter Kmax is constant for turbulent transition in wall bounded parallel flows, and this is confirmed by experiments and is about 370-389. The location of instability initiation in the flow field accords well with the experiments for both pipe Poiseuille flow (r/R=0.58) and plane Poiseuille flow (y/h=0.58). It is also inferred from the proposed method that the transverse energy gradient can serve as the power for the self-sustaining process of wall bounded turbulence. Finally, the relation of "energy gradient method" to the classical "energy method" based on Rayleigh-Orr equation is discussed.
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"abstract": "In this paper, the physics of flow instability and turbulent transition in\nshear flows is studied by analyzing the energy variation of fluid particles\nunder the interaction of base flow with a disturbance. For the first time, a\nmodel derived strictly from physics is proposed to show that the flow\ninstability under finite amplitude disturbance leads to turbulent transition.\nThe proposed model is named as \"energy gradient method.\" It is demonstrated\nthat it is the transverse energy gradient that leads to the disturbance\namplification while the disturbance is damped by the energy loss due to\nviscosity along the streamline. It is also shown that the threshold of\ndisturbance amplitude obtained is scaled with the Reynolds number by an\nexponent of -1, which exactly explains the recent modern experimental results\nby Hof et al. for pipe flow. The mechanism for velocity inflection and hairpin\nvortex formation are explained with reference to analytical results. Following\nfrom this analysis, it can be demonstrated that the critical value of the so\ncalled energy gradient parameter Kmax is constant for turbulent transition in\nwall bounded parallel flows, and this is confirmed by experiments and is about\n370-389. The location of instability initiation in the flow field accords well\nwith the experiments for both pipe Poiseuille flow (r/R=0.58) and plane\nPoiseuille flow (y/h=0.58). It is also inferred from the proposed method that\nthe transverse energy gradient can serve as the power for the self-sustaining\nprocess of wall bounded turbulence. Finally, the relation of \"energy gradient\nmethod\" to the classical \"energy method\" based on Rayleigh-Orr equation is\ndiscussed.",
"arxiv_id": "physics/0607004",
"authors": [
"Hua-Shu Dou"
],
"categories": [
"physics.flu-dyn",
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],
"journal_ref": "International Journal of Physical Science, 6(6), March 2011,\n 1411-1425",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Physics of Flow Instability and Turbulent Transition in Shear Flows",
"url": "https://arxiv.org/abs/physics/0607004"
},
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