Cause-and-effect of linear mechanisms sustaining wall turbulence
| Autor: | Marios-Andreas Nikolaidis, Navid C. Constantinou, Michael Karp, Adrián Lozano-Durán |
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| Rok vydání: | 2021 |
| Předmět: |
Physics
Physical model Linear stability theory Turbulence Mechanical Engineering Fluid Dynamics (physics.flu-dyn) FOS: Physical sciences Physics - Fluid Dynamics Mechanics Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Exponential function Physics::Fluid Dynamics Nonlinear system Flow (mathematics) Mechanics of Materials 0103 physical sciences Mean flow 010306 general physics Parametric statistics |
| Zdroj: | Journal of Fluid Mechanics |
| ISSN: | 1469-7645 0022-1120 |
| Popis: | Despite the nonlinear nature of turbulence, there is evidence that part of the energy-transfer mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities, neutral modes, transient growth from non-normal operators, and parametric instabilities from temporal mean-flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in theoretical and conceptual arguments. Whether the flow follows any or a combination of them remains elusive. Here, we evaluate the linear mechanisms responsible for the energy transfer from the streamwise-averaged mean-flow ($\bf U$) to the fluctuating velocities ($\bf u'$). We use cause-and-effect analysis based on interventions. This is achieved by direct numerical simulation of turbulent channel flows at low Reynolds number, in which the energy transfer from $\bf U$ to $\bf u'$ is constrained to preclude a targeted linear mechanism. We show that transient growth is sufficient for sustaining realistic wall turbulence. Self-sustaining turbulence persists when exponential instabilities, neutral modes, and parametric instabilities of the mean flow are suppressed. We further show that a key component of transient growth is the Orr/push-over mechanism induced by spanwise variations of the base flow. Finally, we demonstrate that an ensemble of simulations with various frozen-in-time $\bf U$ arranged so that only transient growth is active, can faithfully represent the energy transfer from $\bf U$ to $\bf u'$ as in realistic turbulence. Our approach provides direct cause-and-effect evaluation of the linear energy-injection mechanisms from $\bf U$ to $\bf u'$ in the fully nonlinear system and simplifies the conceptual model of self-sustaining wall turbulence. |
| Databáze: | OpenAIRE |
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