Minimal model of quasi-cyclic behaviour in turbulence driven by Taylor--Green forcing
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866916499702153216 |
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| author | Araki, Ryo Bos, Wouter J. T. Goto, Susumu |
| author_facet | Araki, Ryo Bos, Wouter J. T. Goto, Susumu |
| contents | We attempt to formulate the simplest possible model mimicking turbulent dynamics, such as quasi-cyclic behaviour (QCB), using only three variables. To this end, we first conduct direct numerical simulations of three-dimensional flow driven by the steady Taylor--Green forcing to find a similarity between a stable periodic orbit (SPO) at a small Reynolds number ($Re$) and turbulent QCB at higher $Re$. A close examination of the SPO allows the heuristic formulation of a three-equation model, representing the evolution of Fourier modes in three distinct scales. The model reproduces the continuous bifurcation from SPO to turbulence with QCB when $Re$ is varied. We also demonstrate that, by changing model parameters, the proposed model exhibits a discontinuous transition from steady to chaotic solutions without going through an SPO. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_03417 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Minimal model of quasi-cyclic behaviour in turbulence driven by Taylor--Green forcing Araki, Ryo Bos, Wouter J. T. Goto, Susumu Fluid Dynamics We attempt to formulate the simplest possible model mimicking turbulent dynamics, such as quasi-cyclic behaviour (QCB), using only three variables. To this end, we first conduct direct numerical simulations of three-dimensional flow driven by the steady Taylor--Green forcing to find a similarity between a stable periodic orbit (SPO) at a small Reynolds number ($Re$) and turbulent QCB at higher $Re$. A close examination of the SPO allows the heuristic formulation of a three-equation model, representing the evolution of Fourier modes in three distinct scales. The model reproduces the continuous bifurcation from SPO to turbulence with QCB when $Re$ is varied. We also demonstrate that, by changing model parameters, the proposed model exhibits a discontinuous transition from steady to chaotic solutions without going through an SPO. |
| title | Minimal model of quasi-cyclic behaviour in turbulence driven by Taylor--Green forcing |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2112.03417 |