Threshold transient growth as a criterion for turbulent mean profiles
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arXiv
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| Format: | Preprint |
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2022
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| author | Markeviciute, Vilda K. Kerswell, Rich R. |
| author_facet | Markeviciute, Vilda K. Kerswell, Rich R. |
| contents | Lozano-Duran et al (J. Fluid Mech., 914, A8, 2021) have recently identified the ability of streamwise-averaged turbulent streak fields $U(y,z,t)\widehat{\mathbf{x}}$ in minimal channels to produce short-term transient growth as the key linear mechanism needed to sustain turbulence at $Re_τ=180$. Here, in an attempt to extend this result to larger domains and higher $Re_τ$, we model this streak transient growth as a two-stage linear process by first selecting the dominant streak structure expected to emerge over the eddy turnover time on the turbulent mean profile $U(y)\widehat{\mathbf{x}}$, and then examining the secondary growth on this (frozen) streak field $U(y,z)\widehat{\mathbf{x}}$. Choosing the mean streak amplitude and eddy turnover time consistent with simulations captures the growth thresholds found by Lozano-Duran et al. (2021) for sustained turbulence. In a larger domain at $Re_τ=180$, the most energetic near-wall streaks observed in simulations are close to the predicted optimal streaks. This most energetic streak spacing, approaches the optimal streak at $Re_τ=550$ where the secondary growth possible on each also comes together. A key prediction from the model is that the threshold transient growth required to sustain turbulence decreases with increasing $Re_τ$. More fundamentally, the work of Lozano-Duran et al. (2021) and our results suggest a subtle but significant revision of Malkus's (J. Fluid Mech.}, 521, 1, 1956) classic hypothesis concerning realisable turbulent mean profiles. The key property for a realisable turbulent mean profile could be the ability to generate sufficient short-term transient growth rather than dependence on its (long-term) linear stability characteristics which was Malkus's original idea. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_09681 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Threshold transient growth as a criterion for turbulent mean profiles Markeviciute, Vilda K. Kerswell, Rich R. Fluid Dynamics Lozano-Duran et al (J. Fluid Mech., 914, A8, 2021) have recently identified the ability of streamwise-averaged turbulent streak fields $U(y,z,t)\widehat{\mathbf{x}}$ in minimal channels to produce short-term transient growth as the key linear mechanism needed to sustain turbulence at $Re_τ=180$. Here, in an attempt to extend this result to larger domains and higher $Re_τ$, we model this streak transient growth as a two-stage linear process by first selecting the dominant streak structure expected to emerge over the eddy turnover time on the turbulent mean profile $U(y)\widehat{\mathbf{x}}$, and then examining the secondary growth on this (frozen) streak field $U(y,z)\widehat{\mathbf{x}}$. Choosing the mean streak amplitude and eddy turnover time consistent with simulations captures the growth thresholds found by Lozano-Duran et al. (2021) for sustained turbulence. In a larger domain at $Re_τ=180$, the most energetic near-wall streaks observed in simulations are close to the predicted optimal streaks. This most energetic streak spacing, approaches the optimal streak at $Re_τ=550$ where the secondary growth possible on each also comes together. A key prediction from the model is that the threshold transient growth required to sustain turbulence decreases with increasing $Re_τ$. More fundamentally, the work of Lozano-Duran et al. (2021) and our results suggest a subtle but significant revision of Malkus's (J. Fluid Mech.}, 521, 1, 1956) classic hypothesis concerning realisable turbulent mean profiles. The key property for a realisable turbulent mean profile could be the ability to generate sufficient short-term transient growth rather than dependence on its (long-term) linear stability characteristics which was Malkus's original idea. |
| title | Threshold transient growth as a criterion for turbulent mean profiles |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2206.09681 |