Scalar mixing in non-Markovian homogeneous isotropic synthetic turbulence
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| author | Awasthi, Pratyush S. Jossy, Joaquim P. Bhattacharya, Amitabh Gupta, Prateek |
| author_facet | Awasthi, Pratyush S. Jossy, Joaquim P. Bhattacharya, Amitabh Gupta, Prateek |
| contents | We show that non-Markovianity of the velocity field is an essential property of turbulent mixing. We demonstrate this via passive scalar mixing by synthetically generated stochastic velocity fields. Including a separate velocity decorrelation time scale for each spatial scale (random sweeping) yields an essentially non-Markovian velocity field with a finite time memory decaying as -5 (for a decaying spectrum) instead of an exponential decay (Markovian), which is obtained by including a constant time scale for all spatial scales, irrespective of the filtering function. We characterize the Lagrangian mixing statistics of both the Markovian and non-Markovian synthetic fields and compare them against a corresponding incompressible direct numerical simulation (DNS). We also study diffusive passive scalar mixing in the Schmidt number range Sc<1 using the DNS and the synthetic fields. While both the synthetic fields recover the -17/3 scalar spectrum for low Schmidt numbers, the mean gradients in a decaying simulation, as well as the production and dissipation of scalar variance in a statistically stationary simulation, are severely underpredicted by the Markovian fields compared to the non-Markovian fields. Throughout, we compare our results with companion 3D DNS to show the necessity of non-Markovianity in synthetic fields to capture mixing dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01494 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scalar mixing in non-Markovian homogeneous isotropic synthetic turbulence Awasthi, Pratyush S. Jossy, Joaquim P. Bhattacharya, Amitabh Gupta, Prateek Fluid Dynamics We show that non-Markovianity of the velocity field is an essential property of turbulent mixing. We demonstrate this via passive scalar mixing by synthetically generated stochastic velocity fields. Including a separate velocity decorrelation time scale for each spatial scale (random sweeping) yields an essentially non-Markovian velocity field with a finite time memory decaying as -5 (for a decaying spectrum) instead of an exponential decay (Markovian), which is obtained by including a constant time scale for all spatial scales, irrespective of the filtering function. We characterize the Lagrangian mixing statistics of both the Markovian and non-Markovian synthetic fields and compare them against a corresponding incompressible direct numerical simulation (DNS). We also study diffusive passive scalar mixing in the Schmidt number range Sc<1 using the DNS and the synthetic fields. While both the synthetic fields recover the -17/3 scalar spectrum for low Schmidt numbers, the mean gradients in a decaying simulation, as well as the production and dissipation of scalar variance in a statistically stationary simulation, are severely underpredicted by the Markovian fields compared to the non-Markovian fields. Throughout, we compare our results with companion 3D DNS to show the necessity of non-Markovianity in synthetic fields to capture mixing dynamics. |
| title | Scalar mixing in non-Markovian homogeneous isotropic synthetic turbulence |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2601.01494 |