Extending Kolmogorov Theory to Polymeric Turbulence
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917801165324288 |
|---|---|
| author | Chiarini, Alessandro Singh, Rahul K. Rosti, Marco E. |
| author_facet | Chiarini, Alessandro Singh, Rahul K. Rosti, Marco E. |
| contents | The addition of polymers fundamentally alters the dynamics of turbulent flows in a way that defies Kolmogorov predictions. However, we now present a formalism that reconciles our understanding of polymeric turbulence with the classical Kolmogorov phenomenology. This is achieved by relying on an appropriate form of the Kármán-Howarth-Monin-Hill relation, which motivates the definition of extended velocity increments and the associated structure functions, by accounting for the influence of the polymers on the flow. We show, both analytically and numerically, that the ${\rm p}$th-order extended structure functions exhibit a power-law behaviour in the elasto-inertial range of scales, with exponents deviating from the analytically predicted value of ${\rm p}/3$. These deviations are readily accounted for by considering local averages of the total dissipation, rather than global averages, in analogy with the refined similarity hypotheses of Kolmogorov for classical Newtonian turbulence. We also demonstrate the scale-invariance of multiplier statistics of extended velocity increments, whose distributions collapse well for a wide range of scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extending Kolmogorov Theory to Polymeric Turbulence Chiarini, Alessandro Singh, Rahul K. Rosti, Marco E. Fluid Dynamics The addition of polymers fundamentally alters the dynamics of turbulent flows in a way that defies Kolmogorov predictions. However, we now present a formalism that reconciles our understanding of polymeric turbulence with the classical Kolmogorov phenomenology. This is achieved by relying on an appropriate form of the Kármán-Howarth-Monin-Hill relation, which motivates the definition of extended velocity increments and the associated structure functions, by accounting for the influence of the polymers on the flow. We show, both analytically and numerically, that the ${\rm p}$th-order extended structure functions exhibit a power-law behaviour in the elasto-inertial range of scales, with exponents deviating from the analytically predicted value of ${\rm p}/3$. These deviations are readily accounted for by considering local averages of the total dissipation, rather than global averages, in analogy with the refined similarity hypotheses of Kolmogorov for classical Newtonian turbulence. We also demonstrate the scale-invariance of multiplier statistics of extended velocity increments, whose distributions collapse well for a wide range of scales. |
| title | Extending Kolmogorov Theory to Polymeric Turbulence |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2410.03237 |