Self-organization of turbulent flows<\/h2>\n\n\n\n
Turbulence is usually viewed as the breaking up of a large scale flow into ever smaller chaotic motions. A quantitative manifestation of this picture is the energy cascade, with energy flowing from large scales to increasingly smaller ones, where it is eventually dissipated by viscosity.
On the contrary, when most of the energy is concetrated in 2d modes, energy is transferred to progressively larger scales–in an inverse cascade. This process can then terminate in the self-organization of the turbulence into a large scale mean flow, a so-called condensate, on top of small scale fluctuations.<\/p>\n\n\n\n
Although such 2d turbulence may seem like an abstract concept, many natural flows are effectively restricted to two dimensions: planetary-scale flows in the ocean and atmosphere are an example, and they are often made up of coherent currents or vortices in combination with chaotic fluctuations.<\/p>\n\n\n\n
Our work is centered around the following questions: What are the rules of self-organization for the condensate? Which of its features are universal? What happens when the range of fluid-element interactions is below the energy injection scale? Recently, we have also started to explore condensates that have both 2d-like and 3d-like interactions.<\/p>\n\n\n\n
Read more<\/h3>\n\n\n\n\n- Svirsky, A, and Frishman A. “Out-of-equilibrium fluxes shape the self-organization of locally-interacting turbulence<\/a>\u201d.<\/em> Phys. Rev. Lett. 134(20), 204001 <\/em>(2025).<\/li>\n\n\n\n
- Svirsky, A., Herbert, C. and Frishman, A. \u201cTwo-dimensional turbulence with local interactions: statistics of the condensate<\/a>.\u201d <\/em>Phys. Rev. Lett., 131(22), 224003 (2023).<\/li>\n\n\n\n
- Frishman, A. and Herbert C. \u201cTurbulence Statistics in a Two-Dimensional Vortex Condensate<\/a>.\u201d<\/em> Phys. Rev. Lett. 120.20: 204505 (2018).<\/li>\n\n\n\n
- Frishman A.\u00a0\u201cThe culmination of an inverse cascade: mean flow and fluctuations.\u201d<\/a>\u00a0<\/em>Physics of Fluids\u00a029.12: 125102. (2017).<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n\n<\/div>\n\n\n\n
![\"The](\"https:\/\/phsites.technion.ac.il\/frishman\/wp-content\/uploads\/sites\/59\/2025\/06\/nice_plot-1024x480.jpg\")
The large scale flow can either form jets or vortices, depending on the distance of the dissipative scale from the forcing scale in a local version of two dimensional turbulence [Figure from Svirsky, A., and Frishman A.\u00a0Phys. Rev. Lett.\u00a0 134, 204001(2025)].<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
\n\n\n\n\n\nSubcritical transition to turbulence<\/h2>\n\n\n\n
Fluid flow generically becomes turbulent when the Reynolds number, which is the relevant control parameter, is sufficiently increased. In flows where the base state is linearly stable, termed subcritical flows, this transition occurs directly to a turbulent state, with turbulence appearing intermittently in space and time. With increasing Reynolds number, the system transitions between several different phases until finally reaching the homogeneous turbulent state.<\/p>\n\n\n\n
Building on recent progress in the field, our work aims to understand the different possible phases and under which conditions they occur; the role of fluctuations and the mechanisms leading to transitions between phases and the generallity of the subcritical transition scenario.<\/p>\n\n\n\n
\nRead more<\/h3>\n\n\n\n\n- Svirsky, A., Grafke T. and Frishman A. \u201cSelf-Replication of Turbulent Puffs: On the edge between chaotic saddles\u201d, arXiv:2505.05075<\/a><\/em>.<\/li>\n\n\n\n
- Frishman, A. and Grafke T. “Mechanism for turbulence proliferation in subcritical flows<\/a>.”<\/em> Proceedings of the Royal Society A 478.2265: 20220218, (2022).<\/li>\n\n\n\n
- Frishman, A. and Grafke, T. \u201cDynamical landscape of transitional pipe flow<\/a>“,<\/em> Phys, Rev. E 105.4: 045108 (2022).<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n\n<\/div>\n\n\n\n
![\"laminar](\"https:\/\/phsites.technion.ac.il\/frishman\/wp-content\/uploads\/sites\/59\/2025\/06\/many_gaps_zoom1-1024x853.png\")
Laminar gaps randomly open and close in transitional turbulent pipe flow, the level of turbulence along the pipe as a function of time is shown.<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
\n\n\n\n\n\nClouds and their fate<\/h2>\n\n\n\n
Clouds consist of water droplets; as these droplets collide and coallese they grow, until eventually they start falling out of the cloud, producing rain. What fraction of the water in a cloud will remain in it after it rains down? How long will it live? The answer to these questions depends on the initial charatcrestics of the cloud. Our work aims to construct a minimal coarse-grained description of this depdnence, using ideal models of the droplet population dynamics in the cloud.<\/p>\n\n\n\n
\nRead more<\/h3>\n\n\n\n\n- Kapon, S., Jeevanjee N. and Frishman A. “Single-parameter effective dynamics of warm cloud precipitation<\/em>.” arXiv:2409.05398<\/a><\/em> <\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n\n<\/div>\n\n\n\n
![\"\"](\"https:\/\/phsites.technion.ac.il\/frishman\/wp-content\/uploads\/sites\/59\/2025\/06\/combined_plots_with_units-1024x288.png\")
<\/figure>\n\n\n\n![\"Cloud](\"https:\/\/phsites.technion.ac.il\/frishman\/wp-content\/uploads\/sites\/59\/2025\/06\/combined_plots_no_theory-1024x286.png\")
Cloud observables collapse when presented as a function of a dimensionless parameter quantifying accretion vs rainfall<\/figcaption><\/figure>\n\n\n\n![\"clouds\"](\"https:\/\/phsites.technion.ac.il\/frishman\/wp-content\/uploads\/sites\/59\/2025\/06\/Cloudsbackground-picture.jpg\")
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\n\n\n\n\n\nUniversality in the breakup of a fluid bridge<\/h2>\n\n\n\n
The breakup of a fluid object is a singular and dramatic process. We explore how a cylindrical soap film bridge breaks when stretched, and find that it always forms one large central satellite bubble. We show that the size of this bubble is extremely reproducible, and grows with the stretching rate and with the initial bridge aspect ratio. We trace the robustness of the size to an underlying universal dynamical solution.<\/p>\n\n\n\n
\nRead more<\/h3>\n\n\n\n
\n\n\n\n
Subcritical transition to turbulence<\/h2>\n\n\n\n
Fluid flow generically becomes turbulent when the Reynolds number, which is the relevant control parameter, is sufficiently increased. In flows where the base state is linearly stable, termed subcritical flows, this transition occurs directly to a turbulent state, with turbulence appearing intermittently in space and time. With increasing Reynolds number, the system transitions between several different phases until finally reaching the homogeneous turbulent state.<\/p>\n\n\n\n
Building on recent progress in the field, our work aims to understand the different possible phases and under which conditions they occur; the role of fluctuations and the mechanisms leading to transitions between phases and the generallity of the subcritical transition scenario.<\/p>\n\n\n\n
Read more<\/h3>\n\n\n\n\n- Svirsky, A., Grafke T. and Frishman A. \u201cSelf-Replication of Turbulent Puffs: On the edge between chaotic saddles\u201d, arXiv:2505.05075<\/a><\/em>.<\/li>\n\n\n\n
- Frishman, A. and Grafke T. “Mechanism for turbulence proliferation in subcritical flows<\/a>.”<\/em> Proceedings of the Royal Society A 478.2265: 20220218, (2022).<\/li>\n\n\n\n
- Frishman, A. and Grafke, T. \u201cDynamical landscape of transitional pipe flow<\/a>“,<\/em> Phys, Rev. E 105.4: 045108 (2022).<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n\n<\/div>\n\n\n\n
Laminar gaps randomly open and close in transitional turbulent pipe flow, the level of turbulence along the pipe as a function of time is shown.<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
\n\n\n\n\n\nClouds and their fate<\/h2>\n\n\n\n
Clouds consist of water droplets; as these droplets collide and coallese they grow, until eventually they start falling out of the cloud, producing rain. What fraction of the water in a cloud will remain in it after it rains down? How long will it live? The answer to these questions depends on the initial charatcrestics of the cloud. Our work aims to construct a minimal coarse-grained description of this depdnence, using ideal models of the droplet population dynamics in the cloud.<\/p>\n\n\n\n
\nRead more<\/h3>\n\n\n\n\n- Kapon, S., Jeevanjee N. and Frishman A. “Single-parameter effective dynamics of warm cloud precipitation<\/em>.” arXiv:2409.05398<\/a><\/em> <\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n\n<\/div>\n\n\n\n
<\/figure>\n\n\n\n
Cloud observables collapse when presented as a function of a dimensionless parameter quantifying accretion vs rainfall<\/figcaption><\/figure>\n\n\n\n<\/figure>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
\n\n\n\n\n\nUniversality in the breakup of a fluid bridge<\/h2>\n\n\n\n
The breakup of a fluid object is a singular and dramatic process. We explore how a cylindrical soap film bridge breaks when stretched, and find that it always forms one large central satellite bubble. We show that the size of this bubble is extremely reproducible, and grows with the stretching rate and with the initial bridge aspect ratio. We trace the robustness of the size to an underlying universal dynamical solution.<\/p>\n\n\n\n
\nRead more<\/h3>\n\n\n\n
\n\n\n\n
Clouds and their fate<\/h2>\n\n\n\n
Clouds consist of water droplets; as these droplets collide and coallese they grow, until eventually they start falling out of the cloud, producing rain. What fraction of the water in a cloud will remain in it after it rains down? How long will it live? The answer to these questions depends on the initial charatcrestics of the cloud. Our work aims to construct a minimal coarse-grained description of this depdnence, using ideal models of the droplet population dynamics in the cloud.<\/p>\n\n\n\n
Read more<\/h3>\n\n\n\n\n- Kapon, S., Jeevanjee N. and Frishman A. “Single-parameter effective dynamics of warm cloud precipitation<\/em>.” arXiv:2409.05398<\/a><\/em> <\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n\n<\/div>\n\n\n\n
<\/figure>\n\n\n\n
Cloud observables collapse when presented as a function of a dimensionless parameter quantifying accretion vs rainfall<\/figcaption><\/figure>\n\n\n\n<\/figure>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
\n\n\n\n\n\nUniversality in the breakup of a fluid bridge<\/h2>\n\n\n\n
The breakup of a fluid object is a singular and dramatic process. We explore how a cylindrical soap film bridge breaks when stretched, and find that it always forms one large central satellite bubble. We show that the size of this bubble is extremely reproducible, and grows with the stretching rate and with the initial bridge aspect ratio. We trace the robustness of the size to an underlying universal dynamical solution.<\/p>\n\n\n\n
\nRead more<\/h3>\n\n\n\n
<\/figure>\n\n\n\nCloud observables collapse when presented as a function of a dimensionless parameter quantifying accretion vs rainfall<\/figcaption><\/figure>\n\n\n\n
<\/figure>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n\n\n\n\n
Universality in the breakup of a fluid bridge<\/h2>\n\n\n\n
The breakup of a fluid object is a singular and dramatic process. We explore how a cylindrical soap film bridge breaks when stretched, and find that it always forms one large central satellite bubble. We show that the size of this bubble is extremely reproducible, and grows with the stretching rate and with the initial bridge aspect ratio. We trace the robustness of the size to an underlying universal dynamical solution.<\/p>\n\n\n\n