Pinzani-Fokeeva, Natalia, Yarom, Amos · arXiv (Cornell University) · 2021
We construct an approximately conserved current for $2+1$ dimensional, Aristotelian (non boost invariant), fluid flow. When Aristotelian symmetry is enhanced to Galilean symmetry, this current matches the enstrophy current responsible for the inverse cascade in incompressible fluids. Other enhancements of Aristotelian symmetry discussed in this work include Lorentzian, Carrollian and Lifshitz scale symmetry.
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Michael L. Waite · Journal of Fluid Mechanics · 2013
Abstract Direct numerical simulations are used to investigate potential enstrophy in stratified turbulence with small Froude numbers, large Reynolds numbers, and buoyancy Reynolds numbers ( $R{e}_{b} $ ) both smaller and larger than unity. We investigate the conditions under which the potential enstrophy, which is a quartic quantity in the flow variables, can be approximated by its quadratic terms, as is often done in geophysical fluid dynamics. We show that at large scales, the quadratic fraction of the potential enstrophy is determined by $R{e}_{b} $ . The quadratic part dominates for small $R{e}_{b} $ , i.e. in the viscously coupled regime of stratified turbulence, but not when $R{e}_{b} \gtrsim 1$ . The breakdown of the quadratic approximation is consistent with the development of Kelvin–Helmholtz instabilities, which are frequently observed to grow on the layerwise structure of stratified turbulence when $R{e}_{b} $ is not too small.
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Pinzani Fokeeva, Natalia · CERN Document Server (European Organization for Nuclear Research) · 2021
<!--HTML-->Enstrophy is an approximately conserved quantity in 2+1 dimensional fluid flows that has dramatic consequences for the phenomenology of turbulence: it implies an inverse energy cascade in 2+1 dimensions.\nIn this talk, I will illustrate an algorithm to construct an enstrophy current for fluid flows with various degrees of symmetry, including, but not limited to, the well-known case of non-relativistic (Galilean) fluid flows.\nMoreover, I will identify the accidental symmetry associated with enstrophy conservation in a recently realized effective action for hydrodynamics.\nFinally, I will show how horizon symmetries of 3+1 dimensional black holes with Anti-de Sitter asymptotics also lead to enstrophy conservation.
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Shubhadeep Sadhukhan, Roshan Samuel, Franck Plunian et al. · Physical Review Fluids · 2019
In fluid turbulence, enstrophy fluxes are associated either with velocity-to-vorticity transfers (vorticity stretching) or with vorticity-to-vorticity transfers (vorticity advection). In the inertial range, the four fluxes due to vorticity stretching are found to be larger than the one due to vorticity advection.
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Khalid M. Saqr · 2026
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Askar Kazbekov, Keishi Kumashiro, Adam M. Steinberg · Journal of Fluid Mechanics · 2019
The contributions of vortex stretching, dilatation, baroclinic torque and viscous diffusion to Reynolds-averaged enstrophy transport in turbulent swirl flames were experimentally measured using tomographic particle image velocimetry and $\text{CH}_{2}\text{O}$ planar laser induced fluorescence at jet Reynolds numbers of 26 000–51 000. The mean baroclinic torque was determined by subtracting the other terms in the enstrophy transport equation from the mean Lagrangian derivative. Enstrophy production from baroclinic torque was found to be significant relative to the other transport terms across all conditions studies. This result contrasts with direct numerical simulations of flames in homogeneous isotropic turbulence, which show a decreasing relative significance of baroclinic torque with increasing turbulence intensity (e.g. Bobbitt, Lapointe & Blanquart, Phys. Fluids , vol. 28 (1), 2016, 015101). Hence, the significance of baroclinic enstrophy production in flames is not determined entirely by the local turbulence and flame properties, but also depends on the configuration-specific pressure field.
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Sadhukhan, Shubhadeep, Samuel, Roshan, Plunian, Franck et al. · arXiv (Cornell University) · 2020
In this paper we study the enstrophy transers in helical turbulence using direct numerical simulation. We observe that the helicity injection does not have significant effects on the inertial-range energy and helicity spectra ($\sim k^{-5/3}$) and fluxes (constants). We also calculate the separate contributions to enstrophy transfers via velocity to vorticity and vorticity to vorticity channels. There are four different enstrophy fluxes associated with the former channel or vorticity stretching, and one flux associated with the latter channel or vorticity advection. In the inertial range, the fluxes due to vorticity stretching are larger than that due to advection. These transfers too are insensitive to helicity injection.
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Luigi De Rosa, Margherita Marcotullio · ArXiv.org · 2026
We consider the two-dimensional incompressible Navier-Stokes equations with measure initial vorticity. By means of improved Nash inequalities, we establish quantitative estimates for the enstrophy depending on the absolute vorticity decay on balls. The bounds are optimal in several aspects and yield to a conjecturally sharp rate of the dissipation in the Delort's class.
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Marco Baiesi, Christian Maes · Physical Review E · 2005
Insight into the problem of two-dimensional turbulence can be obtained by an analogy with a heat conduction network. It allows the identification of an entropy function associated with the enstrophy dissipation and that fluctuates around a positive (mean) value. While the corresponding enstrophy network is highly nonlocal, the direction of the enstrophy current follows from the Second Law of Thermodynamics. An essential parameter is the ratio of the intensity of driving as a function of wave number , to the dissipation strength , where is the viscosity. The enstrophy current flows from higher to lower values of , similar to a heat current from higher to lower temperature. Our probabilistic analysis of the enstrophy dissipation and the analogy with heat conduction thus complements and visualizes the more traditional spectral arguments for the direct enstrophy cascade. We also show a fluctuation symmetry in the distribution of the total entropy production which relates the probabilities of direct and inverse enstrophy cascades.
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G S. Sidharth · 2026
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Raja Marjieh, Natalia Pinzani-Fokeeva, Bar Tavor et al. · Physical Review Letters · 2022
We study the relation between approximate horizon symmetries of AdS black branes and approximately conserved currents in their dual hydrodynamic description. We argue that the existence of an approximately conserved enstrophy current unique to 2+1 dimensional fluid flow implies that AdS_{4} black branes possess a special class of approximate supertranslations (which we identify).
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S. Musacchio · HAL (Le Centre pour la Communication Scientifique Directe) · 2016
International audience
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Sabatini, Leonardo · AMS Degree Thesis (University of Bologna) · 2024
Lo scopo del presente lavoro di tesi è analizzare il comportamento dell’enstrofia di un getto turbolento temporale. Studi di questo tipo sono già stati svolti in passato nell’ambito della ricerca di flussi a taglio libero. Nello specifico, ci si è concentrati sulla descrizione dell’interfaccia turbolenta/non turbolenta (TNTI), cercando di coglierne le caratteristiche fondamentali. Si è scoperto in tempi recenti che la TNTI è suddivisa in due sottostrati a cui è possibile associare fenomeni differenti, caratteristici di questo tipo d'interfaccia. \nL’analisi è stata svolta partendo dalla ricerca di un criterio per determinare la posizione della TNTI. Determinare un valore di soglia di enstrofia si è rilevato un metodo robusto nella determinazione dell’interfaccia. Per studiarne le caratteristiche si è fatto ricorso ai budget di enstrofia, i quali hanno permesso di visualizzare i principali fenomeni presenti all’interno della TNTI. Il budget medio di enstrofia si è dimostrato utile nel visualizzare la posizione dell’interfaccia, ma inefficace nel determinarne i fenomeni caratteristici. Per tale motivo si è ricorso all’utilizzo di un budget condizionato di enstrofia che ha permesso una descrizione qualitativa dei fenomeni presenti nei sottostrati dell’interfaccia, confermando quanto riportato dagli studi recenti in questo ambito. In particolare, è stata individuata una struttura della TNTI a due strati: il superstrato viscoso (VSL) e il sottostrato turbolento (TSL). \nIl getto temporale si è rilevato particolarmente indicato per questo tipo di studi, garantendo un costo computazionale basso rispetto ad altri flussi di taglio libero.
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Luigi De Rosa, Margherita Marcotullio · arXiv (Cornell University) · 2026
We consider the two-dimensional incompressible Navier-Stokes equations with measure initial vorticity. By means of improved Nash inequalities, we establish quantitative estimates for the enstrophy depending on the absolute vorticity decay on balls. The bounds are optimal in several aspects and yield to a conjecturally sharp rate of the dissipation in the Delort's class.
Cited by 0Open access
Čantrak, Đorđe, Janković, Novica, Ilić, Dejan · 2022
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H." "Miura · National Institute for Fusion Science Repository (National Institute for Fusion Science) · 1995
"A mechanism of enstrophy generation is investigated numerically in a shock-dominated turbulence driven by a random external force which has only the compressible component . Enstrophy is generated, especially on collision of shock, as a pair of vortex tube of opposite sense of rotation behind curved shocks. The roles of various terms in enstrophy equation are clarified in enstrophy generation process. Generation of enstrophy is enhanced by strong alignment of each term of the enstrophy equation with the vorticity vector."
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Elena Piretto, S. Musacchio, F. De Lillo et al. · Physical review. E · 2016
We study the time irreversibility of the direct cascade in two-dimensional turbulence by looking at the time derivative of the square vorticity along Lagrangian trajectories, a quantity called metenstrophy. By means of extensive direct numerical simulations we measure the time irreversibility from the asymmetry of the probability density function of the metenstrophy and we find that it increases with the Reynolds number of the cascade, similarly to what is found in three-dimensional turbulence. A detailed analysis of the different contributions to the enstrophy budget reveals a remarkable difference with respect to what is observed for the energy cascade, in particular the role of the statistics of the forcing to determine the degree of irreversibility.
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S.J. Terrington, Kerry Hourigan, Mark C. Thompson · Journal of Fluid Mechanics · 2023
The Lighthill–Panton and Lyman–Huggins interpretations of vorticity dynamics are extended to the dynamics of enstrophy. There exist two competing definitions of the vorticity current tensor, which describes the flow rate of vorticity in the fluid interior, and the corresponding boundary vorticity flux, which represents the local vorticity creation rate on a boundary. It is demonstrated that each definition of the vorticity current tensor leads to a consistent set of definitions for the enstrophy current, boundary enstrophy flux and the enstrophy dissipation term. This leads to two alternative interpretations of vorticity and enstrophy dynamics: the Lighthill–Panton and Lyman–Huggins interpretations. Although the kinematic evolution of the vorticity and enstrophy fields are the same under each set of definitions, the dynamical interpretation of the motion generally differs. For example, we consider the Stokes flow over a rotating sphere, and find that the flow approaches a steady state where, under the Lyman–Huggins interpretation, there is no enstrophy creation or dissipation. Under the Lighthill–Panton interpretation, however, the steady-state flow features a balance between the continuous generation and subsequent dissipation of enstrophy. Moreover, the Lyman–Huggins interpretation has previously been shown to offer several benefits in understanding the dynamics of vorticity, and therefore it is beneficial to extend this interpretation to the dynamics of enstrophy. For example, the Lyman–Huggins interpretation allows the creation of vorticity, and therefore enstrophy, to be interpreted as an inviscid process, due to the relative acceleration between the fluid and the boundary.
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Jörg Schumacher, Maik Boltes, Herwig Zilken et al. · Chaos An Interdisciplinary Journal of Nonlinear Science · 2008
First Page
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G. Boffetta · 2007
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