michal shavit | Weizmann Institute of Science (original) (raw)

Papers by michal shavit

arXiv (Cornell University), Jun 10, 2024

We find the turbulent energy spectrum of weakly interacting 2D internal gravity waves without rel... more We find the turbulent energy spectrum of weakly interacting 2D internal gravity waves without relying on the hydrostatic approximation. This spectrum is an exact solution of the kinetic equation after the shear modes are removed, and it agrees with the oceanic Garrett-Munk spectrum for frequencies large compared to the Coriolis frequency and vertical scales small compared to the depth of the ocean. Among a continuous family of solutions to the kinetic equation, we show that the turbulent solution is the special solution with non zero angular dependent radial flux. Our solution provides an interesting insight of how turbulent energy cascade proceeds in anisotropic systems-similarly to isotropic turbulence it is self-similar in scale, but its angular part is peaked along the curve of vanishing frequency.

arXiv (Cornell University), Nov 6, 2023

We highlight a non-canonical yet natural choice of variables for an efficient derivation of a kin... more We highlight a non-canonical yet natural choice of variables for an efficient derivation of a kinetic equation for the energy density in non-isotropic systems, including internal gravity waves on a vertical plane, inertial and Rossby waves. The existence of a second quadratic invariant simplifies the kinetic equation and leads to extra conservation laws for resonant interactions. We analytically determine the scaling of the radial turbulent energy spectrum. Our findings suggest the existence of an inverse energy cascade of internal gravity waves, from small to large scales, in practically relevant scenarios.

Physical Review E, 2021

When two resonantly interacting modes are in contact with a thermostat, their statistics is exact... more When two resonantly interacting modes are in contact with a thermostat, their statistics is exactly Gaussian and the modes are statistically independent despite strong interaction. Considering noisedriven system, we show that when one mode is pumped and another dissipates, the statistics (of such cascades) is never close to Gaussian no matter the interaction/noise relation. One finds substantial phase correlation in the limit of strong interaction (weak noise). Surprisingly, for both cascades, the mutual information between modes increases and entropy further decreases when interaction strength decreases. We use the model to elucidate the fundamental problem of far-from equilibrium physics: where the information (entropy deficit) is encoded and how singular measures form. For an instability-driven system (a laser), even a small added noise leads to large fluctuations of the relative phase near the stability threshold, while far from it we show that the conversion into the second harmonic is weakly affected by noise.

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022

This note is devoted to broken and emerging scale invariance of turbulence. Pumping breaks the sy... more This note is devoted to broken and emerging scale invariance of turbulence. Pumping breaks the symmetry: the statistics of every mode explicitly depend on the distance from the pumping. And yet the ratios of mode amplitudes, called Kolmogorov multipliers, are known to approach scale-invariant statistics away from the pumping. This emergent scale invariance deserves an explanation and a detailed study. We put forward the hypothesis that the invariance of multipliers is due to an extreme non-locality of their interactions (similar to the appearance of mean-field properties in the thermodynamic limit for systems with long-range interaction). We analyse this phenomenon in a family of models that connects two very different classes of systems: resonantly interacting waves and wave-free incompressible flows. The connection is algebraic and turns into an identity for properly discretized models. We show that this family provides a unique opportunity for an analytic (perturbative) study of ...

Physical Review Letters, 2020

Is there really such a thing as weak turbulence? Here we analyze turbulence of weakly interacting... more Is there really such a thing as weak turbulence? Here we analyze turbulence of weakly interacting waves using the tools of information theory. It offers a unique perspective for comparing thermal equilibrium and turbulence: the mutual information between modes is shown to be stationary and small in equilibrium but grows linearly with time in weak turbulence. We trace this growth to the concentration of probability on the resonance surfaces, which can go all the way to a singular measure. The surprising conclusion is that no matter how small is the nonlinearity and how close to Gaussian is the statistics of any single amplitude, a stationary phase-space measure is far from Gaussian, as manifested by a large relative entropy. Though it might be upsetting to practitioners of weak turbulence approach, this is a rare piece of good news for turbulence modeling: the resolved scales carry significant information about the unresolved scales. The mutual information between large and small scales is the information capacity of turbulent cascade, setting the limit on the representation of subgrid scales in turbulence modeling.

Physical Review Letters, 2019

Electronic fluids bring into hydrodynamics a new setting: equipotential flow sources embedded ins... more Electronic fluids bring into hydrodynamics a new setting: equipotential flow sources embedded inside the fluid. Here we show that the nonlocal relation between the current and electric field due to momentumconserving interparticle collisions leads to a total or partial field expulsion from such flows. That results in freely flowing currents in the bulk and a boundary jump in the electric potential at current-injecting electrodes. We derive a new type of boundary conditions, appropriate for the case. We then analyze current distribution in free flows, discuss how the field expulsion depends upon the geometry of the electrode, and link the phenomenon to the breakdown of conformal invariance.

arXiv: Chaotic Dynamics, Jan 25, 2021

Never is the difference between thermal equilibrium and turbulence so dramatic, as when a quadrat... more Never is the difference between thermal equilibrium and turbulence so dramatic, as when a quadratic invariant makes the equilibrium statistics exactly Gaussian with independently fluctuating modes. That happens in two very different yet deeply connected classes of systems: incompressible hydrodynamics and resonantly interacting waves. This work presents the first detailed informationtheoretic analysis of turbulence in such strongly interacting systems. The analysis involves both energy and entropy and elucidates the fundamental roles of space and time in setting the cascade direction and the changes of the statistics along it. We introduce a beautifully simple yet rich family of discrete models with triplet interactions of neighboring modes and show that it has quadratic conservation laws defined by the Fibonacci numbers. Depending on how the interaction time changes with the mode number, three types of turbulence were found: single direct cascade, double cascade, and the first ever case of a single inverse cascade. We describe quantitatively how deviation from thermal equilibrium all the way to turbulent cascades makes statistics increasingly non-Gaussian and find the self-similar form of the one-mode probability distribution. We reveal where the information (entropy deficit) is encoded and disentangle the communication channels between modes, as quantified by the mutual information in pairs and the interaction information inside triplets.

Physics Letters B, 2018

Searches for neutrino-less double-beta decay (0ν2β) place an important constraint on models where... more Searches for neutrino-less double-beta decay (0ν2β) place an important constraint on models where light fields beyond the Standard Model participate in the neutrino mass mechanism. While 0ν2β experimental collaborations often consider various massless majoron models, including various forms of majoron couplings and multi-majoron final-state processes, none of these searches considered the scenario where the "majoron" φ is not massless, m φ ∼ MeV, of the same order as the Q-value of the 0ν2β reaction. We consider this parameter region and estimate 0ν2βφ constraints for m φ of order MeV. The constraints are affected not only by kinematical phase space suppression but also by a change in the signal to background ratio charachterizing the search. As a result, 0ν2βφ constraints for m φ > 0 diminish significantly below the reaction threshold. This has phenomenological implications, which we illustrate focusing on high-energy neutrino telescopes. The spectral shape of high-energy astrophysical neutrinos could exhibit features due to resonant νν → φ → νν scattering. Such features fall within the sensitivity range of IceCube-like experiments, if m φ is of order MeV, making 0ν2βφ a key complimentary laboratory constraint on the scenario. Our results motivate a dedicated analysis by 0ν2β collaborations, analogous to the dedicated analyses targeting massless majoron models. 1 Repeated flavour indices are summed-over, and the bracket (HL) denotes contraction to an SU(2) singlet. 2 See Ref. [7] for a recent discussion of 0ν2β in the SM effective field theory.