arXiv subjects

Michal Shavit

Publications and source records attributed to Michal Shavit.

11 recordsLinked to original sources

arXiv2026

Sign-Indefinite Helicity and the Structure of Weak Turbulence in Inertial and Non-Hermitian Waves

We investigate how sign-indefinite quadratic invariants shape turbulent cascades in incompressible flows with broken time-reversal symmetry, where the dynamics supports strongly anisotropic dispersive waves. Focusing on rotating Euler flow and odd-viscous Euler flow, we isolate the wave component study the corresponding weak-turbulence kinetic equation. We show that helicity conservation substantially simplifies the kinetic equation. Fixing the energy flux by a natural gauge choice, we identify the turbulent spectrum as the unique scale-invariant solution that sustains a constant flux of energy from large to small scales. Under a mild approximation motivated by the accumulation of energy near slow modes, we compute the leading angular dependence and uncover an integrable singularity along the slow-mode curve, that agrees with previous results. We then demonstrate that helicity reorganizes cascade directions at the level of resonant triads. Although helicity is globally sign-indefinite, the helical decomposition splits it into sign-definite contributions on each polarization branch. Triads whose three legs lie on the same branch behave as if constrained by a sign-definite invariant and drive an upscale transfer of energy, producing systematic backscatter even when the net cascade is direct. In the helicity-definite limit (single-branch dynamics), the kinetic equation admits an additional scale-invariant solution associated with helicity transport. Finally, we validate the analytical predictions by numerically evaluating the collision integral in the strongly anisotropic limit, revealing a family of stationary solutions in that regime.

physics.flu-dyn↗

arXiv2026

Wave turbulence of inertia--gravity waves: a theory for the oceanic spectrum

We present a derivation using kinetic wave theory of the two-dimensional empirical Garrett--Munk spectrum for ocean internal waves, valid at all frequencies including near-inertial frequencies. This is based directly on the governing equations for a two-dimensional Boussinesq system with constant stratification and rotation. Our results improve on previous work by side-stepping the use of canonical variables, by taking full account of the Coriolis parameter in a non-hydrostatic dispersion relation, by filtering the balanced flow component from the dynamics, by using the conservation laws for energy and two components of pseudomomentum to bring the collision integral into a very simple form, by giving precise convergence conditions for the collision integral, and by finding the unique scale-invariant turbulent wave spectrum that corresponds to turbulent fluxes from small to large wavenumbers. The last step was achieved in the limit of small but nonzero Coriolis parameter. Key results are that any nonzero Coriolis parameter regularizes the singular nature of the non-rotating problem and that the homogeneity properties of the dispersion relation and of the interaction coefficients alone already imply that the spectrum is separable in vertical wavenumber and frequency. Within the restrictions of two-dimensional dynamics, this provides a theoretical framework for internal-wave turbulence consistent with oceanic observations.

physics.flu-dyn↗

arXiv2025

Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves

In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements, however, reveal prominent features that go beyond the predictions of time resonance theory. In this work, we develop a theoretical framework to interpret these signatures by identifying and characterizing an alternative mechanism: space resonances. These arise when wave packets share the same group velocity and remain co-located, leading to long-lived interactions. We further show that gauge-breaking terms in the Hamiltonian give rise to space resonances supported on negative frequencies. By combining sea-surface elevation data, numerical simulations, and analytical theory, we derive the leading-order spatio-temporal spectrum for weakly interacting water waves, providing a unified explanation for its observed features.

nlin.PS↗

arXiv2024

2D Internal Gravity Wave Turbulence

Using weak wave turbulence theory analysis, we distinguish three main regimes for 2D stratified fluids in the dimensionless parameter space defined by the Froude number and the Reynolds number: discrete wave turbulence, weak wave turbulence, and strong nonlinear interaction. These regimes are investigated using direct numerical simulations (DNS) of the 2D Boussinesq equations with shear modes removed. In the weak wave turbulence regime, excluding slow frequencies, we observe a spectrum that aligns with recent predictions from kinetic theory. This finding represents the first DNS-based confirmation of wave turbulence theory for internal gravity waves. At strong stratification, in both the weak and strong interaction regimes, we observe the formation of layers accompanied by spectral peaks at low discrete frequencies. We explain this layering through an inverse kinetic energy cascade and the discreteness of wave-wave interactions at large scales. This analysis allows us to predict the layer thickness and typical flow velocity in terms of the control parameters.

physics.flu-dyn↗

arXiv2024

Turbulent spectrum of 2D internal gravity waves

We find the turbulent energy spectrum of weakly interacting 2D internal gravity waves using the full, non-hydrostatic dispersion relation. This spectrum is an exact solution of a regularized kinetic equation, from which the zero-frequency shear modes have been excised by a careful limiting process. This is a new method in wave kinetic theory. The turbulent spectrum agrees with the 2D oceanic Garrett--Munk spectrum for frequencies large compared to the Coriolis frequency and vertical scales small compared to the depth of the ocean. We show that this turbulent spectrum is the unique power law solution to the steady kinetic equation with a non-zero radial flux. Our solution provides an interesting insight into a turbulent energy cascade in an anisotropic system -- like isotropic turbulence it is self-similar in scale, but its angular part is peaked along the curve of vanishing frequency and is self-similar in frequency.

physics.flu-dyn↗

arXiv2023

The role of sign indefinite invariants in shaping turbulent cascades

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.

physics.flu-dyn↗

arXiv2023

Kinetic equation for weak interaction of directional internal waves

Starting from the two-dimensional Boussinesq equation without rotation, we derive a kinetic equation for weak interaction of internal waves using non-canonical variables. We follow a formalism introduced by P. Ripa in the 80's. The advantage of this formalism is that it describes the system in terms of the natural linear eigenfunctions of eastward and westward propagating internal waves. Using properties of orthogonality of the eigenfunctions with respect to a (pseudo) metric set by the energy we can write non perturbative theory for the interaction of waves given in terms of the expansion amplitudes. The evolution is controlled by a system of equations, with quadratic nonlinearity, which is an exact representation of the original model equations. The dynamics is constrained by the conservation of energy and pseudo-momentum, which can be written simply as a linear combination of the squared absolute value of the amplitudes. The possibility of a generalization of the Fjortoft's argument to internal gravity waves and observation of a non trivial double cascade of energy and pseudo-momentum is discussed.

physics.flu-dyn↗

arXiv2021

Fibonacci turbulence

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 case of a detailed information-theoretic analysis of turbulence in such strongly interacting systems. The analysis 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 neighboring triplet interactions and show that it has families of quadratic conservation laws defined by the Fibonacci numbers. Depending on the single model parameter, 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.

nlin.CD↗

arXiv2020

Singular measures and information capacity of turbulent cascades

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.

physics.flu-dyn↗

arXiv2018

Freely flowing currents and electric field expulsion in viscous electronics

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

cond-mat.mes-hall↗

arXiv2018

Neutrinoless double-beta decay with massive scalar emission

Searches for neutrino-less double-beta decay ($0\nu2β$) place an important constraint on models where light fields beyond the Standard Model participate in the neutrino mass mechanism. While $0\nu2β$ 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, $m_ϕ\sim$~MeV, of the same order as the $Q$-value of the $0\nu2β$ reaction. We consider this parameter region and estimate $0\nu2βϕ$ 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 characterizing the search. As a result, $0\nu2βϕ$ constraints for $m_ϕ>0$ diminish significantly below the reaction threshold. This has phenomenological implications, which we illustrate focusing on high-energy neutrino telescopes. Our results motivate a dedicated analysis by $0\nu2β$ collaborations, analogous to the dedicated analyses targeting massless majoron models.

hep-ph↗