arXiv subjects

Eyal Heifetz

Publications and source records attributed to Eyal Heifetz.

At least 19 recordsLinked to original sources

arXiv2026

From agent-based dynamics to a kinetic theory of jellyfish swarms

Massive jellyfish swarms observed at sea can extend over tens of kilometres and contain millions of individuals, yet the mechanisms governing their formation and large-scale dynamics remain poorly understood. Agent-based models provide a framework for describing this dynamics based on jellyfish responses to ocean currents and environmental cues, but become computationally prohibitive when extended to large populations and spatial scales relevant to ocean circulation. Here we derive a continuous kinetic theory from an active-particle model of jellyfish motion. The resulting Fokker-Planck framework incorporates transport by prescribed currents, stochastic reorientation, direct interactions and stimulated steering, allowing chemical signalling to be represented through a coupled field. We further derive a hydrodynamic closure for large swarms by exploiting the separation between fast orientational and slow spatial dynamics, yielding a reduced density equation suitable for implementation in ocean-current models. This framework provides a route from individual behavioural mechanisms to continuum descriptions of jellyfish populations and establishes a basis for constraining model parameters using observations and in-situ measurements. This approach offers a theoretical foundation for future numerical prediction of large jellyfish swarm formation and evolution in realistic ocean flows.

cond-mat.soft↗

arXiv2026

A conservative low-order model for Boussinesq baroclinic fronts

The internal dynamics of baroclinic fronts are governed by a fundamental interplay: turbulent eddies systematically act to disrupt thermal wind balance, with baroclinic eddies flattening isopycnals and barotropic momentum fluxes intensifying the primary jet, while the ageostrophic overturning circulation acts to restore it. In quasi-balanced models, this restorative adjustment is assumed instantaneous, locking the flow onto a balanced manifold. To conceptually track this mechanism when the adjustment takes a finite time, we construct a low-order model that spans from $\mathcal{O}(1)$ Rossby numbers down to the quasi-balanced limit. Formulated from the continuous Boussinesq equations under a $Ro^2 Ri \sim 1$ scaling, which constrains the horizontal length scale to the Rossby deformation radius, the derivation yields a closed, nonlinear five-dimensional ODE system. The degrees of freedom consist of the domain-averaged along-front vertical shear, the cross-frontal overturning vorticity, the horizontal and vertical buoyancy gradients, and the total eddy energy. We identify two constants of motion that constrain the evolution of the mean flow: the total energy (kinetic energy of the along- and cross-frontal flows, mean potential energy, and eddy energy) and the magnitude of the domain-averaged cross-frontal density gradient. Notably, while the system is energetically conservative, the parameterized turbulent closure renders the dynamics strictly non-Hamiltonian. Bounded by these invariants, the adiabatic adjustment of the front physically reduces to a continuous rotation of the density gradient's slope. By explicitly resolving the inertial lag of the secondary circulation, this framework isolates the individual mechanisms governing frontal adjustment and tracks their continuous dynamic interplay.

physics.flu-dyn↗

arXiv2025

Observation of Large-Scale Kelvin-Helmholtz Instability Wave Driven by a Coronal Mass Ejection

The Kelvin-Helmholtz instability (KHI) can occur when there is a relative motion between two adjacent fluids. In the case of magnetized plasma, the shear velocity must exceed the local Alfvén speed for the instability to develop. The KHI produces nonlinear waves that eventually roll up into vortices and contribute to turbulence and dissipation. In the solar atmosphere KHI has been detected in coronal mass ejections (CMEs), jets, and prominences, mainly in the low corona. Only a few studies have reported the KHI in the upper corona, and its vortex development there has not been previously observed. We report the event with large-scale KHI waves observed from $\sim 6$ to 14~$R_{\odot}$ on 2024-Feb-16 using SOHO/LASCO and STEREO-A coronagraphs. KHI appeared during the passage of a fast CME and evolved into the nonlinear stage showing evidence of vortices. A closely timed subsequent CME in the same region has further developed the fully nonlinear KHI waves along its flank. We find that the radial speed of the CMEs exceeds the estimated local Alfven speed obtained from in-situ Parker Solar Probe (PSP) magnetic field data at perihelia. We propose that such events are rare because the fast CME created specific conditions favorable for instability growth in its trailing edge, including radial elongation of magnetic-field lines, reduced plasma density, and enhanced velocity and magnetic-field shear along the developing interface. The observed growth rate of KHI wave is in qualitative agreement with the theoretical predictions.

astro-ph.SR↗

arXiv2025

On internal wave whispering gallery modes in channels and critical-slope wave attractors

Internal waves are an important feature of stratified fluids, both in oceanic and lake basins and in other settings. Many works have been published on the generic feature of internal wave trapping onto planar wave attractors and super-attractors in 2\&3D and the exceptional class of standing global internal wave modes. However, most of these works did not deal with waves that escape trapping. By using continuous symmetries we analytically prove the existence of internal wave Whispering Gallery Modes (WGMs), internal waves that propagate continuously without getting trapped by attractors. WGMs neutral stability with respect to different perturbations enable whispering gallery beams, a continuum of rays propagating together coherently. The systems' continuous symmetries also enable projection onto 2D planes that yield effective 2D billiards preserving the original dynamics. By examining rays deviating from these WGMs in parabolic channels we discover a new type of wave attractor which is located along the channel instead of across it as in previous works. This new wave attractor leads to a re-understanding of WGMs as sitting at the border between the two basins of attraction. Finally, both critical-slope wave attractors and whispering gallery beams are used to propose explanations for along-channel energy fluxes in submarine canyons and tidal energy intensification near critical slopes.

physics.flu-dyn↗

arXiv2025

Landau levels in a time-dependent magnetic field: the Madelung fluid perspective

We revisit the quantum dynamics of a charged particle in a time-dependent magnetic field, a fundamental problem exhibiting rich non-adiabatic behaviour, from the complementary perspective of the Madelung fluid formulation. We first analyse the system within standard quantum mechanics using perturbation theory around the Landau levels, and then address the same problem through the Madelung perspective. We show that the hydrodynamic formulation not only yields an intuitive derivation of the exact solution, it also provides a clear physical interpretation of non-adiabatic quantum evolution in terms of mechanical energy transfers. In this picture, the sloshing oscillations of the wave function arise from deviations from the force balance between the magnetic Lorentz force and the gradient of the Bohm potential within the Landau levels. More broadly, our study illustrates how the Madelung approach reveals unexpected analogies between quantum dynamics and phenomena familiar from geophysical fluid dynamics.

quant-ph↗

arXiv2025

A novel non-specular mechanism for chaotic ray scattering of internal waves in 3D anisotropic stadiums

Fluids, subject to symmetry breaking by stratification support propagation of anisotropic internal waves - IWs. In the vertical plane, rays representing energy paths obey a non-specular reflection law, as their inclination is solely dictated by their frequency. Although satisfying the linear Poincare equation, in basins having sloping walls, ray dynamics exhibits nonlinear effects such as convergence onto wave-attractors. In contrast, in the horizontal plane of a basin with vertical walls IWs reflect specularly, and follow chaotic ray paths. Here we present a novel analysis of these competing effects in a 3D IW ray billiard of a stadium having sloping walls. We show and explain how varying the walls slope, shifts the ray dynamics between regimes of near-ergodicity, chaotic scattering, and non-chaotic scattering with self-similar patterns, despite the basin being closed. The rich results stemming from the interplay between elliptical ergodicity and hyperbolic focusing relate to a broader context of physical phenomena.

nlin.CD↗

arXiv2024

A Swarm Coherence Mechanism for Jellyfish

We present a theory of jellyfish swarm formation and exemplify it with simulations of active Brownian particles. The motivation for our analysis is the phenomenon of jellyfish blooms in the ocean and clustering of jellyfish in tank experiments. We argue that such clusters emerge due to an externally induced phase transition of jellyfish density, such as convergent flows, which is then maintained and amplified by self-induced stimuli. Our study introduces three mechanisms relevant for a better understanding of jellyfish blooming that have not been taken into account before which are a signaling tracer, jellyfish-wall interaction and ignorance of external stimuli. Our results agree with the biological fact that jellyfish exhibit an extreme sensitivity to stimuli in order to achieve favorable aggregations. Based on our theoretical framework, we are able to provide a clear terminology for future experimental analysis of jellyfish swarming and we pinpoint potential limitations of tank experiments.

nlin.AO↗

arXiv2024

Global Lightning-Ignited Wildfires Prediction and Climate Change Projections based on Explainable Machine Learning Models

Wildfires pose a significant natural disaster risk to populations and contribute to accelerated climate change. As wildfires are also affected by climate change, extreme wildfires are becoming increasingly frequent. Although they occur less frequently globally than those sparked by human activities, lightning-ignited wildfires play a substantial role in carbon emissions and account for the majority of burned areas in certain regions. While existing computational models, especially those based on machine learning, aim to predict lightning-ignited wildfires, they are typically tailored to specific regions with unique characteristics, limiting their global applicability. In this study, we present machine learning models designed to characterize and predict lightning-ignited wildfires on a global scale. Our approach involves classifying lightning-ignited versus anthropogenic wildfires, and estimating with high accuracy the probability of lightning to ignite a fire based on a wide spectrum of factors such as meteorological conditions and vegetation. Utilizing these models, we analyze seasonal and spatial trends in lightning-ignited wildfires shedding light on the impact of climate change on this phenomenon. We analyze the influence of various features on the models using eXplainable Artificial Intelligence (XAI) frameworks. Our findings highlight significant global differences between anthropogenic and lightning-ignited wildfires. Moreover, we demonstrate that, even over a short time span of less than a decade, climate changes have steadily increased the global risk of lightning-ignited wildfires. This distinction underscores the imperative need for dedicated predictive models and fire weather indices tailored specifically to each type of wildfire.

cs.LG↗

arXiv2024

Edge-wave phase-shifts versus normal-mode phase-tilts in an Eady problem with a sloping boundary

One mechanistic interpretation of baroclinic instability is that of mutual constructive interference of Rossby edge-waves. While the two edge-waves and their relative phase-shifts are invoked as part of the mechanistic interpretation, the phase-tilts of the related normal modes are often presented instead. Here we highlight the differences between edge-wave phase-shifts and normal-mode phase-tilts, in the context of an Eady problem modified by the presence of a sloping boundary. We argue and present evidence that the normal-mode phase-tilt is potentially a misleading quantity to use, and edge-wave phase-shifts should be the ones that are mechanistically relevant. We also provide a clarification for the mechanistic rationalization for baroclinic instability in the presence of slopes (such as suppression of growth rates) that is valid over all parameter space, in contrast to previous attempts. We further present evidence that there is a strong correlation between quantities diagnosed from the GEOMETRIC framework with the edge-wave phase-shifts, but not the normal-mode phase-tilts. The result is noteworthy in that the geometric framework makes no explicit reference to the edge-wave structures in its construction, but the correlation suggests that in problems where edge-wave structures are not so well-defined or readily available, the GEOMETRIC framework should still capture mechanistic and dynamical information. Some implications for parameterization of baroclinic instability and relevant eddy-mean feedbacks are discussed. For completeness, we also provide an explicit demonstration that the linear instability problem of the present modified Eady problem is parity-time symmetric, and speculate on some suggestive links between parity-time symmetry, shear instability, and the edge-wave interaction mechanism.

physics.flu-dyn↗

arXiv2024

Relating interfacial Rossby wave interaction in shear flows with Feynman's two-state coupled quantum system model for the Josephson junction

Here we show how Feynman's simplified model for the Josephson junction, as a macroscopic two-state coupled quantum system, has a one-to-one correspondence with the stable dynamics of two interfacial Rossby waves in piecewise linear shear flows. The conservation of electric charge and energy of the superconducting electron gas layers become respectively equivalent to the conservation of wave action and pseudoenergy of the Rossby waves. Quantum-like tunneling is enabled via action-at-a-distance between the two Rossby waves. Furthermore, the quantum-like phenomena of avoided crossing between eigenstates, described by the Klein-Gordon equation, is obtained as well in the classical shear flow system. In the latter, it results from the inherent difference in pseudoenergy between the in-phase and anti-phased normal modes of the interfacial waves. This provides an intuitive physical meaning to the role of the wavefunction's phase in the quantum system. A partial analog to the quantum collapse of the wavefunction is also obtained due to the existence of a separatrix between "normal mode regions of influence" on the phase plane, describing the system's dynamics. As for two-state quantum bits (qubits), the two-Rossby wave system solutions can be represented on a Bloch sphere, where the Hadamard gate transforms the two normal modes/eigenstates into an intuitive computational basis in which only one interface is occupied by a Rossby wave. Yet, it is a classical system which lacks exact analogs to collapse and entanglement, thus cannot be used for quantum computation, even in principle.

physics.class-ph↗

arXiv2023

A physics-based model of swarming jellyfish

We propose a model for the structure formation of jellyfish swimming based on active Brownian particles. We address the phenomena of counter-current swimming, avoidance of turbulent flow regions and foraging. We motivate corresponding mechanisms from observations of jellyfish swarming reported in the literature and incorporate them into the generic modelling framework. The model characteristics is tested in three paradigmatic flow environments.

nlin.AO↗

arXiv2022

From a microscopic inertial active matter model to the Schrödinger equation

Field theories for the one-body density of an active fluid, such as the paradigmatic active model B+, are simple yet very powerful tools for describing phenomena such as motility-induced phase separation. No comparable theory has been derived yet for the underdamped case. In this work, we introduce active model I+, an extension of active model B+ to particles with inertia. The governing equations of active model I+ are systematically derived from the microscopic Langevin equations. We show that, for underdamped active particles, thermodynamic and mechanical definitions of the velocity field no longer coincide and that the density-dependent swimming speed plays the role of an effective viscosity. Moreover, active model I+ contains the Schrödinger equation in Madelung form as a limiting case, allowing to find analoga of the quantum-mechanical tunnel effect and of fuzzy dark matter in the active fluid. We investigate the active tunnel effect analytically and via numerical continuation.

cond-mat.soft↗

arXiv2022

Zero absolute vorticity plane Couette flow as an hydrodynamic representation of quantum energy states under perpendicular magnetic field

Here we extend the Madelung transformation of the Schrödinger equation into a fluid-like form to include the influence of an external electromagnetic field on a charged particle. The vorticity of the Madelung fluid is then in the opposite direction to the imposed magnetic field and equal in magnitude to the cyclotron angular frequency. When the particle motion is confined to a plane, perpendicular to an imposed magnetic field, the equivalent flow dynamics is that of zero absolute vorticity obtained in a quasi 2D rotating frame, where the cyclotron frequency plays a role equivalent to that of the Coriolis frequency in a rotating frame. We show how the Landau levels and the extended modes in the integer quantum Hall effect are all mapped into such zero absolute vorticity-like plane Couette flows, where the latter exhibit a geostrophic-like balance between the magnetic force and the gradients of the quantum (Bohm) potential and the electric force.

physics.flu-dyn↗

arXiv2021

On a formal equivalence between electro-magnetic waves in cold plasma and shallow water inertio-gravity waves

The fundamental dispersion relation of transverse electro-magnetic waves in a cold collisionless plasma is formally equivalent to the two dimensional dispersion relation of inertio-gravity waves in a rotating shallow water system, where the Coriolis frequency can be identified with the plasma frequency, and the shallow water gravity wave phase speed plays the role of the speed of light. Here we examine this formal equivalence in the governing linearised equations, and compare between the propagation wave mechanisms in these seemingly unrelated physical systems.

physics.plasm-ph↗

arXiv2021

A minimal model for vertical shear instability in protoplanetary accretion disks

The Vertical Shear Instability is an axisymmetric effect suggested to drive turbulence in the magnetically inactive zones of protoplanetary accretion disks. Here we examine its physical mechanism in analytically tractable ``minimal models" in three settings that include a uniform density fluid, a stratified atmosphere, and a shearing-box section of a protoplanetary disk. Each of these analyses show that the vertical shear instability's essence is similar to the slantwise convective symmetric instability in the mid-latitude Earth atmosphere, in the presence of vertical shear of the baroclinic jet stream, as well as mixing in the top layers of the Gulf Stream. We show that in order to obtain instability the fluid parcels' slope should exceed the slope of the mean absolute momentum in the disk radial-vertical plane. We provide a detailed and mutually self-consistent physical explanation from three perspectives: in terms of angular momentum conservation, as a dynamical interplay between a fluid's radial and azimuthal vorticity components, and from an energy perspective involving a generalized Solberg-Høiland Rayleigh condition. Furthermore, we explain why anelastic dynamics yield oscillatory unstable modes and isolate the oscillation mechanism from the instability one.

astro-ph.EP↗

arXiv2020

Pairs of surface wave packets with zero-sum energy in the Hawking radiation analog

Here we propose a minimal analog gravity setup and suggest how to select two surface gravity wave packets in order to mimic some key aspects of Hawking radiation from the horizon of non-rotating black holes. Our proposed setup, unlike the scattering problem conventionally studied, constitutes of a constant mean flow over a flat bathymetry, in which the two wave packets possess the same amount of wave action but equal and opposite (sign) amount of energy, thereby mimicking virtual particles created out of near horizon vacuum fluctuations. Attention is given to the physical mechanism relating to the signs of the wave action and energy norm with the wave's intrinsic and total phase speeds. We construct narrow wave packets of equal wave action, the one with positive energy and group speed propagates against the mean flow and escapes from the black hole as Hawking radiation, while the other with negative energy and group speed is drifted by the mean flow and falls into it. Hawking's prediction of low frequency mode amplification is satisfied in our minimal model by construction. We find that the centroid wavenumbers and surface elevation amplitudes of the wave packets are related by simple analytical expressions.

physics.flu-dyn↗

arXiv2020

Wave interactions in neutrally stable shear layers: regular and singular modes, and non-modal growth

In a recent letter, Carpenter and Guha (2019) compared the neutral modes of a smooth two dimensional shear profile without an inflection point to the modes of its corresponding piecewise-linear profile. The regular mode in the smooth profile was identified as the one least sensitive to the numerical resolution, while the singular modes displayed high sensitivity. Here we provide a physical interpretation using a wave interaction approach for understanding the structure and behavior of both the regular and singular modes. The regular modes are the interfacial Rossby waves located at the concentrated mean vorticity gradient of the shear profile. In contrast, the singular modes result from a one way phase-locking interaction between singular vorticity disturbances, passively advected by the mean flow at different levels of the profile, and the interfacial Rossby waves. We show that this one way interaction can also lead to a sustained non-modal growth of the interfacial Rossby waves that cannot be captured by standard eigenvalue analysis.

physics.flu-dyn↗

arXiv2019

On the opposing roles of the Boussinesq and non-Boussinesq baroclinic torques in surface gravity wave propagation

Here we suggest an alternative understanding of the surface gravity wave propagation mechanism based on the baroclinic torque, which operates to translate the interfacial vorticity anomalies at the air-water interface. We demonstrate how the non-Boussinesq term of the baroclinic torque acts against the Boussinesq one to hinder wave propagation. By standard vorticity inversion and mirror imaging, we then show how the existence of the bottom boundary affects the two types of torque. Since the opposing non-Boussinesq torque results solely from the mirror image, it vanishes in the deep water limit and its magnitude is half of the Boussinesq torque in the shallow water limit. This reveals that Boussinesq approximation is valid in the deep water limit, even though the density contrast between air and water is large. The mechanistic roles, played by the Boussinesq and non-Boussinesq parts of the baroclinic torque, remain obscured in the standard derivation where the time-dependent Bernoulli equation is implemented instead of the interfacial vorticity equation. Finally, we note on passing that the Virial theorem for surface gravity waves can be obtained solely from considerations of the dynamics at the air-water interface.

physics.flu-dyn↗