Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.40090

Simulation of non-stationary anisotropic capillary wave turbulence within the framework of the kinetic equation

E. A. Kochurin·A. O. Korotkevich
View original source ↗Read source document ↗Export metadata ↓

Abstract

In the present work, numerical simulation of the evolution of capillary turbulence was performed on the basis of the wave kinetic equation taking into account energy dissipation at small scales. For an isotropic initial condition, the simulation results reproduce the Zakharov--Filonenko power-law turbulence spectrum for the wave action, \(n_k \sim k^{-17/4}\). The main result of the work is the calculation of the evolution for a substantially anisotropic initial condition. The numerical data indicate that, during the evolution of an anisotropic wave-action distribution, a factorized spectrum \(n(k,ϕ) \sim k^{-17/4}F(ϕ)\) is formed in polar coordinates \((k,ϕ)\), where \(F(ϕ)\) is a function of the angle in Fourier space. In the regime of a steady power-law distribution in \(k\), the calculated collision integral vanishes with high accuracy in the inertial interval of wavenumbers (the region of the power-law spectrum). Thus, the work provides evidence for the realization of a new strongly anisotropic turbulence spectrum, similar to Kolmogorov--Zakharov spectra.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

E. A. Kochurin, A. O. Korotkevich. 2026-10-29. Simulation of non-stationary anisotropic capillary wave turbulence within the framework of the kinetic equation. https://arxiv.org/abs/2610.40090

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bubble curtains in a lock-exchange flow: the importance of transient dynamics in the curtain-driven regime

Bubble curtains are line bubble plumes that are used to mitigate saltwater intrusion in ship locks. When the lock gate that separates saline seawater from fresh river water is opened, a lock-exchange flow develops. Installing a bubble curtain at the gate location disrupts this flow and reduces saltwater infiltration. For real-world applications, it is important to quantify how effective the bubble curtain is as a function of the key governing parameters. To this end, we performed multiphase large-eddy simulations that faithfully reproduce earlier experimental results including the two distinct operating regimes: the breakthrough regime and the curtain-driven regime. This paper focuses on the curtain-driven regime and seeks to clarify how the effectiveness of bubble curtains evolves over time. The detailed spatial and temporal data from the simulations, together with the ability to systematically vary the governing parameters, enabled us to overcome several limitations inherent in previous experiments. Furthermore, the simulations were used to obtain parameter values to build a semi-analytical model. Both the simulations and the semi-analytical model successfully capture and elucidate the time evolution of the density field and of the bubble curtain's effectiveness. The findings highlight that the time elapsed since the gate opening and the transient dynamics play a crucial role in determining the performance of bubble curtains for mitigation of salt intrusion.

physics.flu-dyn↗
arXiv2026

The electrostatic-hydrodynamic interaction of two spheres in a linear compressional flow

We investigate the collision dynamics of two like-charged dielectric spheres in a uniaxial compressional flow, accounting for non-continuum lubrication interactions, van der Waals attraction, and the complete finite-dielectric electrostatic interaction. Mutual polarization causes the electrostatic force to behave substantially differently from the point-charge approximation and can produce strong near-field attraction despite far-field Coulomb repulsion, depending on the particle size and charge ratios. We identify a critical electrostatic strength above which particles approaching from the far field cannot reach contact. This threshold corresponds to a saddle-node bifurcation of the relative-trajectory field on the compressional axis. Below this threshold, near-field polarization-induced attraction can increase the upstream interception area and substantially enhance the collision efficiency. We report that electrostatic interactions lead to non-monotonic variations of collision efficiency with electrostatic strength, particle size ratio, and charge ratio. When electrostatic interactions remain repulsive at all separations, increasing their strength suppresses collisions monotonically. Non-continuum lubrication and van der Waals interactions further modify the collision efficiency, although sufficiently strong polarization-induced attraction can dominate these near-field effects. For weak electrostatic interactions, a perturbation analysis expresses the leading correction to the collision efficiency as a weighted average of the electrostatic force along the limiting colliding trajectory, with the weight concentrated in the lubrication region; this prediction agrees closely with the numerical results. These results demonstrate that finite-size polarization and near-field hydrodynamic interactions jointly govern the collision behaviour of like-charged particles in compressional flows.

physics.flu-dyn↗
arXiv2026

A hybrid framework integrating physics-informed neural operators with conventional methods for turbulence

We develop large-eddy simulation nets (LESnets), a hybrid framework that integrates physics-informed neural operators with conventional computational methods for accurate and efficient simulation of wall-bounded turbulence. LESnets incorporates the large-eddy simulation (LES) equations into the training of the factorized Fourier neural operator (F-FNO), requiring no labeled training data and accommodating flexible time horizons during training. Boundary conditions are enforced as hard constraints and a wall model based on the law of the wall is incorporated to improve physical consistency and enable reliable coarse-grid simulations at high Reynolds numbers. Furthermore, the immersed boundary method (IBM) is embedded in the physics-informed loss function to accommodate complex geometries with boundaries that are not aligned with the computational grid. In addition, the subgrid-scale (SGS) model coefficient is optimized during training using a single flow snapshot. The framework is evaluated on turbulent channel flows at friction Reynolds numbers $Re_τ \approx 180$, $590$, $1000$, and $2000$ and turbulent flows over periodic hills at Reynolds numbers $Re_h \approx 5600$ and $10595$. Numerical results show that LESnets achieves predictive accuracy and computational efficiency comparable to those of the implicit U-Net enhanced Fourier neural operator (IUFNO) and F-FNO, while attaining accuracy comparable to that of conventional LES with greater computational efficiency. These results support the integration of physics-informed neural operators with established computational methods as a promising approach to accurate and efficient simulation of wall-bounded turbulence.

physics.flu-dyn↗