Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.37289

Mode-2 solitary waves in continuous stratifications

Alex Doak·Ricardo Barros·Paul l A. Milewski
View original source ↗Read source document ↗Export metadata ↓

Abstract

Computed herein are examples of mode-2 internal solitary waves to the Dubreil-Jacotin-Long (DJL) equation. These are localised, fully nonlinear waves in a continuously stratified, inviscid fluid under the Boussinesq and rigid-lid approximations. The equation is solved directly using finite differences on a periodic domain, enabling the computation of both generalised solitary waves, which possess oscillatory mode-1 tails, and embedded solitary waves, whose tails vanish. Two stratifications are considered. The first is a double pycnocline, generalising the three-layer system considered by Doak et al. (2022) by replacing each infinitesimal interface with a pycnocline of finite thickness. The second stratification, a surface mixed layer above an exponentially stratified layer, shows that embedded mode-2 solitary waves are not restricted to double-pycnocline stratifications. These are the first mode-2 solitary waves of the DJL equation computed for stratifications that are asymmetric about mid-depth.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alex Doak, Ricardo Barros, Paul l A. Milewski. 2026-10-27. Mode-2 solitary waves in continuous stratifications. https://arxiv.org/abs/2610.37289

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

KEEP EXPLORING

Related papers

arXiv2026

Differential Geometry of Deterministic Stokesian Dynamics

We present a differential geometric framework for the motion of a non-Brownian particle in the presence of fixed obstacles in a quiescent fluid, in the deterministic Stokesian regime. While one may think (owing to the Helmholtz Minimum Dissipation Theorem) that the hydrodynamic resistance tensor could be the natural candidate for a Riemannian metric shaping the particle trajectories, we demonstrate that the trajectories driven by constant external forces are \emph{not} geodesics of this bare resistance metric. Instead, they experience a geometric drift due to the curvature induced by the presence of obstacles. By rigorously incorporating translational-rotational coupling through a modified effective resistance tensor $\tilde{\mathbf{R}} = \mathbf{R}_{\mathbf{FU}} - \mathbf{R}_{\mathbf{Fω}}\mathbf{R}_{\mathbf{Tω}}^{-1}\mathbf{R}_{\mathbf{Fω}}^T$, which accounts for the hidden dissipation savings afforded by particle rotation, we introduce a unified geometric formalism. We prove that the physical particle trajectories are exact geodesics of a conformally scaled metric, $\tilde{g}_{ij} = \mathcal{D}(\mathbf{x})\tilde{R}_{ij}$, where $\mathcal{D}$ is the instantaneous power dissipation. This framework establishes that the affine parameter along the trajectory corresponds strictly to the cumulative energy dissipated. We apply this theory to the scattering of a spherical particle by a fixed spherical obstacle, showing that the exact analytical trajectory derived previously by the author is recovered as a geodesic of the dissipation-scaled manifold.

physics.flu-dyn↗
arXiv2026

CraftSPH: A composable framework for differentiable smoothed particle hydrodynamics implemented in PyTorch

Smoothed particle hydrodynamics (SPH) is well suited to large-deformation fluid problems, and the growing use of automatic differentiation in engineering applications has motivated interest in differentiable SPH solvers. In this study, a composable differentiable SPH framework, CraftSPH, has been developed. In CraftSPH, major computational operations are implemented as independent modules that users can combine to construct solvers for different purposes. This design supports high-accuracy discretization and both explicit and implicit computation within a common framework, while allowing individual components to be maintained and extended. Selected numerical operations also support automatic differentiation (AD) for physical-parameter estimation and potential coupling with deep learning models. These capabilities were demonstrated through forward and inverse analyses. Forward analyses using an implicit SPH scheme with high-accuracy discretization showed good agreement with analytical and reference solutions for Poiseuille flow and a rising bubble, while capturing the key experimental trends in two- and three-dimensional dam-break problems. In inverse analyses, explicit and implicit SPH schemes were used to estimate kinematic viscosity in Taylor-Green vortex flow and Reynolds number in lid-driven cavity flow. The results also showed that the choice of operations included in the computational graph affects the computed gradients. Together, these findings demonstrate that CraftSPH enables users to assemble problem-specific solvers for forward and inverse analyses within a common framework.

physics.flu-dyn↗
arXiv2026

Submerged Immiscible Oil Jet: Breakup Dynamics and Droplet Size Modelling

Immiscible liquid-liquid jets occur in numerous industrial and environmental settings, including oil spill response and liquid-liquid extraction, yet the coupled evolution of turbulence, interfacial instability, and droplet size distribution across transitional to turbulent regimes remains poorly understood. We present a combined experimental and theoretical investigation of a silicone oil jet injected into refractive-index-matched sugar water, employing simultaneous Particle Image Velocimetry (PIV) and Planar Laser-Induced Fluorescence (PLIF). Beyond the breakup region, mean velocity and Reynolds stress profiles exhibit self-similarity. Proper Orthogonal Decomposition (POD) of the volume fraction reveals a systematic shift in the dominant instability mechanism with increasing Reynolds number: axisymmetric Rayleigh-Plateau modes govern breakup at low Reynolds numbers, sinuous and varicose modes coexist in the transitional regime, and Kelvin-Helmholtz-driven shear-layer breakup dominates at higher Reynolds numbers. Droplet sizes are extracted from PLIF images using a convolutional neural network-based segmentation approach. In the transitional regime, a bimodal droplet size distribution is observed, reflecting the coexistence of shear-induced breakup and Rayleigh-Plateau instability. As the Reynolds number increases and turbulent dissipation intensifies, the distribution evolves toward a single mode with smaller characteristic droplet sizes. To predict the droplet size distribution, existing population balance models are extended to include droplet coalescence. Incorporating coalescence substantially improves agreement with experimental measurements, particularly for larger droplets. These findings demonstrate that turbulent dissipation, interfacial instabilities, and droplet coalescence collectively govern the evolution of droplet size distribution in immiscible liquid-liquid jets.

physics.flu-dyn↗