Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2009.04073

Kelvin wake pattern at small Froude numbers

Ravindra Pethiyagoda·Timothy J. Moroney·Christopher J. Lustri·Scott W. McCue
View original source ↗Read source document ↗Export metadata ↓

Abstract

The surface gravity wave pattern that forms behind a steadily moving disturbance is well known to comprise divergent waves and transverse waves, contained within a distinctive V-shaped wake. In this paper, we are concerned with a theoretical study of the limit of a slow-moving disturbance (small Froude numbers), for which the wake is dominated by transverse waves. We consider three configurations: flow past a submerged source singularity, a submerged doublet, and a pressure distribution applied to the surface. We treat the linearised version of these problems and use the method of stationary phase and exponential asymptotics to demonstrate that the apparent wake angle is less than the classical Kelvin angle and to quantify the decrease in apparent wake angle as the Froude number decreases. These results complement a number of recent studies for sufficiently fast-moving disturbances (large Froude numbers) where the apparent wake angle has been also less than the classical Kelvin angle. As well as shedding light on the wake angle, we also study the fully nonlinear problems for our three configurations under various limits to demonstrate the unique and interesting features of Kelvin wake patterns at small Froude numbers.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ravindra Pethiyagoda, Timothy J. Moroney, Christopher J. Lustri, Scott W. McCue. 2021-01-28. Kelvin wake pattern at small Froude numbers. https://doi.org/10.1017/jfm.2021.193

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

KEEP EXPLORING

Related papers

arXiv2026

Self-similar Features in Secondary Breakup of a Droplet and Ligament Mediated Fragmentation under Extreme Conditions

Droplet formation is relevant in many applications spanning natural and artificial settings. A physical understanding of aerobreakup or air-assisted secondary atomization and predicting size distributions in these applications is non-trivial. We show that extreme airflow speeds induce catastrophic breakup, which, although chaotic and seemingly obscure, is not hopelessly unstructured. In the present study, through shockwave-induced breakups, we investigate the associated intermediate processes at smaller spatiotemporal scales at very high Weber numbers ($We \sim 10^3-10^4$). We show that microscale protrusions decorate the disintegrating droplet interface and eventually fragment, resulting in the generation of daughter droplets. We discover these undulations to follow breakup patterns (sub-secondary breakup) that resemble a scaled-down version of secondary atomization. The consistent topology across a vast range of scales $(10^{-6}m-10^{-2}m)$ suggests a self-similar mechanism bridged by local Weber number. The normalized size distribution of the resultant droplets exhibits universality and $We$ invariance within the investigated range of extreme conditions, including transient statistics for subsequent time periods. This conforms to a modified gamma distribution characterized by ligament shape factors, which tend toward the limiting behavior associated with the maximum corrugations physically possible. Scaling laws based on the $We$ are derived for the averaged diameter as $\sim {We}^{-1/3}$, using a high-energy aerodynamic breakup mechanism and subsequently used to derive a time-integrated distribution. These observations reinforce the idea of a self-similar mechanism for the catastrophic droplet breakups, encompassing multiscale deformation cascades, self-similar sub-secondary breakups, maximally corrugated ligaments, and universal droplet size distributions.

physics.flu-dyn↗
arXiv2026

Particle Trajectories Beneath Fully Nonlinear Waves Generated by Horizontal Seabed Motion

We investigate fully nonlinear water waves and fluid-particle dynamics generated by the horizontal motion of a seabed obstacle with prescribed time-dependent velocity. The governing equations are the full Euler equations, formulated in a time-dependent conformal domain that simultaneously maps the moving free surface and seabed onto fixed boundaries. The main contribution of this work is a Lagrangian formulation for computing particle trajectories in the resulting genuinely unsteady conformal domain. We derive a closed-form trajectory system in the canonical domain in which the time dependence of the conformal map is entirely represented by the real and imaginary parts of an analytic function that can be evaluated spectrally from the surface. We apply the formulation to waves generated by horizontal submarine landslide motion and characterize particle displacements throughout the fluid as functions of the initial particle position and Froude number. Our findings identify distinct regions in which particle motion is predominantly associated with the moving seabed, the generated wave, or the combined action of both. The results reveal a transition in the dominant mechanism driving particle motion: at low Froude numbers, particle displacements are primarily associated with the moving seabed, whereas at high Froude numbers the generated wave becomes increasingly dominant, particularly near the free surface and away from the obstacle path.The numerical predictions are benchmarked against laboratory data available in the literature, showing good agreement and providing a quantitative assessment of the model accuracy. Moreover, laboratory topographies beyond those considered here can be readily incorporated into the numerical framework through a Hermite interpolation procedure.

physics.flu-dyn↗
arXiv2026

Goal-Oriented Weighting of Reynolds-Stress Data for Learning Turbulence Models in Complex Flows

Data-driven turbulence models for the Reynolds-averaged Navier-Stokes (RANS) equations offer a promising route to improving predictions of complex flows. Such models, specifically the turbulence constitutive relations, can be learned efficiently from high-fidelity Reynolds-stress data without evaluating the RANS equations during training. However, conventional losses weight all tensor-component and spatial errors equally, although their influence on a quantity of interest (QoI) can differ significantly; reducing the aggregate stress error therefore does not necessarily lead to an improved QoI prediction. Training against flow-level observations accounts for this dependence but requires repeated, potentially expensive RANS solutions. In canonical shear flows, physical reasoning can identify the shear component as the only one relevant for the mean-flow prediction. Motivated by this example, we propose a goal-oriented method to select and weight Reynolds-stress training data for complex flows. For a specified QoI, a single offline adjoint evaluation quantifies its sensitivity to local perturbations of each Reynolds-stress component. These sensitivities are converted into fixed weights in the supervised loss, enabling training without further RANS solutions. We validate the weighting in square-duct and periodic-hill flows, then apply it to a film-cooling jet in crossflow, where it improves velocity and cooling-effectiveness predictions over uniformly weighted training despite using a velocity-only QoI. Beyond turbulence modelling, this work suggests a broader strategy for aligning supervised learning with downstream prediction goals while preserving training efficiency.

physics.flu-dyn↗