arXiv subjects

Emanuele Zuccoli

Publications and source records attributed to Emanuele Zuccoli.

3 recordsLinked to original sources

arXiv2026

A free-surface-only closure model for linear waves on general deep-water flows

We present a novel, spatially two-dimensional (2D) set of equations to study the propagation of linear deep-water surface waves over a general steady three-dimensional (3D) background free surface flow. No assumptions of a flat background free surface, nor of an irrotational background flow, are made. The resulting model is not only a significant theoretical simplification, but also results in orders of magnitude faster computations. The linearized Euler equations are evaluated on the free surface of the base flow, and a closure condition is proposed to account for the vertical derivatives at the free surface. This generalizes a recent result for purely rotating background flows (Zuccoli, Brambley & Barkley, 2025, arXiv:2405.12078). The final model consists of five coupled first order partial differential equations (PDEs) to be solved on the 2D free surface, involving five unknowns: the horizontal and vertical perturbation velocities; the free surface perturbation height; and unexpectedly the gradient of perturbation pressure with depth at the surface. Two test problems are used to validate the model: a uni-directional vortical depth-varying base flow with a flat free surface; and perturbations to a travelling Gerstner wave solution. Eigenvalues and eigenfunctions of the linearized Euler equations are computed and compared with those of the model. Results show remarkable agreement between the two. Our study finds for the first time, to the best of our knowledge, that sufficiently steep two-dimensional Gerstner waves are unstable.

physics.flu-dyn↗

arXiv2025

A deep-water closure model for surface waves on axisymmetric swirling flows

We consider the propagation of linear gravity waves on the free surface of steady, axisymmetric flows with purely azimuthal velocity. We propose a two-dimensional set of governing equations for surface waves valid in the deep-water limit. These equations come from a closure condition at the free surface that reduces the three-dimensional Euler equations in the bulk of the fluid to a set of two-dimensional equations applied only at the free surface. Since the closure condition is not obtained rigorously, it is validated numerically through comparisons with full three-dimensional calculations for vortex flows, including for a Lamb-Oseen vortex. The model presented here overcomes three limitations of existing models, namely: it is not restricted to potential base flows; it does not assume the base flow to have a flat free surface; and it does not require the use of infinite-order differential operators (such as $\tanh(\nabla)$) in the governing equations. The model can be applied in the case of rapid swirl (large Froude number) where the base free surface is substantially deformed. Since the model contains only derivatives of finite order, it is readily amenable to standard numerical study.

physics.flu-dyn↗

arXiv2024

Trapped Free Surface Waves for a Lamb-Oseen Vortex Flow

Trapped surface waves have been observed in a swimming pool trapped by, and rotating around, the cores of vortices. To investigate this effect, we have numerically studied the free-surface response of a Lamb--Oseen vortex to small perturbations. The fluid has finite depth but is laterally unbounded. The numerical method used is spectrally accurate, and uses a novel non-reflecting buffer region to simulate a laterally unbounded fluid. While a variety of linear waves can arise in this flow, we focus here on surface gravity waves. We investigate the linear modes of the vortex as a function of the perturbation azimuthal mode number and the vortex rotation rate. We find that at low rotation rates, linear modes decay by radiating energy to the far field, while at higher rotation rates modes become nearly neutrally stable and trapped in the vicinity of the vortex. While trapped modes have previously been seen in shallow water surface waves due to small perturbations of a bathtub vortex, the situation considered here is qualitatively different owing to the lack of an inward flow and the dispersive nature of non-shallow-water waves. We also find that for slow vortex rotation rates, trapped waves propagate in the opposite direction to the vortex rotation, whereas, above a threshold rotation rate, waves co-rotate with the flow.

physics.flu-dyn↗