arXiv subjects

Malek Abid

Publications and source records attributed to Malek Abid.

6 recordsLinked to original sources

arXiv2023

Exploring the Weber dependency of jet fragmentation: a Direct Numerical Simulation investigation

Jet fragmentation is investigated through a Direct Numerical Simulation campaign using Basilisk (Popinet & collaborators 2013). The simulations span over one order of magnitude of gaseous Weber numbers (13 to 165), i.e. over the second wind-induced and atomization regimes, and the jets develop over distances up to 28 nozzle diameters. The study focuses on the size and velocity distributions of droplets, as well as their joint distribution. Two models derived from different theoretical backgrounds, the statistical description of the turbulence intermittency (Novikov & Dommermuth 1997) and the empirical description of the ligament-mediated fragmentation (Villermaux et al. 2004), are compared for describing the droplet size distribution close to the nozzle. The characteristics of the size-velocity joint distribution are explained using the vortex ring theory (Saffman 1992) which highlights two sources of fragmentation. Finally, the joint histogram of the particulate Reynolds and Ohnesorge numbers is analysed and a normalisation is suggested. It reveals that the delimitations of the droplet phase space, once properly normalised, are self-similar and independent of the gaseous Weber number, both numerically and experimentally.

physics.flu-dyn↗

arXiv2023

The superharmonic instability and wave breaking in Whitham equations

The Whitham equation is a model for the evolution of surface waves on shallow water that combines the unidirectional linear dispersion relation of the Euler equations with a weakly nonlinear approximation based on the KdV equation. We show that large-amplitude, periodic, traveling-wave solutions to the Whitham equation and its higher-order generalization, the cubic Whitham equation, are unstable with respect to the superharmonic instability (i.e. a perturbation with the same period as the solution). The threshold between superharmonic stability and instability occurs at the maxima of the Hamiltonian and $\mathcal{L}_2$-norm. We examine the onset of wave breaking in traveling-wave solutions subject to the modulational and superharmonic instabilities. We present new instability results for the Euler equations in finite depth and compare them with the Whitham results. We show that the Whitham equation more accurately approximates the wave steepness threshold for the superharmonic instability of the Euler equations than does the cubic Whitham equation. However, the cubic Whitham equation more accurately approximates the wave steepness threshold for the modulational instability of the Euler equations than does the Whitham equation.

physics.flu-dyn↗

arXiv2023

Free surface water-waves generated by instability of an exponential shear flow

The stability of an exponential current in water to infinitesimal perturbations in the presence of gravity and capillarity is investigated. Some new results on the generation of gravity-capillary waves are presented which supplement the previous works of Morland, Saffman \& Yuen (1991) and Young \& Wolfe (2014), namely in finite depth. To consider perturbations of much larger scales, a specific attention is paid to the stability of the exponential current only in the presence of gravity.

physics.flu-dyn↗

arXiv2022

The Cubic Vortical Whitham Equation

The cubic-vortical Whitham equation is a model for wave motion on a vertically sheared current of constant vorticity in a shallow inviscid fluid. It generalizes the classical Whitham equation by allowing constant vorticity and by adding a cubic nonlinear term. The inclusion of this extra nonlinear term allows the equation to admit periodic, traveling-wave solutions with larger amplitude than the Whitham equation. Increasing vorticity leads to solutions with larger amplitude as well. The stability of these solutions is examined numerically. All moderate- and large-amplitude solutions, regardless of wavelength, are found to be unstable. A formula for a stability cutoff as a function of vorticity and wavelength for small-amplitude solutions is presented. In the case with zero vorticity, small-amplitude solutions are unstable with respect to the modulational instability if kh > 1.252, where k is the wavenumber and h is the mean fluid depth.

physics.flu-dyn↗

arXiv2018

Nonlinear water waves in shallow water in the presence of constant vorticity: A Whitham approach

Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface elevation and the horizontal velocity are derived. Using Riemann invariants of these equations, that are obtained analytically, a closed-form nonlinear evolution equation for the surface elevation is derived. A dispersive term is added to this equation using the exact linear dispersion relation. With this new single first-order partial differential equation, vorticity effects on undular bores are studied. Within the framework of weakly nonlinear waves, a KdV-type equation and a Whitham equation with constant vorticity are derived from this new model and the effect of vorticity on solitary waves and periodic waves is considered. Futhermore, within the framework of the new model and the Whitham equation a study of the effect of vorticity on the breaking time of dispersive waves and hyperbolic waves as well is carried out.

physics.flu-dyn↗

arXiv2006

Vortex sheet dynamics and turbulence

The nonlinear evolution of a vortex sheet driven by the Kelvin--Helmholtz instability is characterized by the formation of a spiral possessing complex stretching and intensity patterns. We show that the power energy spectrum of a single two-dimensional vortex sheet tends to the usual fluid turbulent spectrum, with an exponent of -3. Using numerical simulations and asymptotic methods, we demonstrate the relation between this power law and the singularities in the geometry and vorticity distribution of the sheet.

physics.class-ph↗