Arnaud Goullet

A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

The spatial evolution of nonlinear long-crested irregular waves characterized by the JONSWAP spectrum is studied numerically using a nonlinear wave model based on a pseudospectral (PS) method and the modified nonlinear Schrodinger (MNLS) equation. In addition, new laboratory experiments with two different spectral bandwidths are carried out and a number of wave probe measurements are made to validate these two wave models. Strongly nonlinear wave groups are observed experimentally and their propagation and interaction are studied in detail. For the comparison with experimental measurements, the two models need to be initialized with care and the initialization procedures are described. The MNLS equation is found to approximate reasonably well for the wave fields with a relatively smaller Benjamin–Feir index, but the phase error increases as the propagation distance increases. The PS model with different orders of nonlinear approximation is solved numerically, and it is shown that the fifth-order model agr...

Large amplitude internal solitary waves in a two-layer system of piecewise linear stratification

We study large amplitude internal solitary waves in a two-layer system where each layer has a constant buoyancy frequency (or Brunt–Vaisala frequency). The strongly nonlinear model originally derived by Voronovich [J. Fluid Mech. 474, 85 (2003)] under the long wave assumption for a density profile discontinuous across the interface is modified for continuous density stratification. For a wide range of depth and buoyancy frequency ratios, the solitary wave solutions of the first two modes are described in detail for both linear-constant and linear-linear density profiles using a dynamical system approach. It is found that both mode-1 and mode-2 solitary waves always point into the layer of smaller buoyancy frequency. The width of mode-1 solitary waves is found to increase with wave amplitude while that of mode-2 solitary waves could decrease. Mode-1 solitary wave of maximum amplitude reaches the upper or lower wall depending on its polarity. On the other hand, mode-2 solitary wave of maximum amplitude can ...

A coaxial vortex ring model for vortex breakdown

Abstract A simple–yet plausible–model for B-type vortex breakdown flows is postulated; one that is based on the immersion of a pair of slender coaxial vortex rings in a swirling flow of an ideal fluid rotating around the axis of symmetry of the rings. It is shown that this model exhibits in the advection of passive fluid particles (kinematics) just about all of the characteristics that have been observed in what is now a substantial body of published research on the phenomenon of vortex breakdown. Moreover, it is demonstrated how the very nature of the fluid dynamics in axisymmetric breakdown flows can be predicted and controlled by the choice of the initial ring configurations and their vortex strengths. The dynamic intricacies produced by the two ring + swirl model are illustrated with several numerical experiments.

An iterative method to solve a regularized model for strongly nonlinear long internal waves

We present a simple iterative scheme to solve numerically a regularized internal wave model describing the large amplitude motion of the interface between two layers of different densities. Compared with the original strongly nonlinear internal wave model of Miyata [10] and Choi and Camassa [2], the regularized model adopted here suppresses shear instability associated with a velocity jump across the interface, but the coupling between the upper and lower layers is more complicated so that an additional system of coupled linear equations must be solved at every time step after a set of nonlinear evolution equations are integrated in time. Therefore, an efficient numerical scheme is desirable. In our iterative scheme, the linear system is decoupled and simple linear operators with constant coefficients are required to be inverted. Through linear analysis, it is shown that the scheme converges fast with an optimum choice of iteration parameters. After demonstrating its effectiveness for a model problem, the iterative scheme is applied to solve the regularized internal wave model using a pseudo-spectral method for the propagation of a single internal solitary wave and the head-on collision between two solitary waves of different wave amplitudes.

Two-Vortex Models for Vortex Breakdown

A simple Hamiltonian dynamical systems model for vortex breakdown of the bubble-type (B-type) is developed and analyzed. This model is constructed using the flow induced by two point vortices moving in a half-plane immersed in an ideal (= inviscid and incompressible) fluid with an ambient uniform horizontal velocity. It is shown — using a combination of modern dynamical systems theory and numerical analysis — that the flows generated by this model capture most of the dynamical features exhibited in B-type vortex breakdown, including the existence of chaotic regimes. Examples are provided to illustrate the variety and complexity of vortex breakdown type flows that can be produced with these models.Copyright

CONTROL OF CHAOTIC ADVECTION

A method of chaos reduction for Hamiltonian systems is applied to control chaotic advection. By adding a small and simple term to the stream function of the system, the construction of invariant tori has a stabilization effect in the sense that these tori act as barriers to diffusion in phase space and the controlled Hamiltonian system exhibits a more regular behaviour.

Using Chaos for Fluid Mixing in Pulsed Micro Flows

Even though mixing is crucial in many microfluidic applications where biological and chemical reactions are needed, efficient mixing remains a challenge since the Reynolds number of these flows is typically low, thus excluding turbulence as a potential mechanism for stirring. While various approaches relying on clever geometries, cross-flows, miniature stirrers or external fields have been used in the past, our work has focused on generating stirring in microchannels of simple geometry by merely pulsing flow rates at the inlets through which the two fluids are brought into the device. Flow visualizations from experiments, as well as numerical simulations, have indicated that the majority of the mixing takes place in the confluence region. Even though it has been shown in previous work that good mixing can be achieved at relatively large scales using this technique, one of the challenges is to make sure that mixing occurs at small scales (i.e., particle scales) as well. To address this issue, we carefully study the dynamics of tracer particles using both computational fluid dynamics and dynamical systems theory, and explore the parameter space in terms of the Reynolds number, Strouhal number and phase difference between the two inlet flows. Specifically, we generate a bifurcation diagram in which both regular and chaotic dynamics occur. As expected, the chaotic regime exhibits stretching and folding of material lines at all (large and small) scales, and is thus promising as an effective mixing tool.Copyright