Papers by Filippo Chiodi
The transport of dense particles by a turbulent flow depends on two dimensionless numbers. Depend... more The transport of dense particles by a turbulent flow depends on two dimensionless numbers. Depending on the ratio of the shear velocity of the flow to the setting velocity of the particles (or the Rouse number), sediment transport takes place in a thin layer localised at the surface of the sediment bed (bed-load) or over the whole water depth (suspendedload). Moreover, depending on the sedimentation Reynolds number, the bed-load layer is embedded in the viscous sub-layer or is larger. We propose here a two-phase flow model able to describe both viscous and turbulent shear flows. Particle migration is described as resulting from normal stresses, but is limited by turbulent mixing and shear-induced diffusion of particles. Using this framework, we theoretically investigate the transition between bed-load and suspended-load.
The river bar instability is revisited, using a hydrodynamical model based on Reynolds averaged N... more The river bar instability is revisited, using a hydrodynamical model based on Reynolds averaged Navier-Stokes equations. The results are contrasted with the standard analysis based on shallow water Saint-Venant equations. We first show that the stability of both transverse modes (ripples) and of small wavelength inclined modes (bars) predicted by the Saint-Venant approach are artefacts of this hydrodynamical approximation. When using a more reliable hydrodynamical model, the dispersion relation does not present any maximum of the growth rate when the sediment transport is assumed to be locally saturated. The analysis therefore reveals the fundamental importance of the relaxation of sediment transport towards equilibrium as it it is responsible for the stabilisation of small wavelength modes. This dynamical mechanism is characterised by the saturation number, defined as the ratio of the saturation length to the water depth L sat /H. This dimensionless number controls the transition from ripples (transverse patterns) at small L sat /H to bars (inclined patterns) at large L sat /H. At a given value of the saturation number, the instability presents a threshold and a convective-absolute transition, both controlled by the channel aspect ratio β. We have investigated the characteristics of the most unstable mode as a function of the main parameters, L sat /H, β and of a subdominant parameter controlling the relative influence of drag and gravity on sediment transport. As previously found, the transition from alternate bars to multiple bars is mostly controlled by the river aspect ratio β. By contrast, in the alternate bar regime (large L sat /H), the selected wavelength does not depend much on β and approximately scales as H 2/3 L
The hairs of a painting brush withdrawn from a wetting liquid self-assemble into clumps whose siz... more The hairs of a painting brush withdrawn from a wetting liquid self-assemble into clumps whose sizes rely on a balance between liquid surface tension and hairs bending rigidity. Here we study the situation of an immersed carpet in an evaporating liquid bath : the free extremities of the hairs are forced to pierce the liquid interface. The compressive capillary force on the tip of flexible hairs leads to buckling and collapse. However we find that the spontaneous association of hairs into stronger bundles may allow them to resist capillary buckling. We explore in detail the different structures obtained and compare them with similar patterns observed in micro-structured surfaces such as carbon nanotubes "forests".
Thesis manuscript by Filippo Chiodi
My work focused on the soliton solutions of the bidimensional Gardner equation through the Hirota... more My work focused on the soliton solutions of the bidimensional Gardner equation through the Hirota method. The 2D Gardner equation is an ad hoc construction which includes terms from 1D Gardner and the bidimensional terms form KP equation. The method I used was developed by the japanese mathematician Hirota and provides a way to find only solitonic solutions in nonlinear equations. The results I obtained are indeed a class of coherent structures which are a combination of one or more solitons. In detail, I found that solutions of 2D Gardner can be: a positive or negative soliton; a positive or negative table top (soliton with truncated crest); a kink (infinte length soliton); a breather (pair of two solitons that propagate pulsing out of phase); a Mach's stem (two o more positive solitons interacting). In the second part of my work I studied a different approach to extract solitonic solutions. First I found a transformation to map the 2D Gardner equation into the 1D Gardner equation. Since the latter has been exactly solved through the Hirota method, it could be possible to find the solitonic solutions of 2D Gardner by applying the inverse transformation. Even if, in general, when transforming a 2D equation into a 1D equation one loses information, this method was proven successful in the case of the nonlinear Schroedinger equation (NLSE). Since I have verified the agreement of the solutions obtained by these two methods, we are encouraged to believe that the transformation method can be applied also to 2D Gardner equation.
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Papers by Filippo Chiodi
Thesis manuscript by Filippo Chiodi