arXiv subjects

François G. Schmitt

Publications and source records attributed to François G. Schmitt.

4 recordsLinked to original sources

arXiv2024

Hidden Turbulence in van Gogh's \textbf{\textit{The Starry Night}}

Turbulent skies have often inspired artists, particularly in the iconic swirls of Vincent van Gogh's \textbf{\textit{The Starry Night}}. For an extended period, debate has raged over whether the flow pattern in this masterpiece adheres to Kolmogorov's theory of turbulence. In contrast to previous studies that examined only part of this painting, {\textit{all and only the}} whirls/eddies in the painting are taken into account in this work, following the Richardson-Kolmogorov's cascade picture of turbulence. Consequently, the luminance's Fourier power spectrum spontaneously exhibits a characteristic $-5/3$ Kolmogorov-like power-law. This result suggests that van Gogh had a very careful observation of real flows, so that not only the sizes of whirls/eddies in \textbf{\textit{The Starry Night}} but also their relative distances and intensity follow the physical law that governs turbulent flows. Moreover, a "$-1$"-like power-law persists in the spectrum below the scales of the smallest whirls, hinting at Batchelor-type scalar turbulence with a high Schmidt number. Our study thus unveils the hidden turbulence captured within \textbf{\textit{The Starry Night}}.

physics.flu-dyn↗

arXiv2020

Fluctuations and correlations of reactive scalars near chemical equilibrium in incompressible turbulence

The statistical properties of species undergoing chemical reactions in a turbulent environment are studied. We focus on the case of reversible multi-component reactions of second and higher orders, in a condition close to chemical equilibrium sustained by random large-scale reactant sources, while the turbulent flow is highly developed. In such a state a competition exists between the chemical reaction that tends to dump reactant concentration fluctuations and enhance their correlation intensity and the turbulent mixing that on the contrary increases fluctuations and remove relative correlations. We show that a unique control parameter, the Damkhöler number ($Da_θ$) that can be constructed from the scalar Taylor micro-scale, the reactant diffusivity and the reaction rate characterises the functional dependence of fluctuations and correlations in a variety of conditions, i.e., at changing the reaction order, the Reynolds and the Schmidt numbers. The larger is such a Damkhöler number the more depleted are the scalar fluctuations as compared to the fluctuations of a passive scalar field in the same conditions, and vice-versa the more intense are the correlations. A saturation in this behaviour is observed beyond $Da_θ\simeq \mathcal{O}(10)$. We provide an analytical prediction for this phenomenon which is in excellent agreement with direct numerical simulation results.

physics.flu-dyn↗

arXiv2018

Propelled micro-probes in turbulence

The temporal statistics of incompressible fluid velocity and passive scalar fields in developed turbulent conditions is investigated by means of direct numerical simulations along the trajectories of self-propelled point-like probes drifting in a flow. Such probes are characterised by a propulsion velocity which is fixed in intensity and direction; however, like vessels in a flow they are continuously deviated by their intended course as the result of local sweeping of the fluid flow. The recorded time-series by these moving probes represent the simplest realisation of transect measurements in a fluid flow environment. We investigate the non trivial combination of Lagrangian and Eulerian statistical properties displayed by the transect time-series. We show that, as a result of the homogeneity and isotropy of the flow, the single-point acceleration statistics of the probes follows a predictable trend at varying the propulsion speed, a feature that is also present in the scalar time-derivative fluctuations. Further, by focusing on two-time statistics we characterize how the Lagrangian-to-Eulerian transition occurs at increasing the propulsion velocity. The analysis of intermittency of temporal increments highlights in a striking way the opposite trends displayed by the fluid velocity and passive scalars.

physics.flu-dyn↗

arXiv2016

A Lagrangian model of copepod dynamics: Clustering by escape jumps in turbulence

Planktonic copepods are small crustaceans that have the ability to swim by quick powerful jumps. Such an aptness is used to escape from high shear regions, which may be caused either by flow per- turbations, produced by a large predator (i.e., fish larvae), or by the inherent highly turbulent dynamics of the ocean. Through a combined experimental and numerical study, we investigate the impact of jumping behaviour on the small-scale patchiness of copepods in a turbulent environment. Recorded velocity tracks of copepods displaying escape response jumps in still water are here used to define and tune a Lagrangian Copepod (LC) model. The model is further employed to simulate the behaviour of thousands of copepods in a fully developed hydrodynamic turbulent flow obtained by direct numerical simulation of the Navier-Stokes equations. First, we show that the LC velocity statistics is in qualitative agreement with available experimental observations of copepods in tur- bulence. Second, we quantify the clustering of LC, via the fractal dimension $D_2$. We show that $D_2$ can be as low as ~ 2.3 and that it critically depends on the shear-rate sensitivity of the proposed LC model, in particular it exhibits a minimum in a narrow range of shear-rate values. We further investigate the effect of jump intensity, jump orientation and geometrical aspect ratio of the copepods on the small-scale spatial distribution. At last, possible ecological implications of the observed clustering on encounter rates and mating success are discussed

physics.flu-dyn↗