arXiv subjects

Fernando Mellibovsky

Publications and source records attributed to Fernando Mellibovsky.

8 recordsLinked to original sources

arXiv2026

Emergence of chaos and fractality in the basin boundary of subcritical shear flow

From a dynamical systems perspective of subcritical transition in shear flows, the basin boundary separating the laminar and turbulent attractors, along with the edge state that governs the long-term dynamics on that boundary, are of fundamental interest. As the Reynolds number is increased from small values, a multiplicity of simple exact coherent structures (ECS) appear in phase space, of which one often undertakes the role of the edge state. At higher values of the Reynolds number, however, the dynamics on the basin boundary and the edge state are sensitive to initial conditions, as shown by a wealth of numerical and experimental studies. The mechanism behind this transition remains unclear. To address this, we examine the subcritical regime of Taylor-Couette flow using a minimal computational box and reveal a generic mechanism whereby the edge state becomes chaotic. The first step in this process involves the formation of a heteroclinic tangle between a travelling-wave-type ECS and an independently engendered chaotic saddle. The interaction causes the basin boundary to incorporate the saddle, thus inheriting its fractal structure, while the edge state itself remains the simple ECS. The transition of the edge state to chaos requires a second step: the formation of a heteroclinic cycle involving the ECS and the chaotic saddle. In consequence, the observation of a simple non-chaotic edge state at given values of the parameters is no guarantee that the same situation will hold at nearby values.

physics.flu-dyn↗

arXiv2024

Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow

The transition to chaos in the subcritical regime of counter-rotating Taylor-Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics are found to be remarkably well approximated by a simple discrete map that admits rigorous proof of its chaotic nature. The chaotic set that arises for the map features densely distributed periodic points that are in one-to-one correspondence with unstable periodic orbits (UPOs) of the Navier-Stokes system. This supports the increasingly accepted view that UPOs may serve as the backbone of turbulence and, indeed, we demonstrate that it is possible to reconstruct every statistical property of chaotic fluid flow from UPOs.

nlin.CD↗

arXiv2024

Effects of turbulence boundary conditions on Spalart-Allmaras RANS simulations for active flow control applications

We assess the suitability of Reynolds-Averaged Navier-Stokes (RANS) simulation using the Spallart-Almaras (SA) turbulence model as a closure in analysing the performance of fluidic Active Flow Control (AFC) applications. In particular, we focus on the optimal set of actuation parameters found by Tousi et al. [1, 2] for a SD7003 airfoil at a Reynolds number Re = 6 e4 and post-stall angle of attack alpha = 14 degrees fitted with a Synthetic Jet Actuator (SJA). The Large Eddy Simulation (LES) presented in that work is taken as the reference to identify the best choice of boundary conditions for the turbulence field nu' at both domain inlet and jet orifice in two-dimensional RANS-SA computations. Although SA-RANS is far less accurate than LES, our findings show that it can still predict macroscopic aggregates such as lift and drag coefficients quite statisfactorily and at a much lower computational cost, provided that turbulence levels of the actuator jet are set to a realistic value. An adequate value of nu'is instrumental in capturing the correct flow behaviour of the reattached boundary layers for close-to-optimal actuated cases. This validates the use of RANS-SA as a reliable and cost-effective simulation method for the preliminary optimisation of SJA parameters in AFC applications.

physics.flu-dyn↗

arXiv2024

Feigenbaum universality in subcritical Taylor-Couette flow

Feigenbaum universality is shown to occur in subcritical shear flows. Our testing ground is the counter-rotation regime of the Taylor-Couette flow, where numerical calculations are performed within a small periodic domain. The accurate computation of up to the seventh period doubling bifurcation, assisted by a purposely defined Poincar\'e section, has enabled us to reproduce the two Feigenbaum universal constants with unprecedented accuracy in a fluid flow problem. We have further devised a method to predict the bifurcation diagram up to the accumulation point of the cascade based on the detailed inspection of just the first few period doubling bifurcations. Remarkably, the method is applicable beyond the accumulation point, with predictions remaining valid, in a statistical sense, for the chaotic dynamics that follows.

physics.flu-dyn↗

arXiv2022

Square cylinder in the interface of two different-velocity streams

We investigate the incompressible flow past a square cylinder immersed in the wake of an upstream nearby splitter plate separating two streams of different velocity. The bottom stream Reynolds number, based on the square side, $Re_B=56$ is kept constant while the top-to-bottom Reynolds numbers ratio $R\equiv Re_T/Re_B$ is increased in the range $R\in[1,6.5]$, corresponding to a coupled variation of the bulk Reynolds number $Re\equiv(Re_T+Re_B)/2\in[56,210]$ and an {\it equivalent} nondimensional shear parameter $K\equiv2(R-1)/(R+1)\in[0,1.4667]$. The onset of vortex-shedding, at $R=2.1\pm0.1$ (corresponding to $Re=86.8\pm2.8$, $K=0.71\pm0.04$), is pushed to higher $Re$ as compared to the square cylinder in the classic configuration. The advent of three-dimensionality is triggered by a mode-C-type instability at $R\simeq3.1$ ($Re\simeq115$, $K\simeq1.02$) with wavelength $\lambda_z\simeq2.4$, much as reported for open circular rings and square cylinders placed at an incidence. The resulting solution is period-doubled and exhibits a triad of spanwise symmetries: a mirror reflection and two spatiotemporal symmetries involving the evolution by half a period (two vortex-shedding cycles) followed by either specular reflection or a half-wavelength shift. The path towards spatio-temporal chaos is initiated thereafter with a modulational period-doubling tertiary bifurcation at $R\in(3.4,3.8)$ that also doubles the spanwise periodicity. The ensuing nonlinear solution repeats only after four vortex shedding periods and retains only a spatiotemporal invariance consisting in the evolution by half a period (two vortex-shedding cycles) followed by mirror reflection about a streamwise-cross-stream plane. At slighlty higher values of $R\geq4$, the flow has become spatio-temporally chaotic, but the main features of mode C are still clearly distinguishable.

physics.flu-dyn↗

arXiv2016

Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier--Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.

physics.flu-dyn↗

arXiv2013

Streamwise-localized solutions at the onset of turbulence in pipe flow

Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulence arises from one such solution branch.

physics.flu-dyn↗

arXiv2011

From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow

We study numerically a succession of transitions in pipe Poiseuille flow that leads from simple travelling waves to waves with chaotic time-dependence. The waves at the origin of the bifurcation cascade possess a shift-reflect symmetry and are both axially and azimuthally periodic with wave numbers κ = 1.63 and n = 2, respectively. As the Reynolds number is increased, successive transitions result in a wide range of time dependent solutions that includes spiralling, modulated-travelling, modulated-spiralling, doubly-modulated-spiralling and mildly chaotic waves. We show that the latter spring from heteroclinic tangles of the stable and unstable invariant manifolds of two shift-reflect-symmetric modulated-travelling waves. The chaotic set thus produced is confined to a limited range of Reynolds numbers, bounded by the occurrence of manifold tangencies. The states studied here belong to a subspace of discrete symmetry which makes many of the bifurcation and path-following investigations presented technically feasible. However, we expect that most of the phenomenology carries over to the full state-space, thus suggesting a mechanism for the formation and break-up of invariant states that can sustain turbulent dynamics.

physics.flu-dyn↗