Related papers: Bifurcations of a plane parallel flow with Kolmogo…
We investigate here linear stability in a canonical three-dimensional boundary layer generated by the superposition of a spanwise pressure gradient upon an otherwise standard channel flow. As the main result, we introduce a simple…
We derive the normal form for the delay-induced Hopf bifurcation in the first-order phase-locked loop with time delay by the multiple scaling method. The resulting periodic orbit is confirmed by numerical simulations. Further detailed…
We investigate the linear Floquet stability of two fluid layers undergoing oscillations in the direction parallel to the flexible wall that separates them. This canonical configuration is inspired by the cerebrospinal fluid flow in the…
We study two-dimensional (2D) binary-fluid turbulence by carrying out an extensive direct numerical simulation (DNS) of the forced, statistically steady turbulence in the coupled Cahn-Hilliard and Navier-Stokes equations. In the absence of…
In line with Pomeau's conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes…
This study examines the relaminarization of turbulent puffs in pipe flow using highly resolved direct numerical simulations at Reynolds numbers of 1880, 1900, and 1920. The exponential decay of the total energy of streamwise velocity…
A three-layer asymptotic structure for turbulent pipe flow is proposed, revealing in terms of intermediate variables, the existence of a Reynolds-number invariant logarithmic region. It provides a theoretical foundation for addressing…
We investigate the persistence and regularity of spectral submanifolds (SSMs) in high-dimensional parametric dynamical systems undergoing a Hopf bifurcation. By analyzing how resonances in the linearized spectrum near bifurcation points…
We study the stability of two-fluid flow through a plane channel at Reynolds numbers of a hundred to a thousand in the linear and nonlinear regimes. The two fluids have the same density but different viscosities. The fluids, when miscible,…
In this paper, we use the well-known background method to obtain a rigorous lower bound on the volume flow rate through a helical pipe driven by a pressure differential in the limit of large Reynolds number. As a consequence, we also obtain…
The bifurcation diagram of a truncation to six degrees of freedom of the equations for quasi-geostrophic, baroclinic flow is investigated. Period doubling cascades and Shil'nikov bifurcations lead to chaos in this model. The low dimension…
Tipping in multistable systems occurs usually by varying the input slightly, resulting in the output switching to an often unsatisfactory state. This phenomenon is manifested in thermoacoustic systems. This thermoacoustic instability may…
We study the statistics of the relative separation between two fluid particles in a spatially smooth and temporally random flow. The Lagrangian strain is modelled by a telegraph noise, which is a stationary random Markov process that can…
Laboratory experiments point out the existence of patterns made of alternately laminar and turbulent oblique bands in plane Couette flow in its way to/from turbulence as the Reynolds number R is varied. Many previous theoretical and…
Transition from steady state to intermittent chaos in the cubical lid-driven flow is investigated numerically. Fully three-dimensional stability analyses have revealed that the flow experiences an Andronov-Poincar\'e-Hopf bifurcation at a…
Upon decreasing the Reynolds number, plane Couette flow first forms alternately turbulent and laminar oblique bands out of featureless turbulence below some upper threshold R_t. These bands exist down to a global stability threshold R_g…
Lubrication expressions for the friction coefficients of a spherical particle moving in a fluid between and along two parallel solid walls are explicitly evaluated in the low-Reynolds-number regime. They are used to determine lubrication…
We study the modulational stability problem for the traveling periodic waves (called Stokes waves) in an infinitely deep fluid by using pseudo-differential operators in conformal variables. We derive the criteria and the normal forms for…
The Landau-Lifshitz fluctuating hydrodynamics is used to study the statistical properties of the linearized Kolmogorov flow. The relative simplicity of this flow allows a detailed analysis of the fluctuation spectrum from near equilibrium…
The planar laminar flow resulting from the impingement of two gaseous jets of different density issuing into an open space from aligned steadily fed slot nozzles of semi-width $R$ separated a distance $2H$ is investigated by numerical and…