Session Z06: Flow Instability: Nonlinear Dynamics (12:15pm - 1:00pm CST)

Effects of an imposed axial flow on a Ferrofluidic Taylor-Couette flow

We investigate the effects of an externally imposed axial mass flux (axial pressure gradient, axial through flow) on ferrofluidic Taylor-Couette flow under the influence of either an axial or a transverse magnetic field. Without an imposed axial through flow, due to the symmetry-conserving axial field and the symmetry-breaking transverse field, it gives rise to various vortex flows in ferrofluidic Taylor-Couette flow such as wavy Taylor vortex flow (wTVF), wavy spiral vortex flow (wSPI) and wavy vortex flows (wTVF$_{H_x}$ and wSPI$_{H_x}$), which are typically produced by a nonlinear interaction of rotational, shear and magnetic instabilities. In addition, when an axial through flow is imposed to a ferrofluidic Taylor-Couette flow in the presence of either an axial or a transverse magnetic field, previously unknown new helical vortex structures are observed. In particular, we uncover modulated Mixed-Cross-Spirals with a combination of at least three different dominant azimuthal wavenumbers. Emergence of such new flow states indicates richer but potentially more controllable dynamics in ferrofluidic flows, i.e., an imposed axial through flow will be a new controllable factor/parameter in applications of a ferrofluidic and magnetic flows.   

Bifurcation scenario for the low-frequency oscillations of the turbulent flow over an airfoil near stalling conditions.

In addition to the sudden drop of lift, two phenomena appear around an airfoil near stalling conditions: hysteresis and low-frequency oscillations. They are investigated here numerically for an OA209 airfoil at low Mach number M$=$0.2 and high Reynolds number Re$=$1.8 10$^{\mathrm{6}}$. A combination of various numerical and theoretical approaches is performed in the framework of RANS equations. Steady computations show the co-existence of three branches of solutions: high-lift and low-lift solutions, connected by a branch of intermediate-lift solutions. Their global stability analysis then reveals the destabilization of low-frequency modes on the low-lift and high-lift steady branches. The low-frequency oscillations emerging from the Hopf bifurcation points are captured with unsteady RANS computations in a narrow range of angles of attack. They are characterized by Strouhal number St $=$0.02 an order of magnitude lower than those associated to vortex-shedding. A one-equation model is finally proposed to show that the onset of these low-frequency oscillations is related to a subcritical bifurcation while their disappearance occurs via a homoclinic bifurcation.   

Objective identification of kinematic instabilities in shear flows

A kinematic approach for the identification of flow instabilities in the Lagrangian frame is presented. We define the instability as the increased folding, or wrinkling, of lines of fluid particles which is described by the curvature change over a finite time interval. Because the curvature is frame invariant and independent of its parametrization, the identification is objective and applicable to flows of general complexity. No assumptions or knowledge of the averaged solution of the flow field are required, as the identification only depends on the kinematics of the material lines. Examples of a temporally developing jet flow, a separated shear flow over an airfoil at moderate Reynolds number, and the onset of a wake instability behind a circular cylinder are presented.   

Towards a Fluidic Excitable System

Excitable systems occur frequently in both living and engineering systems. Forest fires, the propagation of axon potentials or the cAMP waves of the amoebae Dictyostelium, are familiar yet still fascinating systems that exhibit excitability. Previous works have shown that topologically complex networks interconnecting explicitly oscillatory or excitable elements that are subject to a refractory time after each excitation, can display rich emerging dynamics. But what if such excitable elements are not (presumably) available? In this talk, we propose a realization of a fluidic resistor with non-monotonic differential resistance, and discuss how a connected series of such fluidic elements could result in excitatory-like behavior, without an explicit refractory time. In the absence of any time dependence in the pressure input and output the system exhibits emerging dynamics in the form of self-sustained waves, which travel through the tubes.  Using finite element hydrodynamic simulations we explore the behavior of the non-linear fluidic element, show internal accumulation and depletion of volume in the tube, akin to a fluidic capacitance, and a long range volume pressure coupling, all necessary components for the excitable behavior of the fluidic system.   

Tailoring Volume Dispersion in Fluidic Excitable Systems

A network of elastic fluidic tubes that exhibit a non-monotonic differential conductance can exhibit excitatory behavior for a broad range of material parameters [1,2]. In the absence of any time dependence in the pressure input and output the system dynamics emerges spontaneously in the form of self-sustained waves, which travel through the tubes. These volume and pressure pulses result in areas of the fluidic network having a transient higher volume than the baseline volume. In this work we explore how, by tuning the material parameters such as the non-linearity of the fluidic resistor and the elasticity of the tube wall we can tailor how the local volume accumulation is dispersed in the system. A biological fluidic system endowed with non-linearities in the fluidic conductance (such as our own vasculature) could harness such mechanisms to facilitate hemodynamic control. [1] M Ruiz-Garcia, E Katifori, arXiv:2003.10003 [2] M Ruiz-Garcia, E Katifori, arXiv:2001.01811   

Propagating localized structures in a 1D Faraday experiment

h $-abstract-$\backslash $pard $\backslash $f2 In a previous communication -March meeting 2020- we presented the first experimental evidence of the?[U+2028]existence of trains of propagating oscillons or localized structures in a 1D Faraday experiment in water. $\backslash $pardIn this work we present a quantitative analysis of their dynamics as well as the dynamics of phase diffusion. results indicate that this scenario can be well modelled by the use of a modified version of the parametrically driven damped non-linear Schr\"{o}dinger equation.?[U+2028]?[U+2028]$\backslash $pard-/abstract-$\backslash $\tex