Session M24: Transitional Flows & Nonlinear Dynamics

Live

Newtonian fluids are known to exhibit hydrodynamic instabilities and/or transition to turbulence at sufficiently enough Reynolds numbers. Recently it has been discovered that in simple shear flows (like pressure-driven flows in a pipe or between two plates) there exist unstable coherent structures that organise the turbulent dynamics close to the laminar-turbulent transition. The corresponding dynamics are low-dimensional and can be described by a relatively small number of well-chosen degrees of freedom. Complex fluids, in general, and polymer solutions, in particular, do not flow like Newtonian fluids. Their flows exhibit instabilities at very low Reynolds numbers that are driven not by inertia, but rather by anisotropic elastic stresses. Further increase of the flow rate results in a chaotic flow, the so-called purely elastic turbulence. The mechanism of this new type of chaotic motion is poorly understood. In this talk I will discuss our recent attempts to generalise the Newtonian theory of the transition to turbulence to the purely elastic case. We identify the relevant coherent structures and construct a viscoelastic self-sustaining process that can organise flow dynamics close to the transition.   

Live

Polymer-induced drag reduction is bounded by an asymptotic limit of maximum drag reduction (MDR). For decades, researchers have presumed that MDR reflects the convergence to an ultimate flow state that is not further changed by polymers. Our simulation shows that, as drag reduction converges to its invariant limit, the underlying dynamics continues to evolve with no sign of convergence. The stage of asymptotic drag reduction is not represented by any single flow state, but encompasses states with varying dynamical patterns, all of which are partially sustained by polymer elasticity.   

Live

In transitional shear flows, transient turbulent local spots appear in the system with perturbation, and they decay or spread in a random fashion. Various patterns are formed by these transient turbulent spots before the flow becomes universally turbulent. For transitional pipe flow, a sequence of phases is observed experimentally as Reynolds number (Re) increases. Those phases are characterized by decaying local turbulent spots (puffs) for Re < 2040, splitting and propagating turbulent spots (puffs) for 2040 < Re < 2250, asymmetric expansion of turbulent regions (weak slugs) for 2250 < Re < 4500, and symmetric expansion of turbulent regions (strong slugs) for Re > 4500. An earlier stochastic model for puff decaying and splitting focused on the dynamics and fluctuations within a single puff and did not include stream-wise interactions arising through shear. Here, we extend the earlier model and include the neglected stream-wise interactions. Our extended model recapitulates the full phase diagram of the transition, including weak and strong slug behavior. The model is not restricted to one dimension and is extendable to other transitional shear flows. It can also be shown to reduce to excitable media dynamics in special cases.   

Live

Vortex interactions appear in many fluid systems, from the wake behind an airplane in flight to that of a ship moving through the water. This is because friction between a fluid and a solid boundary can generate vorticity in the fluid. A simple example is the vortex ring, yet even the interaction between two vortex rings can cause instabilities that break the symmetries of the flow. When two vortex rings of equal size collide head-on at moderate Reynolds number, the rings undergo an instability that brings the two vortex cores together at several points around the circumference of the rings. As the two vortex cores touch, there is an annihilation of the opposing vorticity from each ring which results in reconnection between the original two vortex rings. These reconnections have a complicated 3D structure that is difficult to measure experimentally, leading many studies to focus on numerical simulation. By scanning a laser sheet across the collision of two dyed vortex rings, we are able to reconstruct a tomographic 3D visualization of the vortex ring collision and reconnection as it occurs. This 3D visualization allows for comparison between the structure of reconnections in experiment and the predictions from numerical models.   

Live

When a straight vortex tube is endowed with core-size perturbations, the differential rotation along the tube leads to the tilting of vortex lines and formation of twist waves. The waves propagate and collide, resulting in a drastic expansion of the vortex core and the formation of an annular structure with high azimuthal vorticity, a process known as vortex bursting. In this talk we examine vortex bursting using numerical simulations on straight vortex tubes with initial perturbations. We investigate the early twist generation, the bursting intensity, and the late-time flow evolution including secondary bursting phenomena along the tube. Further, we analyze the effect of Reynolds number and initial perturbation amplitude on the flow evolution and discuss possible vortex bursting related instabilities in vortical structures beyond straight tubes.   

Live

The vortex behind a NACA0012 wing profile was experimentally studied in a towing tank at
University of Malaga. The wingtip includes a synthetic jet that acts as an active flow controller. The
efficiency of this synthetic jet was studied for a variety of frequencies and amplitudes for the case
of Reynolds number 40×10³. Particle Image Velocimetry was used to characterize the velocity
field at different distances behind the wing and, thus, the created wake. Furthermore, the results
were analyzed using Proper Orthogonal Decomposition, which helps to characterize the different
flow dynamics. The influence of the various jet configurations on the principal modes was also
explored.   

Live

Using triple (G, h, k_B), I construct Quantum Vortex Field Equation (QVFE) u_t=▽u▽(D(u)▽u) extended from u_t=▽u△u.
The exact solutions describe deformations of quantum gravity.
My object is giving an automorphism representation of CFT. The Hecke algebra models intertwining operators of unramified principal series of vortex growth or contract. I explain the role of spectral triple of Boltzmann-Planck irredicible group in the QVFE. These exact analytical solutions in a complex torus S¹ or spheres Sⁿ visually and precisely describe the dynamical behaviours of vertex core and vortex filament under gravity effect, including their period and maximum deformation of mass and velocity.
L discovers some important facts on quantum vortex, as the character distribution, push-forward, pull-back and simple flip confinite endomorphisms, as on light propagation periodity and ergodity as light speed is ν_c = 2n + √3 ∈ S¹. Another an interesting fact is on vortex core spin law: α¹=½√3 + ½i; α²=½+ ½√3i; α³ = i; α⁶ = -1; α⁹ = -i; α¹²= +1 = I_d .
The key results prove that:
1. Maximum light speed is not 3x10⁸m/s;
2. All are governed by Quantum Gravity and Boltzmann - Planck dual groupoid;
3. Boltzmann variety is topological form of cusp or vertex point; Planck variety is then of circle or smooth manifolds.   

Live

We show unequivocal evidence for formation of excimers in liquid He II created by ionizing radiation produced through neutron capture. Laser beams induced fluorescence of the excimers. The fluorescence was recorded by a camera at a rate of 55.6 Hz with the ability to determine the location of an event with an uncertainty of 5 microns. The technique enables measurement of turbulence around macroscopic size (liter+) objects or vortex matter in three dimensions under conditions of extreme Reynolds number. Using thermal counterflow techniques we explored excimer flow in cryogenic He.   

Live

We experimentally study a steady, localized blob of turbulence generated and sustained by the collision of multiple vortex rings. Through PIV and 3D PTV we examine the mass flux, distributions of kinetic energy and enstrophy, and turbulence statistics. Our measurements reveal that the blob consists of a turbulent core surrounded by comparatively quiescent fluid. The intensity and geometry of the turbulent blob can be controlled by altering properties of the injected coherent vortex loops. This system provides an ideal playground to investigate the generation and the decay of turbulence with controlled inputs of energy, enstrophy, and helicity.   

Live

The helicity of a laminar vortex ring is prescribed by its geometry in the forms of writhe and twist. In viscous fluids, helicity is not conserved, but nonetheless its evolution is naturally characterized by the geometry and topology of the vorticity field. By generating helical vortices using hydrofoils, we are able to measure their helicity and its evolution over a range of Reynolds numbers. Fully resolved DNS simulations with adaptive mesh refinement provide complementary insight. We present an analytic model for helicity evolution in vortex tubes with a natural geometric interpretation and compare its predictions to experiments and simulations.   

Live

Understanding the non-reacting flow field is crucial for optimizing burner design, stability and validation of numerical data. The Stereo Particle Image Velocimetry (SPIV) technique is used to observe the double swirl-stabilized burner 's non-reacting turbulent flow structure. Components of velocity such as axial, radial and tangential and turbulent parameters such as turbulent intensity and Reynolds stress are also obtained. The burner is configured with two swirlers such as inner and outer swirler and bluff body along with three annuli i.e inner, outer and co-flow. The swirl numbers (S) of inner and outer swirlers are 0.82 and 0.88 respectively and both are medium range swirlers. The effect of inner and outer bulk velocities on turbulent flow structures is presented, where the outer bulk velocity remained constant in the first three cases and the inner bulk velocity remained constant in the remaining three cases. It is observed that the velocity is axially dominant by an increase in inner bulk velocity where as increase in outer bulk velocity shows radial spread. The tubulent parameters also observed to be increased by increasing inner and outer bulk velocities.