Transitions in large eddy simulation of box turbulence

One promising decomposition of turbulent dynamics is that into building blocks such as equilibrium and periodic solutions and orbits connecting these. While the numerical approximation of such building blocks is feasible for flows in small domains and at low Reynolds numbers, computations in developed turbulence are currently out of reach because of the large number of degrees of freedom necessary to represent Navier-Stokes flow on all relevant spatial scales. We mitigate this problem by applying large eddy simulation (LES), which aims to model, rather than resolve, motion on scales below the filter length, which is fixed by a model parameter. By considering a periodic spatial domain, we avoid complications that arise in LES modelling in the presence of boundary layers. We consider the motion of an LES fluid subject to a constant body force of the Taylor-Green type as the separation between the forcing length scale and the filter length is increased. In particular, we discuss the transition from laminar to weakly turbulent motion, regulated by simple invariant solution, on a grid of $32^3$ points

A homoclinic tangle on the edge of shear turbulence

Experiments and simulations lend mounting evidence for the edge state hypothesis on subcritical transition to turbulence, which asserts that simple states of fluid motion mediate between laminar and turbulent shear flow as their stable manifolds separate the two in state space. In this Letter we describe a flow homoclinic to a time-periodic edge state. Its existence explains turbulent bursting through the classical Smale-Birkhoff theorem. During a burst, vortical structures and the associated energy dissipation are highly localized near the wall, in contrast to the familiar regeneration cycle

Splitting of a turbulent puff in pipe flow

International audienceThe transition to turbulence of the flow in a pipe of constant radius is numerically studied over a range of Reynolds numbers where turbulence begins to expand by puff splitting. We first focus on the case Re = 2300 where splitting occurs as discrete events. Around this value only long-lived pseudo-equilibrium puffs can be observed in practice, as typical splitting times become very long. When Re is further increased, the flow enters a more continuous puff splitting regime where turbulence spreads faster. Puff splitting presents itself as a two-step stochastic process. A splitting puff first emits a chaotic pseudopod made of azimuthally localized streaky structures at the downstream (leading) laminar-turbulent interface. This structure can later expand azimuthally as it detaches from the parent puff. Detachment results from a collapse of turbulence over the whole cross-section of the pipe. Once the process is achieved a new puff is born ahead. Large-deviation consequences of elementary stochastic processes at the scale of the streak are invoked to explain the statistical nature of splitting and the Poisson-like distributions of splitting times reported by Avila, Moxey, de Lozar, Avila, Barkley and Hof (2011 Science 333 192–196)

Wrap, tilt and stretch of vorticity lines around a strong thin straight vortex tube in a simple shear flow

the mechanism of wrap, tilt and stretch of vorticity lines around a strong thin straight vortex tube of circulation &#915; starting with a vortex filament in a simple shear flow (U=SX2x^1, S being a shear rate) is investigated analytically. an asymptotic expression for the vorticity field is obtained at a large reynolds number &#915;/&#957; » 1, &#957; being the kinematic viscosity of fluid, and during the initial time St « 1 of evolution as well as St « (&#915;/&#957;)1/2. the vortex tube, which is inclined from the streamwise (X1) direction both in the vertical (X2) and spanwise (X3) directions, is tilted, stretched and diffused under the action of the uniform shear and viscosity. the simple shear vorticity is on the other hand, wrapped and stretched around the vortex tube by a swirling motion, induced by it to form double spiral vortex layers of high azimuthal vorticity of alternating sign. the magnitude of the azimuthal vorticity increases up to O((&#915;/&#957;)1/3S) at distance r=O((&#915;/&#957;)1/3 (&#957;t)1/2) from the vortex tube. the spirals induce axial flows of the same spiral shape with alternate sign in adjacent spirals which in turn tilt the simple shear vorticity toward the axial direction. as a result, the vorticity lines wind helically around the vortex tube accompanied by conversion of vorticity of the simple shear to the axial direction. the axial vorticity increases in time as s2t, the direction of which is opposite to that of the vortex tube at r=O((&#915;/&#957;)1/2 (&#957;t)1/2) where the vorticity magnitude is strongest. in the near region r « (&#915;/&#957;)1/3 (&#957;t)1/2, on the other hand, a viscous cancellation takes place in tightly wrapped vorticity of alternate sign, which leads to the disappearance of the vorticity normal to the vortex tube. only the axial component of the simple shear vorticity is left there, which is stretched by the simple shear flow itself. as a consequence, the vortex tube inclined toward the direction of the simple shear vorticity (a cyclonic vortex) is intensified, while the one oriented in the opposite direction (an anticyclonic vortex) is weakened. the growth rate of vorticity due to this effect attains a maximum (or minimum) value of ±S2/33/2 when the vortex tube is oriented in the direction of X^1+X^2[minus-or-plus sign] X^3. the present asymptotic solutions are expected to be closely related to the flow structures around intense vortex tubes observed in various kinds of turbulence such as helical winding of vorticity lines around a vortex tube, the dominance of cyclonic vortex tubes, the appearance of opposite-signed vorticity around streamwise vortices and a zig-zag arrangement of streamwise vortices in homogeneous isotropic turbulence, homogeneous shear turbulence and near-wall turbulence.</p

Travelling-waves consistent with turbulence-driven secondary flow in a square duct

We present numerically determined travelling-wave solutions for pressure-driven flow through a straight duct with a square cross-section. This family of solutions represents typical coherent structures (a staggered array of counter-rotating streamwise vortices and an associated low-speed streak) on each wall. Their streamwise average flow in the cross-sectional plane corresponds to an eight vortex pattern much alike the secondary flow found in the turbulent regime