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Register a new userEdge tracking in spatially developing boundary layer flows
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Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel shear flows with a linearly stable base flow, this concept is adapted here to the case of a spatially developing Blasius boundary layer. Longer time horizons fundamentally change the nature of the problem due to the loss of stability of the base flow due to Tollmien--Schlichting (TS) waves. We demonstrate, using a moving box technique, that efficient long-time tracking of edge trajectories is possible for the parameter range relevant to bypass transition, even if the asymptotic state itself remains out of reach. The flow along the edge trajectory features streak switching observed for the first time in the Blasius boundary layer. At long enough times, TS waves co-exist with the coherent structure characteristic of edge trajectories. In this situation we suggest a reinterpretation of the edge as a manifold dividing the state space between the two main types of boundary layer transition, i.e. bypass transition and classical transition.
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This fluid dynamics video submitted to the Gallery of Fluid motion shows a turbulent boundary layer developing under a 5 metre-long flat plate towed through water. A stationary imaging system provides a unique view of the developing boundary layer as it would form over the hull of a ship or fuselage of an aircraft. The towed plate permits visualisation of the zero-pressure-gradient turbulent boundary layer as it develops from the trip to a high Reynolds number state ($Re_tau approx 3000$). An evolving large-scale coherent structure will appear almost stationary in this frame of reference. The visualisations provide an unique view of the evolution of fundamental processes in the boundary layer (such as interfacial bulging, entrainment, vortical motions, etc.). In the more traditional laboratory frame of reference, in which fluid passes over a stationary body, it is difficult to observe the full evolution and lifetime of turbulent coherent structures. An equivalent experiment in a wind/water-tunnel would require a camera and laser that moves with the flow, effectively `chasing eddies as they advect downstream.
Subcritical transition to turbulence in spatially developing boundary layer flows can be triggered efficiently by finite amplitude perturbations. In this work, we employ adjoint-based optimization to identify optimal initial perturbations in the Blasius boundary layer, culminating in the computation of the subcritical transition critical energy threshold and the associated fully localized critical optimum in a spatially extended configuration, the so called minimal seed. By dynamically rescaling the variables with the local boundary layer thickness, we show that the identified edge trajectory approaches the same attracting phase space region as previously reported edge trajectories, and reaches the region more efficiently.
In this paper, we derive consistent shallow water equations for bi-layer flows of Newtonian fluids flowing down a ramp. We carry out a complete spectral analysis of steady flows in the low frequency regime and show the occurence of hydrodynamic instabilities, so called roll-waves, when steady flows are unstable.
Numerical analysis of a shear layer between a cool liquid n-decane hydrocarbon and a hot oxygen gas at supercritical pressures shows that a well-defined phase equilibrium can be established. Variable properties are considered with the product of density and viscosity in the gas phase showing a nearly constant result within the laminar flow region with no instabilities. Sufficiently thick diffusion layers form around the liquid-gas interface to support the case of continuum theory and phase equilibrium. While molecules are exchanged for both species at all pressures, net mass flux across the interface shifts as pressure is increased. Net vaporization occurs for low pressures while net condensation occurs at higher pressures. For a mixture of n-decane and oxygen, the transition occurs around 50 bar. The equilibrium values at the interface quickly reach their downstream asymptotes. For all cases, profiles of diffusing-advecting quantities collapse to a similar solution (i.e., function of one independent variable). Validity of the boundary layer approximation and similarity are shown in both phases for Reynolds numbers greater than 239 at 150 bar. Results for other pressures are also taken at high Reynolds numbers. Thereby, the validity of the boundary layer approximation and similarity are expected. However, at very high pressures, the similar one-dimensional profiles vary for different problem constraints.
In linearly stable shear flows at moderate Re, turbulence spontaneously decays despite the existence of a codimension-one manifold, termed the edge of chaos, which separates decaying perturbations from those triggering turbulence. We statistically analyse the decay in plane Couette flow, quantify the breaking of self-sustaining feedback loops and demonstrate the existence of a whole continuum of possible decay paths. Drawing parallels with low-dimensional models and monitoring the location of the edge relative to decaying trajectories we provide evidence, that the edge of chaos separates state space not globally. It is instead wrapped around the turbulence generating structures and not an independent dynamical structure but part of the chaotic saddle. Thereby, decaying trajectories need not cross the edge, but circumnavigate it while unwrapping from the turbulent saddle.
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