Internal Report

Edge states and transition to turbulence in boundary layers

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Taras Khapko Doctoral thesis 2016 Download 5.6 Mb
ISSN 0348-467X


The focus of this thesis is the numerical study of subcritical transition to turbulence in boundary-layer flows. For the most part, boundary layers with uniform suction are considered. Constant homogeneous suction counteracts the spatial growth of the boundary layer, rendering the flow parallel. This allows to access the asymptotic dynamics and enables research approaches which are not feasible in the context of spatially developing flows.
In the first part, the laminar–turbulent separatrix of the asymptotic suction boundary layer (ASBL) is investigated numerically by means of an edge-tracking algorithm. Consideration of extended domains allows for robust localisation of the attracting structures on the separatrix. In all considered set-ups, the obtained edge states experience recurrent dynamics, going through calm and bursting phases. During calm phases, most of the coherent structures decay, apart from the active core. This active core consists of a single low-speed streak which develops a sinuous instability leading to a breakdown of the whole structure and a burst in terms of energy. During these bursts new streaks are generated, with the structure growing in size again, and the active core is re-created with a shift in the spanwise direction. The edge states in ASBL and their dynamics show resemblance with the resulting state of edge tracking in spatially developing boundary layers. Moreover, the self-sustaining mechanism bears many similarities with the classical regeneration cycle of near-wall turbulence. The recurrent simple structure active during calm phases is compared to the nucleation of turbulence events in bypass transition originating from delocalised initial conditions. The implications on the understanding of the bypass-transition process and the edge state's role are discussed.
Based on this understanding, a model is constructed which predicts the position of the nucleation of turbulent spots during free-stream turbulence induced transition in spatially developing boundary-layer flow. This model is used together with a probabilistic cellular automaton (PCA), which captures the spatial spreading of the spots. The latter is developed based entirely on data from numerical simulations. The PCA supplied with the modelled nucleation rates is able to correctly reproduce the main statistical characteristics of the transition process.
The last part of the thesis is concerned with the spatio-temporal aspects of turbulent ASBL in extended numerical domains near the onset of sustained turbulence. Turbulence at the onset and events leading to laminarisation are studied by adiabatically decreasing the Reynolds number, starting from a fully turbulent state. The different behaviour observed in ASBL, i.e. absence of sustained laminar–turbulent patterns, which have been reported in other wall-bounded flows, is associated with different character of the large-scale flow. This hypothesis was tested by artificially preventing large-scale fluctuations above a certain wall-normal distance in ASBL. In addition, an accurate quantitative estimate for the lowest Reynolds number with sustained turbulence is obtained.