Abstract
A modelling methodology to reproduce the experimental measurements of a turbulent flow in the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries that occur in the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.
Highlights
Turbulent flows are ubiquitous in natural phenomena and engineering applications (Pope 2000), and a mathematically tractable description of them is desirable for their prediction and control
In this paper we show that the dynamics of the turbulent wake can be approximated by a simple nonlinear Langevin equation, the deterministic part of which accounts for the broken symmetries that occur in the laminar and transitional regimes and the stochastic part of which accounts for the turbulent fluctuations
In this paper we have shown that this behaviour can be captured by a simple nonlinear model consisting of two coupled stochastic differential equations
Summary
Turbulent flows are ubiquitous in natural phenomena and engineering applications (Pope 2000), and a mathematically tractable description of them is desirable for their prediction and control. The threshold of instability (α > 0), (1.1) is associated with symmetry breaking since the steady-state solutions are not invariant under the x → −x symmetry This model can be directly obtained from the Navier–Stokes equations through a weakly nonlinear expansion around the critical bifurcating point (Meliga et al 2009) and has been used extensively for the description of laminar flows undergoing supercritical bifurcations (Drazin & Reid 2004). It was recently shown that the steady bifurcated state (responsible for the loss of rotational symmetry) and the unsteady bifurcated state (responsible for the vortex shedding) persist at high Reynolds numbers and fully turbulent regimes (Grandemange, Gohlke & Cadot 2014; Rigas et al 2014). Hereafter we demonstrate our modelling approach considering the dynamics associated with the first steady bifurcation given by (1.1)
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