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This work develops a low-dimensional nonlinear stochastic model of symmetry-breaking coherent structures from experimental measurements of a turbulent axisymmetric bluff body wake. Traditional model reduction methods decompose the field into a set of modes with fixed spatial support but time-varying amplitudes. However, this fixed basis cannot resolve the mean flow deformation due to variable Reynolds stresses, a central feature of Stuarts nonlinear stability mechanism, without the further assumption of weakly nonlinear interactions. Here, we introduce a parametric modal basis that depends on the instantaneous value of the unsteady aerodynamic center of pressure, which quantifies the degree to which the rotational symmetry of the wake is broken. Thus, the modes naturally interpolate between the unstable symmetric state and the nonlinear equilibrium. We estimate the modes from experimental measurements of the base pressure distribution by reducing the symmetry via phase alignment and averaging conditioned on the center of pressure. The amplitude dependence of the symmetric mode deviates significantly from the polynomial scaling predicted by weakly nonlinear analysis, confirming that the parametric basis is crucial for capturing the effect of strongly nonlinear interactions. We also introduce a second model term capturing axisymmetric fluctuations associated with the mean-field deformation. We then apply the Langevin regression system identification method to construct a stochastically forced nonlinear model for these two generalized mode coefficients. The resulting model reproduces empirical power spectra and probability distributions, suggesting a path towards developing interpretable low-dimensional models of globally unstable turbulent flows from experimental measurements.
A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on a combined effect of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A couple
We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral $tau$-approach. We find that compressibility decreases the $alpha$ effect a
Compressibility effects in a turbulent transport of temperature field are investigated applying the quasi-linear approach for small Peclet numbers and the spectral $tau$ approach for large Peclet numbers. Compressibility of a fluid flow reduces the t
With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose a new discretization scheme for the biharmonic term (the 4th-order derivative term) of the Cahn-Hilliard equation. This novel sc
Hilbert-Huang transform is a method that has been introduced recently to decompose nonlinear, nonstationary time series into a sum of different modes, each one having a characteristic frequency. Here we show the first successful application of this a