arXiv subjects

Georgios Rigas

Publications and source records attributed to Georgios Rigas.

27 records · Page 2Linked to original sources

arXiv2021

Efficient global resolvent analysis via the one-way Navier-Stokes equations. Part 1. Forced response

Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more than one inhomogeneous spatial coordinate remains computationally expensive. In this two-part paper, we show how efficient and accurate approximations of resolvent modes can be obtained using a well-posed spatial marching method for flows that contain a slowly varying direction. In this first part of the paper, we derive a well-posed and convergent one-way equation describing the downstream-traveling waves supported by the linearized Navier-Stokes equations. Integrating these equations, which requires significantly less CPU and memory resources than a direct solution of the linearized Navier-Stokes equations, approximates the action of the resolvent operator on a forcing vector. This capability is leveraged in part 2 of the paper to compute approximate resolvent modes. The method is validated and demonstrated using the examples of a simple acoustics problem and a supersonic turbulent jet.

physics.flu-dyn↗

arXiv2021

An empirical mean-field model of symmetry-breaking in a turbulent wake

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 Stuart's 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.

physics.flu-dyn↗

arXiv2021

Nonlinear stochastic modeling with Langevin regression

Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative macroscopic behavior are known, it is often difficult to derive a stochastic model that is consistent with observations. This is especially true for systems such as turbulence where the perturbations do not behave like Gaussian white noise, introducing non-Markovian behavior to the dynamics. We address these challenges with a framework for identifying interpretable stochastic nonlinear dynamics from experimental data, using both forward and adjoint Fokker-Planck equations to enforce statistical consistency. If the form of the Langevin equation is unknown, a simple sparsifying procedure can provide an appropriate functional form. We demonstrate that this method can effectively learn stochastic models in two artificial examples: recovering a nonlinear Langevin equation forced by colored noise and approximating the second-order dynamics of a particle in a double-well potential with the corresponding first-order bifurcation normal form. Finally, we apply the proposed method to experimental measurements of a turbulent bluff body wake and show that the statistical behavior of the center of pressure can be described by the dynamics of the corresponding laminar flow driven by nonlinear state-dependent noise.

cond-mat.stat-mech↗

arXiv2021

Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets

Response modes computed via linear resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In this study, a data-driven approach is taken to quantitatively improve linear resolvent models by deducing an optimal eddy-viscosity field that maximizes the projection of the dominant resolvent mode to the energy-optimal coherent structure educed using spectral proper orthogonal decomposition (SPOD) of data from high-fidelity simulations. We use large-eddy simulation databases for round isothermal jets at subsonic, transonic, and supersonic conditions and show that the optimal eddy viscosity substantially improves the alignment between resolvent and SPOD modes, reaching over 90% alignment at those frequencies where the jet exhibits a low-rank response. We then consider a fixed model for the eddy viscosity and show that with the calibration of a single constant, the results are generally close to the optimal one. In particular, the use of a standard Reynolds-Averaged-Navier-Stokes (RANS) eddy-viscosity resolvent model, with a single coefficient, provides substantial agreement between SPOD and resolvent modes for three turbulent jets and across the most energetic wavenumbers and frequencies.

physics.flu-dyn↗

arXiv2020

Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin-Helmholtz, and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211-237) at low Strouhal number ($St$) and non-zero azimuthal wavenumbers ($m$). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes, and sensitivity analysis distinguishes the three mechanisms and the regions of frequency-wavenumber space where each dominates, finding lift-up to be dominant as $St/m \rightarrow 0$. Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core.

physics.flu-dyn↗

arXiv2020

Non-linear input/output analysis: application to boundary layer transition

We extend linear input/output (resolvent) analysis to take into account nonlinear triadic interactions by considering a finite number of harmonics in the frequency domain using the harmonic balance method. Forcing mechanisms that maximize the drag are calculated using a gradient-based ascent algorithm. By including nonlinearity in the analysis, the proposed frequency-domain framework identifies the worst-case disturbances for laminar-turbulent transition. We demonstrate the framework on a flat-plate boundary layer by considering three-dimensional spanwise-periodic perturbations triggered by a few optimal forcing modes of finite amplitude. Two types of volumetric forcing are considered, one corresponding to a single frequency/spanwise-wavenumber pair, and a multi-harmonic where a harmonic frequency and wavenumber are also added. Depending on the forcing strategy, we recover a range of transition scenarios associated with K-type and H-type mechanisms, including oblique and Tollmien-Schlichting waves, streaks and their breakdown. We show that nonlinearity plays a critical role in optimizing growth by combining and redistributing energy between the linear mechanisms and the higher perturbation harmonics. With a very limited range of frequencies and wavenumbers, the calculations appear to reach the early stages of the turbulent regime through the generation and breakdown of hairpin and quasi-streamwise staggered vortices.

physics.flu-dyn↗

arXiv2017

Spectral analysis of jet turbulence

Informed by LES data and resolvent analysis of the mean flow, we examine the structure of turbulence in jets in the subsonic, transonic, and supersonic regimes. Spectral (frequency-space) proper orthogonal decomposition is used to extract energy spectra and decompose the flow into energy-ranked coherent structures. The educed structures are generally well predicted by the resolvent analysis. Over a range of low frequencies and the first few azimuthal mode numbers, these jets exhibit a low-rank response characterized by Kelvin-Helmholtz (KH) type wavepackets associated with the annular shear layer up to the end of the potential core and that are excited by forcing in the very-near-nozzle shear layer. These modes too the have been experimentally observed before and predicted by quasi-parallel stability theory and other approximations--they comprise a considerable portion of the total turbulent energy. At still lower frequencies, particularly for the axisymmetric mode, and again at high frequencies for all azimuthal wavenumbers, the response is not low rank, but consists of a family of similarly amplified modes. These modes, which are primarily active downstream of the potential core, are associated with the Orr mechanism. They occur also as sub-dominant modes in the range of frequencies dominated by the KH response. Our global analysis helps tie together previous observations based on local spatial stability theory, and explains why quasi-parallel predictions were successful at some frequencies and azimuthal wavenumbers, but failed at others.

physics.flu-dyn↗

arXiv2017

Symmetry breaking in a 3D bluff-body wake

The dynamics of a three-dimensional axisymmetric bluff-body wake are examined at low Reynolds regimes where transitions take place through spatio-temporal symmetry breaking. A linear stability analysis is employed to identify the critical Reynolds number associated with symmetry breaking, and the associated eigenmodes, known as global modes. The analysis shows that the axisymmetric stable base flow breaks the rotational symmetry through a pitchfork $m=1$ bifurcation, in agreement with previously reported results for axisymmetric wakes. Above this threshold, the stable base flow is steady and three-dimensional with planar symmetry. A three-dimensional global stability analysis around the steady reflectionally symmetric base flow, assuming no homogeneous directions, predicts accurately the Hopf bifurcation threshold, which leads to asymmetric vortex shedding. DNS simulations validate the stability results and characterize the flow topology during the early chaotic regime.

physics.flu-dyn↗

arXiv2017

Toward a chaotic adjoint for LES

Adjoint-based sensitivity analysis methods are powerful tools for engineers who use flow simulations for design. However, the conventional adjoint method breaks down for scale-resolving simulations like large-eddy simulation (LES) or direct numerical simulation (DNS), which exhibit the chaotic dynamics inherent in turbulent flows. Sensitivity analysis based on least-squares shadowing (LSS) avoids the issues encountered by conventional methods, but has a high computational cost. The following report outlines a new, more computationally efficient formulation of LSS, non-intrusive LSS, and estimates its cost for several canonical flows using Lyapunov analysis.

physics.flu-dyn↗