This paper develops a spatial input-output approach to investigate the dynamics of a turbulent boundary layer subject to a localized single frequency excitation. This method uses one-way spatial integration to reformulate the problem in terms of spatial evolution equations. The technique is used to examine the effect of localized periodic actuation at a given temporal frequency, based on an experimental set-up in which an active large-scale is introduced into the outer layer of a turbulent boundary layer. First, the large-scale structures associated with the phase-locked modal velocity field obtained from spatial input-output analysis are shown to closely match those computed based on hot-wire measurements. The approach is then used to further investigate the response of the boundary layer to the synthetically generated large-scale. A quadrant trajectory analysis indicates that the spatial input-output response produces shear stress distributions consistent with those in canonical wall-bounded turbulent flows in terms of both the order and types of events observed. The expected correspondence between the dominance of different quadrant behavior and actuation frequency is also observed. These results highlight the promise of a spatial input-output framework for analyzing the formation and streamwise evolution of structures in actuated wall-bounded turbulent flows.
This work extends the input-output approach to the study of wall-bounded shear flows manipulated using actuators common in experimental flow control studies. In particular, we adapt this powerful analytical framework to investigate the flow response to specified geometric actuation patterns (e.g., different plasma actuators) that can be applied over a range of different temporal input signals. For example, the commonly studied steady-state (time-averaged) flow response corresponds to a superposition of step responses in our modeling framework. The approach takes advantage of the linearity of t…
This paper employs an input-output based approach to analyze convective velocities and the transport of fluctuations in turbulent channel flows. The convective velocity for a fluctuating quantity associated with streamwise-spanwise wavelength pairs at each wall-normal location is obtained through the maximization of the power spectral density associated with the linearized Navier-Stokes equations with a turbulent mean profile and delta-correlated Gaussian forcing. We first demonstrate that the mean convective velocities computed in this manner agree well with those reported previously in the l…
This paper describes a robust linear time-invariant output-feedback control strategy to reduce turbulent fluctuations, and therefore skin-friction drag, in wall-bounded turbulent fluid flows, that nonetheless gives performance guarantees in the nonlinear turbulent regime. The novel strategy is effective in reducing the supply of available energy to feed the turbulent fluctuations, expressed as reducing a bound on the supply rate to a quadratic storage function. The nonlinearity present in the equations that govern the dynamics of the flow is known to be passive and can be considered as a feedb…
Stochastic linear modelling proposed in Tissot, Mémin & Cavalieri (J. Fluid Mech., vol. 912, 2021, A51) is based on classical conservation laws subject to a stochastic transport. Once linearised around the mean flow and expressed in the Fourier domain, the model has proven its efficiency to predict the structure of the streaks of streamwise velocity in turbulent channel flows. It has been in particular demonstrated that the stochastic transport by unresolved incoherent turbulence allows to better reproduce the streaks through lift-up mechanism. In the present paper, we focus on the study of st…
We examine amplifying behavior of small perturbations about Reynolds-averaged Navier-Stokes solutions (RANS) of a $M_j = 0.9$ subsonic turbulent jet using input-output (I/O) analysis. Singular value decomposition (SVD) of the resolvent of the linearized Navier-Stokes (LNS) equations forms an orthonormal set of I/O mode pairs, sorted in descending order by the magnitude of the corresponding singular values. In this study we design a filter to restrict input forcings to be active only in regions where turbulent kinetic energy (TKE) of jet turbulence is high. For an output domain, we directly imp…
The decomposition of hydrodynamic and acoustic components of cavity flows can aid the understanding of the flow-acoustic interaction, which produces a variety of adverse effects in applications. We apply the approach of combining the resolvent analysis and Doak's momentum potential theory to examine the input-output flow-acoustic characteristics of compressible flow over an open cavity at Re=10,000. The methodology can decompose hydrodynamic and acoustic components from an input-output framework. We further localize the forcing at the leading-edge and front wall of the cavity and filter with a…
We study the input-output response of a streamwise constant projection of the Navier-Stokes equations for plane Couette flow, the so-called 2D/3C model. Study of a streamwise constant model is motivated by numerical and experimental observations that suggest the prevalence and importance of streamwise and quasi-streamwise elongated structures. Periodic spanwise/wall-normal (z-y) plane stream functions are used as input to develop a forced 2D/3C streamwise velocity field that is qualitatively similar to a fully turbulent spatial field of DNS data. The input-output response associated with the 2…
The aim of this paper is to substantiate the importance of non-normality of shear flow linear operators and its consequence -- the non-modal dynamics of the perturbations -- in the formation of acoustic wave output of time-developing free shear/mixing layers. Initially, the linear transient dynamics of spatial Fourier harmonics is considered in a 3D homentropic parallel unbounded inviscid constant shear flow which can model the central/body part of the shear layer. The non-modal approach allows to capture the only linear mechanism of the acoustic wave generation -- \textit{the linear vortex-wa…
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 …
The mechanisms governing the low-frequency unsteadiness in the shock wave/turbulent boundary layer interaction at Mach 2 are considered. The investigation is conducted based on the numerical database issued from large-eddy simulations covering approximately 300 cycles of the low-frequency shock fluctuations. The evaluation of the spectrum in the interaction zone indicates that the broadband low-frequency unsteadiness is predominantly two-dimensional, and can be isolated via spanwise averaging. Empirically derived transfer functions are computed using the averaged flow field, and indicate the o…
Wind turbines operate in the atmospheric boundary layer, where they are exposed to the turbulent atmospheric flows. As the response time of wind turbine is typically in the range of seconds, they are affected by the small scale intermittent properties of the turbulent wind. Consequently, basic features which are known for small-scale homogeneous isotropic turbulence, and in particular the well-known intermittency problem, have an important impact on the wind energy conversion process. We report on basic research results concerning the small-scale intermittent properties of atmospheric flows an…
We present a new approach for constructing data-driven subgrid stress models for large eddy simulation of turbulent flows. The key to our approach is representation of model input and output tensors in the filtered strain rate eigenframe. Provided inputs and outputs are selected and non-dimensionalized in a suitable manner, this yields a model form that is symmetric, Galilean invariant, rotationally invariant, reflectionally invariant, and unit invariant. We use this model form to train a simple and efficient neural network model using only one time step of filtered direct numerical simulation…
We employ a recently introduced structured input-output analysis (SIOA) approach to analyze streamwise and spanwise wavelengths of flow structures in stably stratified plane Couette flow. In the low-Reynolds number ($Re$) low-bulk Richardson number ($Ri_b$) spatially intermittent regime, we demonstrate that SIOA predicts high amplification associated with wavelengths corresponding to the characteristic oblique turbulent bands in this regime. SIOA also identifies quasi-horizontal flow structures resembling the turbulent-laminar layers commonly observed in the high-$Re$ high-$Ri_b$ intermittent …
Transient growth and resolvent analyses are routinely used to assess non-asymptotic properties of fluid flows. In particular, resolvent analysis can be interpreted as a special case of viewing flow dynamics as an open system in which free-stream turbulence, surface roughness, and other irregularities provide sources of input forcing. We offer a comprehensive summary of the tools that can be employed to probe the dynamics of fluctuations around a laminar or turbulent base flow in the presence of such stochastic or deterministic input forcing and describe how input-output techniques enhance reso…
There exists a large body of previous work using reduced two-dimensional models of the SOL, which model fluctuations in the drift-plane but approximate parallel transport with effective loss terms. Full size three-dimensional simulations of SOL turbulence in experimental geometries are now possible, but are far more computationally expensive than 2D models. We therefore use a flux-tube geometry model of the scrape-off layer to compare the results of 2D simulations to 3D simulations with a similar setup, looking for systematic differences. Overall there is good agreement in the basic radial pro…
Target Parameterization in Diffusion Models for Nonlinear Spatiotemporal System Identification
Université Marie et Louis Pasteur, SUPMICROTECH, CNRS, institut FEMTO-ST（玛丽-路易·巴斯蒂安大学，SUPMICROTECH，法国国家科学研究中心，FEMTO-ST研究所）；LLF, CNRS, Université Paris Cité（LLF，法国国家科学研究中心，巴黎cité大学）
Input-output analysis of transitional channel flows has proven to be a valuable analytical tool for identifying important flow structures and energetic motions. The traditional approach abstracts the nonlinear terms as forcing that is unstructured, in the sense that this forcing is not directly tied to the underlying nonlinearity in the dynamics. This paper instead employs a structured singular value-based approach that preserves certain input-output properties of the nonlinear forcing function in an effort to recover the larger range of key flow features identified through nonlinear analysis,…
We adopt an input-output approach to analyze the effect of persistent white-in-time structured stochastic base flow perturbations on the mean-square properties of the linearized Navier-Stokes equations. Such base flow variations enter the linearized dynamics as multiplicative sources of uncertainty that can alter the stability of the linearized dynamics and their receptivity to exogenous excitations. Our approach does not rely on costly stochastic simulations or adjoint-based sensitivity analysis. We provide verifiable conditions for mean-square stability and study the frequency response of th…
