Estimating large-scale structures in wall turbulence using linear models

2018 ◽  
Vol 842 ◽  
pp. 146-162 ◽  
Author(s):  
Simon J. Illingworth ◽  
Jason P. Monty ◽  
Ivan Marusic
Keyword(s):  
Linear Model ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Linear Models ◽  
Systems Approach ◽  
Wall Turbulence ◽  
Linear Estimator ◽  
Small Scale ◽  
Spanwise Direction ◽  
Time Resolved

A dynamical systems approach is used to devise a linear estimation tool for channel flow at a friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}=1000$. The estimator uses time-resolved velocity measurements at a single wall-normal location to estimate the velocity field at other wall-normal locations (the data coming from direct numerical simulations). The estimation tool builds on the work of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) by using a Navier–Stokes-based linear model and treating any nonlinear terms as unknown forcings to an otherwise linear system. In this way nonlinearities are not ignored, but instead treated as an unknown model input. It is shown that, while the linear estimator qualitatively reproduces large-scale flow features, it tends to overpredict the amplitude of velocity fluctuations – particularly for structures that are long in the streamwise direction and thin in the spanwise direction. An alternative linear model is therefore formed in which a simple eddy viscosity is used to model the influence of the small-scale turbulent fluctuations on the large scales of interest. This modification improves the estimator performance significantly. Importantly, as well as improving the performance of the estimator, the linear model with eddy viscosity is also able to predict with reasonable accuracy the range of wavenumber pairs and the range of wall-normal heights over which the estimator will perform well.

scholarly journals Hybrid MARMA-NARX model for flow forecasting based on the large-scale climate signals, sea-surface temperatures, and rainfall

2018 ◽  
Vol 49 (6) ◽  
pp. 1788-1803 ◽  
Author(s):  
Mohammad Ebrahim Banihabib ◽  
Arezoo Ahmadian ◽  
Mohammad Valipour
Keyword(s):  
Linear Model ◽  
Hybrid Model ◽  
Large Scale ◽  
Linear Models ◽  
Moving Average ◽  
Effective Parameters ◽  
Forecasting Accuracy ◽  
Local Factor ◽  
Non Linear ◽  
Climate Signals

Abstract In this study, to reflect the effect of large-scale climate signals on runoff, these indices are accompanied with rainfall (the most effective local factor in runoff) as the inputs of the hybrid model. Where one-year in advance forecasting of reservoir inflows can provide data to have an optimal reservoir operation, reports show we still need more accurate models which include all effective parameters to have more forecasting accuracy than traditional linear models (ARMA and ARIMA). Thus, hybridization of models was employed for improving the accuracy of flow forecasting. Moreover, various forecasters including large-scale climate signals were tested to promote forecasting. This paper focuses on testing MARMA-NARX hybrid model to enhance the accuracy of monthly inflow forecasts. Since the inflow in different periods of the year has in linear and non-linear trends, the hybrid model is proposed as a means of combining linear model, monthly autoregressive moving average (MARMA), and non-linear model, nonlinear autoregressive model with exogenous (NARX) inputs to upgrade the accuracy of flow forecasting. The results of the study showed enhanced forecasting accuracy through using the hybrid model.

Turbulent spots in a channel: large-scale flow and self-sustainability

2013 ◽  
Vol 731 ◽  
Author(s):  
Grégoire Lemoult ◽  
Jean-Luc Aider ◽  
José Eduardo Wesfreid
Keyword(s):  
Large Scale ◽  
Large Time ◽  
Rectangular Channel ◽  
Small Scale ◽  
Turbulent Spot ◽  
Time Resolved ◽  
Image Velocimetry ◽  
Streamwise Streaks ◽  
Large Scale Flow ◽  
Scale Motion

AbstractUsing a large-time-resolved particle image velocimetry field of view, a developing turbulent spot is followed in space and time in a rectangular channel flow for more than 100 advective time units. We show that the flow can be decomposed into a large-scale motion consisting of an asymmetric quadrupole centred on the spot and a small-scale part consisting of streamwise streaks. From the temporal evolution of the energy of the streamwise and spanwise velocity perturbations, it is suggested that a self-sustaining process can occur in a turbulent spot above a given Reynolds number.

scholarly journals Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160077 ◽  
Author(s):  
W. J. Baars ◽  
N. Hutchins ◽  
I. Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Wall Turbulence ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Scale Interaction ◽  
High Reynolds ◽  
Near Wall

Small-scale velocity fluctuations in turbulent boundary layers are often coupled with the larger-scale motions. Studying the nature and extent of this scale interaction allows for a statistically representative description of the small scales over a time scale of the larger, coherent scales. In this study, we consider temporal data from hot-wire anemometry at Reynolds numbers ranging from Re τ ≈2800 to 22 800, in order to reveal how the scale interaction varies with Reynolds number. Large-scale conditional views of the representative amplitude and frequency of the small-scale turbulence, relative to the large-scale features, complement the existing consensus on large-scale modulation of the small-scale dynamics in the near-wall region. Modulation is a type of scale interaction, where the amplitude of the small-scale fluctuations is continuously proportional to the near-wall footprint of the large-scale velocity fluctuations. Aside from this amplitude modulation phenomenon, we reveal the influence of the large-scale motions on the characteristic frequency of the small scales, known as frequency modulation. From the wall-normal trends in the conditional averages of the small-scale properties, it is revealed how the near-wall modulation transitions to an intermittent-type scale arrangement in the log-region. On average, the amplitude of the small-scale velocity fluctuations only deviates from its mean value in a confined temporal domain, the duration of which is fixed in terms of the local Taylor time scale. These concentrated temporal regions are centred on the internal shear layers of the large-scale uniform momentum zones, which exhibit regions of positive and negative streamwise velocity fluctuations. With an increasing scale separation at high Reynolds numbers, this interaction pattern encompasses the features found in studies on internal shear layers and concentrated vorticity fluctuations in high-Reynolds-number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

scholarly journals An adaptive two-stage analog/regression model for probabilistic prediction of small-scale precipitation in France

2018 ◽  
Vol 22 (1) ◽  
pp. 265-286 ◽  
Author(s):  
Jérémy Chardon ◽  
Benoit Hingray ◽  
Anne-Catherine Favre
Keyword(s):  
Regression Model ◽  
Large Scale ◽  
Linear Models ◽  
Transfer Functions ◽  
Small Scale ◽  
Probabilistic Prediction ◽  
Two Stage ◽  
Precipitation Occurrence ◽  
Seasonal Stratification ◽  
Local Weather

Abstract. Statistical downscaling models (SDMs) are often used to produce local weather scenarios from large-scale atmospheric information. SDMs include transfer functions which are based on a statistical link identified from observations between local weather and a set of large-scale predictors. As physical processes driving surface weather vary in time, the most relevant predictors and the regression link are likely to vary in time too. This is well known for precipitation for instance and the link is thus often estimated after some seasonal stratification of the data. In this study, we present a two-stage analog/regression model where the regression link is estimated from atmospheric analogs of the current prediction day. Atmospheric analogs are identified from fields of geopotential heights at 1000 and 500 hPa. For the regression stage, two generalized linear models are further used to model the probability of precipitation occurrence and the distribution of non-zero precipitation amounts, respectively. The two-stage model is evaluated for the probabilistic prediction of small-scale precipitation over France. It noticeably improves the skill of the prediction for both precipitation occurrence and amount. As the analog days vary from one prediction day to another, the atmospheric predictors selected in the regression stage and the value of the corresponding regression coefficients can vary from one prediction day to another. The model allows thus for a day-to-day adaptive and tailored downscaling. It can also reveal specific predictors for peculiar and non-frequent weather configurations.

scholarly journals Time evolution of uniform momentum zones in a turbulent boundary layer

2018 ◽  
Vol 842 ◽  
pp. 554-590 ◽  
Author(s):  
A. Laskari ◽  
R. de Kat ◽  
R. J. Hearst ◽  
B. Ganapathisubramani
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Small Scale ◽  
Residence Times ◽  
Time Resolved ◽  
Image Velocimetry ◽  
Measurement Plane ◽  
Very High ◽  
Flow States

Time-resolved planar particle image velocimetry was used to analyse the structuring of a turbulent boundary layer into uniform momentum zones (UMZs). The instantaneous peak-detection method employed by Adrian et al. (J. Fluid Mech., vol. 422, 2000, pp. 1–54) and de Silva et al. (J. Fluid Mech., vol. 786, 2016, pp. 309–331) is extended to account for temporal coherence of UMZs. The resulting number of zones detected appears to follow a normal distribution at any given instant. However, the extreme cases in which the number of zones is either very high or very low, are shown to be linked with two distinct flow states. A higher than average number of zones is associated with a large-scale $Q2$ event in the log region which creates increased small-scale activity within that region. Conversely, a low number of zones corresponds to a large-scale $Q4$ event in the log region and decreased turbulent activity away from the wall. The residence times, within the measurement plane, of zones belonging to the latter scenario are shown to be on average four times larger than those of zones present during higher than average zone structuring states. For both cases, greater residence times are observed for zones of higher momentum that are generally closer to the free stream.

scholarly journals Testing pseudo-linear models of responses to natural scenes in primate retina

2016 ◽  
Author(s):  
Alexander Heitman ◽  
Nora Brackbill ◽  
Martin Greschner ◽  
Alexander Sher ◽  
Alan M. Litke ◽  
...  
Keyword(s):  
Linear Model ◽  
Visual Processing ◽  
Large Scale ◽  
Linear Models ◽  
Ganglion Cells ◽  
Visual Stimuli ◽  
Natural Scenes ◽  
Natural Environments ◽  
Linear Filtering ◽  
Fixational Eye Movements

A central goal of systems neuroscience is to develop accurate quantitative models of how neural circuits process information. Prevalent models of light response in retinal ganglion cells (RGCs) usually begin with linear filtering over space and time, which reduces the high-dimensional visual stimulus to a simpler and more tractable scalar function of time that in turn determines the model output. Although these pseudo-linear models can accurately replicate RGC responses to stochastic stimuli, it is unclear whether the strong linearity assumption captures the function of the retina in the natural environment. This paper tests how accurately one pseudo-linear model, the generalized linear model (GLM), explains the responses of primate RGCs to naturalistic visual stimuli. Light responses from macaque RGCs were obtained using large-scale multi-electrode recordings, and two major cell types, ON and OFF parasol, were examined. Visual stimuli consisted of images of natural environments with simulated saccadic and fixational eye movements. The GLM accurately reproduced RGC responses to white noise stimuli, as observed previously, but did not generalize to predict RGC responses to naturalistic stimuli. It also failed to capture RGC responses when fitted and tested with naturalistic stimuli alone. Fitted scalar nonlinearities before and after the linear filtering stage were insufficient to correct the failures. These findings suggest that retinal signaling under natural conditions cannot be captured by models that begin with linear filtering, and emphasize the importance of additional spatial nonlinearities, gain control, and/or peripheral effects in the first stage of visual processing.

scholarly journals Large-scale influences in near-wall turbulence

2007 ◽  
Vol 365 (1852) ◽  
pp. 647-664 ◽  
Author(s):  
Nicholas Hutchins ◽  
Ivan Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Wall Turbulence ◽  
Small Scale ◽  
Scale Separation ◽  
Large Scale Motion ◽  
High Reynolds ◽  
Scale Motion ◽  
Near Wall Turbulence ◽  
Near Wall

Hot-wire data acquired in a high Reynolds number facility are used to illustrate the need for adequate scale separation when considering the coherent structure in wall-bounded turbulence. It is found that a large-scale motion in the log region becomes increasingly comparable in energy to the near-wall cycle as the Reynolds number increases. Through decomposition of fluctuating velocity signals, it is shown that this large-scale motion has a distinct modulating influence on the small-scale energy (akin to amplitude modulation). Reassessment of DNS data, in light of these results, shows similar trends, with the rate and intensity of production due to the near-wall cycle subject to a modulating influence from the largest-scale motions.

Wall turbulence manipulation by large-scale streamwise vortices

2002 ◽  
Vol 473 ◽  
pp. 23-58 ◽  
Author(s):  
GAETANO IUSO ◽  
MICHELE ONORATO ◽  
PIER GIORGIO SPAZZINI ◽  
GAETANO MARIA DI CICCA
Keyword(s):  
Large Scale ◽  
Time Derivative ◽  
Vortex Generator ◽  
Turbulent Channel Flow ◽  
Wall Turbulence ◽  
Spanwise Direction ◽  
Streamwise Vortices ◽  
Turbulent Structures ◽  
Reduced Frequency ◽  
Flow Manipulation

This paper describes an experimental study of the manipulation of a fully developed turbulent channel flow through large-scale streamwise vortices originated by vortex generator jets distributed along the wall in the spanwise direction. Apart from the interest in flow management itself, an important aim of the research is to observe the response of the flow to external perturbations as a technique for investigating the structure of turbulence. Considerable mean and fluctuating skin friction reductions, locally as high as 30% and 50% respectively, were measured for an optimal forcing flow intensity. Mean and fluctuating velocity profiles are also greatly modified by the manipulating large-scale vortices; in particular, attenuation of the turbulence intensity was measured. Moreover the flow manipulation caused an increase in longitudinal coherence of the wall organized motions, accompanied by a reduced frequency of burst events, demonstrated by a reduction of the velocity time derivative PDFs and by an higher intermittency. A strong transversal periodic organization of the flow field was observed, including some typical behaviours in each of the periodic boxes originated by the interaction of the vortex pairs. Results are interpreted and discussed in terms of management of the near-wall turbulent structures and with reference to the wall turbulence regeneration mechanisms suggested in the literature.

Investigation of Combustion Oscillations of Premixed Dump Combustor Using Time-Resolved Particle Image Velocimetry

2014 ◽  
Author(s):  
Ramgopal Sampath ◽  
Vikram Ramanan ◽  
S. R. Chakravarthy
Keyword(s):  
Heat Release ◽  
Shear Layer ◽  
Large Scale ◽  
Velocity Fields ◽  
Small Scale ◽  
Pressure Amplitude ◽  
Time Resolved ◽  
Dump Combustor ◽  
Large Scale Vortex ◽  
Chemiluminescent Intensity

The present work deals with time-resolved investigation of the flow field during acoustic self-excitation by a lean premixed flame in a dump combustor with varying equivalence ratio at a constant air flow rate. Simultaneous measurements of pressure fluctuations, velocity fields using Time resolved Particle imaging velocimetry (TR-PIV) and CH* chemiluminescence were performed. The pressure, velocity and chemiluminescent intensity time traces were Fourier transformed to estimate the frequency and amplitudes. Conditions of maximum pressure amplitude correspond to the prevalence of intermittent bursts in pressure, velocity, and chemiluminescent intensity. Further, Proper orthogonal decomposition (POD) is applied to the chemiluminescent intensity and velocity fields. The POD mode shapes are able to capture the modes pertaining to both the acoustic and vortex mode of flame/flow oscillations. The burst oscillations are understood by examining the sequence of time-resolved velocity and chemiluminescent intensity during their growth and decay regimes. The growth of oscillations is promoted by the flame heat release fluctuations following the pattern of the large-scale vortex roll-up in the recirculation zone downstream of the dump plane, causing a tendency of acoustic excitation at the vortex mode. As the amplitude rises, the natural acoustic mode of the duct is simultaneously amplified, leading to small-scale vortices shed from the step corner at the acoustic time scale. These small-scale vortices adversely interact with the large-scale vortex controlling the heat release, resulting in its weakening and hence the decay of oscillations. This behavior was further observed in the spatially averaged vorticity along the shear layer. In addition to this, the time traces of the pressure and the velocity fluctuations at the shear layer and located half step height from the separation point were overlapped. The overlapped time traces showed a drift in the instantaneous phase during which the growth and decay of the oscillations were observed.

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