Romain Mathis

Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers

© 2009 Cambridge University Press. Online edition of the journal is available at http://journals.cambridge.org/action/displayJournal?jid=FLM

Predictive Model for Wall-Bounded Turbulent Flow

Elucidating Turbulent Flow When needing to mix two fluids rapidly, turbulent flow can be beneficial. However, in most cases, the churning and tumbling motions of a fluid during turbulent flow reduce the efficiency of a device or process. When fluid flows past a solid object, the bulk of the turbulent motion is concentrated at the surface boundary, but it is unclear to what extent these inner motions are influenced by flow far from the boundary. Marusic et al. (p. 193; see the Perspective by Adrian) demonstrate a nonlinear connection between inner-layer motions and the large-scale outer-layer motions in wind tunnel experiments. A simple model was able to describe the relationship mathematically while accurately mapping the experimental data. A nonlinear relationship is developed for turbulent flow past an object. The behavior of turbulent fluid motion, particularly in the thin chaotic fluid layers immediately adjacent to solid boundaries, can be difficult to understand or predict. These layers account for up to 50% of the aerodynamic drag on modern airliners and occupy the first 100 meters or so of the atmosphere, thus governing wider meteorological phenomena. The physics of these layers is such that the most important processes occur very close to the solid boundary—the region where accurate measurements and simulations are most challenging. We propose a mathematical model to predict the near-wall turbulence given only large-scale information from the outer boundary layer region. This predictive capability may enable new strategies for the control of turbulence and may provide a basis for improved engineering and weather prediction simulations.

Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows

Recent investigations by Monty et al. [J. Fluid Mech. 632, 431 (2009)] showed that important modal differences exist between channels/pipes and boundary layers, mainly in the largest energetic scales. In addition, Mathis et al. [J. Fluid Mech. 628, 311 (2009)] recently reported and quantified a nonlinear scale interaction in zero-pressure gradient turbulent boundary layers, whereby the large-scale motion amplitude modulates the small-scale motions. In this study, a comparison of this modulation effect of the streamwise velocity component is undertaken for all three flows for matched Reynolds number and measurement conditions. Despite the different large-scale phenomena in these internal and external wall-bounded flows, the results show that their amplitude modulation influence remains invariant in the inner region with some differences appearing in the outer region.

The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers

A defining feature of the inner-outer interactions in wall-bounded turbulent flows is the imprint of the outer large-scale motions on the inner small scale. Recently, Mathis et al. [“Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers,” J. Fluid Mech. 628, 311 (2009)] quantified this imprint by applying the Hilbert transform to small-scale components of the fluctuating streamwise velocity, u. They found that the wall-normal profile of the amplitude modulation between the large scale and the envelope of the small scale exhibits strong resemblance to the skewness profile of u. In this study, we assess this apparent relationship and show that the Reynolds number trend in the skewness profile of u is strongly related to the amplitude modulation effect of the small scales by the large. This observation also leads to an alternative diagnostic for the amplitude modulation effect, which is one component of the skewness factor based on a scale decomposition.

Inner-layer intensities for the flat-plate turbulent boundary layer combining a predictive wall-model with large-eddy simulations

Time series velocity signals obtained from large-eddy simulations (LES) within the logarithmic region of the zero-pressure gradient turbulent boundary layer over a smooth wall are used in combination with an empirical, predictive inner-outer wall model [I. Marusic, R. Mathis, and N. Hutchins, “Predictive model for wall-bounded turbulent flow,” Science 329, 193 (2010)10.1126/science.1188765] to calculate the statistics of the fluctuating streamwise velocity in the inner region. Results, including spectra and moments up to fourth order, are compared with equivalent predictions using experimental time series, as well as with direct experimental measurements at Reynolds numbers Re_τ = 7300, 13 600, and 19 000. The LES combined with the wall model are then used to extend the inner-layer predictions to Reynolds numbers Reτ = 62 000, 100 000, and 200 000 that lie within a gap in log (Re_τ) space between laboratory measurements and surface-layer, atmospheric experiments. The present results support a loglike increase in the near-wall peak of the streamwise turbulence intensities with Re_τ and also provide a means of extending LES results at large Reynolds numbers to the near-wall region of wall-bounded turbulent flows.

A wall-shear stress predictive model

Following the approach of Marusic et al. (2010b), here we develop a predictive model for the fluctuating wall-shear stress, where the only required input is large-scale information of the streamwise velocity at a location in the outer, logarithmic region of the flow. The model consists of two components, incorporating a superposition and modulation effect of outer region motions that interact with the flow field in the viscous sublayer. The model is seen to capture Reynolds number trends reliably.

Modeling bed shear-stress fluctuations in a shallow tidal channel

Recently, Mathis et al. (2013) developed a model for predicting the instantaneous fluctuations of the wall shear-stress in turbulent boundary layers. This model is based on an inner-outer scale interaction mechanism, incorporating superposition, and amplitude-modulation effects, and the only input required for the model is a time series measurement of the streamwise velocity signal taken in the logarithmic region of the flow. The present study applies this new approach for the first time to environmental flows, for which the near-bed information is typically inaccessible. The data used here are acoustic Doppler velocimeter time series measurements from a shallow tidal channel (Suisun Slough in North San Francisco Bay). We first extract segments of data sharing properties with canonical turbulent boundary layers. The wall (bed) shear-stress model is then applied to these selected data. Statistical and spectral analysis demonstrates that the field data predictions are consistent with laboratory and DNS results. The model is also applied to the whole available data set to demonstrate, even for situations far from the canonical boundary layer case, its ability to preserve the overall Reynolds number trend. The predicted instantaneous bed stress is highly skewed and amplitude modulated with the variations in the large-scale streamwise velocity. Finally, the model is compared to conventional methods employed to predict the bed shear-stress. A large disparity is observed, but the present model is the only one able to predict both the correct spectral content and the probability density function.

Reynolds Number Dependence of the Amplitude Modulated Near-Wall Cycle

The interaction in turbulent boundary layers between very large scale motions centred nominally in the log region (termed superstructures) and the small scale motions is investigated across the boundary layer. This analysis is performed using tools based on Hilbert transforms. The results, across a large Reynolds number range, show that in addition to the large-scale log region structures superimposing a footprint (or mean shift) on to the near-wall fluctuations, the small-scale structures are also subject to a high degree of amplitude modulation due to the large structures. The amplitude modulation effect is seen to become progressively stronger as the Reynolds number increases.

Reconstruction of wall shear-stress fluctuations in a shallow tidal river

In this paper, we investigate the applicability of the predictive wall shear-stress model, recently developed by Mathis et al. J. Fluid Mech. 715, 163–180, 2013, [17], to environmental flows where near-wall information is typically inaccessible. This wall-model, which embeds the scale interaction mechanisms of superposition and modulation, is able to reconstruct the instantaneous wall (bed) shear-stress fluctuations in turbulent boundary layers. The database considered here comes from field measurements using acoustic Doppler velocimeters carried out in a shallow tidal channel (Suisun Slough in North San Francisco Bay). The model is first applied to a selected subset of data sharing common properties with the canonical turbulent boundary layer. Statistics and energy content of these predictions are found to be consistent with laboratory predictions and DNS results. The model is then used on the whole dataset, whose some of them having properties far from the canonical case. Even for these situations, the model is able to preserve the overall Reynolds trend. This study shows the great capability of the model for environmental applications, which is the only one able to predict both the correct energetic content and probability density function.