Spectral stochastic estimation of high-Reynolds-number wall-bounded turbulence for a refined inner-outer interaction model

Abstract

For wall-bounded flows, the model of Marusic et al. [Science 329, 193 (2010)] allows one to predict the statistics of the streamwise fluctuating velocity in the inner region, from a measured input signal in the logarithmic region. Normally, a user-defined large-scale portion of the input forms the large-scale content in the prediction by scaling its amplitude, as well as temporally shifting the signal to account for the physical inclination of these scales. Incoherent smaller scales are then fused to the prediction via universally expressed fluctuations that are subject to an amplitude modulation. Here we present a refined version of the model using spectral linear stochastic estimation, which eliminates a user-defined scale separation of the input. Now, an empirically derived transfer kernel comprises an implicit filtering via a scale-dependent gain and phase; this kernel captures the coherent portion in the prediction. An additional refinement of the model embodies a relative shift between the stochastically estimated scales in the prediction and the modulation envelope of the universal small scales. Predictions over a three-decade span of Reynolds numbers, Re τ ∼ O(10 3) to O(10 6), highlight promising applications of the refined model to high-Reynolds-number flows, in which coherent scales become the primary contributor to the fluctuating energy.

Investigation of the flow inside an urban canopy immersed into an atmospheric boundary layer using laser Doppler anemometry

“…• linear interactions between the inertial layer and the roughness sublayer are evidenced in the low-frequency range with 2 max = 0.45 ; this coherence level, although significant, is lower than for smooth wall boundary layer flow (Baars et al 2016) where a maximum coherence level of 2 = 0.8 was observed between the viscous wall region and the logarithmic layer. However, it is worth noting that this maximum is reached at equivalent wavelength for both flows ( x = 40 ); • linear interactions are also evidenced between the canopy region and the roughness sublayer with 2 max ∈ [0.2;0.6] , depending on the depth inside the canopy; at given height, strong spatial heterogeneity is observed; the points in the upstream and side neighbourhood of the cubes have the highest level of coherence, indicating the contribution of the shear layers and wakes induced by the cubes to the turbulence in the roughness sublayer; in contrast, the lowest level of coherence is consistently observed in the downstream region of the cubes, which confirms the sheltering effect of the cubes; • a rather low level of coherence is obtained between the canopy and the inertial layer with 2 ≤ 0.3 for all points.…”

“…As suggested by Baars et al (2016), a cut-off frequency can be defined for short-time motions using a coherence threshold level min = 0.05 , for which linear interactions become negligible. For our urban boundary layer flow, it is of the order of f cut, ≈ 0.4U e ∕ , or conversely in wavenumber The coherence between the streamwise velocity inside the canopy and in the outer flow is now analyzed using the LDA measurements in the canopy and the HWA measurements in the roughness sublayer ( z = 1.5h ) and in the inertial sublayer ( z = 5h ) (Fig.…”

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

“…Kernel H is equal to the inputoutput cross-spectrum, divided by the input spectrum, and may be expressed in terms of a gain, |H(z; f )|, and phase, φ(z; f ). Intuitively, the gain is the scaling factor for each Fourier mode during a linear stochastic estimate of the output [39][40][41], whereas the scale-dependent phase accounts …”

“…Moving forward, the linear kernel may be used for a linear stochastic estimate of the TBL flow field [39,41,43], which aids in visualizing the large-scale streamwise velocity fluctuations that are …”

An input–output based analysis of convective velocity in turbulent channels

“…of Baars et al (2016) and figure 5(b) ofBaars et al (2017). Furthermore, the contours of two-dimensional spectral coherence of 0.1, 0.3, and 0.5 are shown to collapse when scaled with the wall-normal height of the structures; indicating the presence of self-similar structures, seefigure 4ofMadhusudanan et al (2019).Thus, y + ∼ λ + z with a constant of proportionality α between 0.55 and 0.43,Figure 10: The structures of height/width aspect ratio 1 with an inclination angle β in analogy withPerry & Chong (1982).…”