Characterising Momentum Flux Events in High Reynolds Number Turbulent Boundary Layers

Abstract

The momentum flux in a canonical turbulent boundary layer is known to have a time-series signature that is characterised by a highly intermittent variation, which includes very short periods of intense flux activity. Here, we study the variation in these flux signal characteristics across almost a decade of flow Reynolds number (Reτ) by analysing datasets acquired using miniature cross-wire probes with matched spatial resolution. The analysis is facilitated by conditionally sampling the signal based on the quadrant (Qi; i = 1–4) and magnitude of the flux, revealing fractional cumulative contribution from Q4 to increase at a much faster rate than from Q2 with Reτ. An episodic description of the flux signal is subsequently undertaken, which associates this rapid increase in Q4 contributions with the emergence of extreme and rare flux events with Reτ. The same dataset is also used to test Townsend’s hypothesis on the active and inactive components of the momentum flux, which are obtained for the first time by implementing a spectral linear stochastic estimation-based decomposition methodology. While the active component is found to be the dominant contributor to the mean momentum flux consistent with Townsend’s hypothesis, the inactive component is found to be small but non-zero, owing to the non-linear interactions associated with the modulation phenomenon. Finally, an episodic description of the active and inactive momentum flux signal is undertaken to highlight the starkly different time series characteristics of the two flux components. The inactive flux signal is found to comprise individual statistically significant events associated with all four quadrants, leading to a small net contribution to the total flux.

Momentum flux fluctuations in wall turbulence: a formula beyond the law of the wall

“…(3a), u < 0 with w > 0 is more important to uw < 0 than u > 0 with w < 0 at z/δ 0.01 so long as z lies in the constant-flux sublayer. [13][14][15][16][17][18][19] The results in Fig. 4 appear to confirm our formula of Eq.…”

“…They are meandering with lengths 20δ. 21,25 Although they might modulate uw over a scale ∝ δ, 6,17,36 such a modulation is not important at least to our modeling. From power laws τ −1/2 at τ 10z/U for the standard deviation and skewness of uw τ (Fig.…”

“…Actually, according to time-series analyses, fluctuations in the first quadrant u > 0 and w > 0 and the third quadrant u < 0 and w < 0 tend to have shorter durations than those in the other quadrants. [13][14][15][16][17] We use Eq. (3b) to smooth uw − uw over a timescale τ .…”

“…7(a), the fraction F N and the fractional contribution F uw are dependent only on the threshold h. For the above case h ≃ 2, while F N has decayed significantly, F uw is still close to unity. 13,[15][16][17][18] That is, fluctuations at h 2 are not important to the mean momentum flux uw . They have cancelled out one another.…”

“…(1c). Since the fluctuations of the momentum flux uw are crucial to our understanding of wall turbulence, 1,[11][12][13][14][15][16][17][18][19][20][21] we explore a formula beyond the law of the wall. The result is…”