Estimating instantaneous surface momentum fluxes in boundary layers using a deep neural network

Abstract

Within turbulent boundary layers, the relationship between instantaneous surface momentum fluxes and streamwise velocities is more complicated than that between their ensemble averages described by the law of the wall. Although these fluxes need to be considered in large eddy simulations, the conventional approaches are not feasible. As an alternative, we have developed a deep neural network with the long short-term memory algorithmthat estimates instantaneous fluxes from a sequence of streamwise velocities. The velocities measured in a wind tunnel were used for training and validation. The trained deep neural network successfully estimates the instantaneous surface momentum flux with a suitable running average.

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

“…4(a) and (d), we observe convex distributions such that the momentum flux uw τ is enhanced negatively when the streamwise velocity U + u τ deviates from its average U . 11 Those of E(uw τ ) in Figs. 4(b) and (e) are similar.…”

“…For the constant-flux sublayer, instantaneous values of the velocity fluctuations u and w at a given distance z are known to scatter elliptically on the u-w plane with the major axis lying from the second quadrant u < 0 and w > 0 to the fourth quadrant u > 0 and w < 0. 1,[11][12][13] To model such fluctuations, we decompose the vector (u, w) into two orthogonal vectors (u , w ) and (u ⊥ , w ⊥ ) as…”

“…This model is often used to estimate the wall stress at each time t. [4][5][6][7][8][9][10][11] However, it is too approximate. We need smoothing in space [8][9][10] or in time 9,10 so as to have uw and U + u in Eq.…”

“…(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…”

“…For smoothing in Eq. (3b), a timescale τ 10z/U is necessary 11 to remove fluctuations that have not been incorporated into Eq. (3a).…”