The wall region in turbulent shear flow

Abstract

Hot-film measurements in a fully developed channel flow have been made in an attempt to gain more insight into the process of Reynolds stress production. The background for this effort is the observation of a certain sequence of events (deceleration, ejection and sweep) in the wall region of turbulent flows by Corino (1965) and Corino & Brodkey (1969). The instantaneous product signal uv was classified according to the sign of its components u and v, and these classified portions were then averaged to obtain their contributions to the Reynolds stress $-\rho\overline{uv} $. The signal was classified into four categories; the two main ones were that with u negative and v positive, which can be associated with the ejection-type motion of Corino & Brodkey (1969), and that with u positive and v negative, associated with the sweep-type motion. It was found that over the wall region investigated, 3·5 [les ] y [les ] 100, these two types of motion give rise to a stress considerably greater than the total Reynolds stress. Two other types of motion, (i) u negative, v negative, corresponding to low-speed fluid deflected towards the wall, and (ii) u positive, v positive, corresponding to high-speed fluid reflected outwards from the wall, were found to account for the ‘excess’ stress produced by the first two categories, which give contributions of opposite sign.The autocorrelations of the classified portions of uv were obtained to determine the relative time scales of these four types of motion. The positive stress producing motions (u < 0, v > 0 and u > 0, v < 0) were found to have significantly larger time scales than the negative stress producing motions (u < 0, v < 0 and u > 0, v > 0). It was further surmised that turbulent energy dissipation is associated with the Reynolds stress producing motions, since these result in localized shear regions in which the dissipation is several orders of magnitude greater than the average dissipation at the wall.

Turbulent boundary layers and channels at moderate Reynolds numbers

“…In the former, the contribution of the two dominant quadrants, Q2 and Q4, increases near the centreline, and is compensated by a parallel increase of the two counter-gradient quadrants Ql and Q3 (see e.g. Wallace, Eckelmann & Brodkey 1972). Most of this increase is simply due to taking fractions with respect to a total stress that vanishes at the centreline, while the contributions of the individual quadrants do not.…”

Transport processes in and above two-dimensional urban street canyons under different stratification conditions: results from numerical simulation

“…There is a consensus that turbulent motions dominate the pollutant removal in the skimming flow regime. A quadrant analysis [37] is usually adopted to quantify the contribution of each quadrant to the turbulent pollutant flux w c , where w and c are the fluctuation of vertical velocity and pollutant concentration from their temporal average (denoted by the overbar), respectively. The first quadrant (w > 0, c > 0) is called ejections, which are the "ejection" of slow-moving fluid from the urban canyon into the shear layer above, while the third quadrant (w < 0, c < 0) is called sweeps, which are the replacement of ejected fluid with relatively high-speed fluid from outside the street canyon.…”

Large-Eddy Simulation of Flow and Pollutant Transports in and Above Two-Dimensional Idealized Street Canyons

“…To elucidate the momentum transport mechanism (Table 2), quadrant analysis (Wallace et al 1972;Lu and Willmarth 1973;Nakagawa and Nezu 1977) is employed to partition the current LES-calculated u w (Fig. 10).…”