Reappraisal of plane wall jet self-similarity

There is a general consensus that the characteristic velocity and length scales for a plane wall jet exhibit power law with distance downstream of the jet nozzle/slot, x; however, no definitive values are given for the power-law exponents. In view of this, plane wall jet self-similarity is reappraised using a compilation of experimental and direct numerical data of plane wall jets. The plots of compensated distributions of the maximum velocity U_max and length $y 1 / 2$⁠, the location where the velocity is equal to $U max / 2$ in the outer part of the flow, reveal that these variables follow the power laws $U max ∼ y 1 / 2 n$ and $y 1 / 2 ∼ x m$⁠, where $n ∼ − 1 / 2$ and $m ∼ 1$⁠, which comply with self-similarity solutions. While $n ∼ − 1 / 2$ is in agreement with the existing results, the linear growth of $y 1 / 2$ contrasts with the common belief that m should be less than 1. It is argued that the limited ranges of x and Reynolds numbers (Re) used in the previous studies prevent this latter behavior to be observed. This behavior emerges when these data are compiled into a single set, allowing a reasonable range of x and Re. It is further observed that only one velocity scale, either U_max or $u τ$⁠, the friction velocity, is needed for the outer region, which complies with a requirement imposed by self-similarity under a linear growth $y 1 / 2$⁠. In the inner region, either $ν / u τ$ or $y 1 / 2 , i n$ (the location where the velocity is equal to $U max / 2$ in the inner part) can be used as a scaling velocity, while $u τ$ should be the adequate scaling velocity. The present analysis provides some support to the argument that scaling could be universal, at least when the Reynolds number is large enough and the flow is allowed to evolve over a very long distance.