Growth laws and self-similarity in the confined mixing zone of unstratified and strongly stably stratified isokinetic mixing-layers past a splitter plate

Abstract

The velocity U and the mixing scalar field Θ of turbulent wake flows developing downstream of a slender splitter plate were studied experimentally for unstratified and strongly stably stratified conditions in a square channel with water as fluid. The experimental program comprises five different Reynolds numbers spanning [Formula: see text]–60 000 for [Formula: see text] (isokinetic conditions) between the two planar, initially separated streams and five relative density stratifications from [Formula: see text] to 10%, since mixing studies for these stratification strengths are rather limited. This full-channel Reynolds number uses the hydraulic diameter [Formula: see text] of the mixing section as the characteristic length scale. These experiments challenge the corresponding numerical calculations based on Reynolds-averaged Navier–Stokes approaches relying on the Boussinesq approximations of the first and second kind. The development of the mixing scalar field Θ was measured by two fundamentally different approaches: laser induced fluorescence (LIF) in the downstream x– y mid-plane and wire-mesh sensors (WMSs) in discrete lateral y– z planes. This allows for a direct comparison of both sensing techniques at locations where both planes intersect. For the unstratified conditions, it is shown that the downstream developing wake velocity deficit decay agrees well with the theoretical approach. The concentration fields based on LIF and WMS profiles of the mean and fluctuating (root mean square, RMS) data confirm self-similarity by introducing a mixing scalar Θ for both techniques. In the approximate limit, it is shown that the mean concentration field can be well described by an error function and the corresponding RMS data by a Gaussian profile in self-similar coordinates. By using the momentum thickness θm at the splitter plate as the normalization parameter, the downstream developing width of the mixing zone [Formula: see text] becomes independent for [Formula: see text]. The mean and the RMS values of the concentration field Θ for the stably stratified experiments show self-similarity in the core of the concentration field but also a departure from the error function and Gaussian profile in the outer parts. Introducing a local gradient Richardson number Rig, it is shown that both the growth and growth-suppression of the mixing zone are well described by the Miles–Howard criterion for all the stratified experiments considered, even though this criterion was originally developed for shear layers.