Layers and internal waves in uniformly stratified fluids stirred by vertical grids

Abstract

Laboratory experiments in which uniformly stratified fluids are stirred by horizontally moving vertical grids, or arrays of vertical rods, are reviewed to examine their consistency and to compare their findings, particularly those relating to the generation of layers. Selected experiments are of three types, those in which (a) turbulence spreads from a horizontally confined region where it is continuously generated by an oscillating grid; (b) grid stirring is maintained throughout a rectangular tank; or (c) a 'cloud' of turbulence decays after a short period of horizontally localized grid mixing. In all the experiments turbulence is generated over the full vertical extent of the tank. In the experiments of types (a) and (c) layers of comparable scale are observed to intrude into the ambient fluid from the turbulent region. In the type (b) experiments, layers form only when the time interval between the passage of the grid through the stratified fluid is sufficiently long, allowing turbulence to decay substantially between grid strokes. Two mechanisms are found to be dominant in the production of layers. In experiments of type (a) and (c) overturning eddies in the turbulent region of scale significantly larger than the Ozmidov length scale collapse and spread, intruding and forming layers in the adjoining laminar region. Internal shear waves propagating ahead of the intrusions have a vertical wavelength that is approximately twice the layer height. In type (b) experiments, layers are formed through a process described by Holford & Linden (Dyn. Atmos. Oceans, vol. 30, 1999a, pp. 173-198): the bending of vortices shed by the grid bars. The height of the layers is approximately half the vertical wavelength of internal shear waves that travel at the speed of the grid. It is proposed that the flow field of the shear waves bends the vortices, resulting in diapycnal mixing that forms the layers. The relationship of layers and internal shear waves in the experiments is therefore as follows: in type (a) and (c) experiments internal waves are generated by layers intruding from the turbulent region into the quiescent stratified region, but in experiments of type (b) internal waves drive and dictate the height of the layers; layers are generated as a consequence of vortex bending by internal waves. There is insufficient evidence to establish whether zigzag instability, either of vortex pairs or of vortex streets shed by a moving grid, accounts for the layers in any of the three types of grid experiments. The Phillips and Posmentier instability may reinforce layers formed by other processes. The generation of pancake vortices or vortical mode motion is left for later review.

The linear instability of the stratified plane Couette flow

“…In figure 11 (right) we report a visualisation of the buoyancy perturbation b once the instability has saturated. One observes an weakly inclined layering of the density field which is a common feature in stratified turbulent shear flows (see Thorpe 2016, for a review). Again we have a very good agreement with the linear theory: a distinct spatial pattern appears and both vertical and horizontal wavelengths correspond to the predicted values.…”

Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities

“…Since this class of instability is also often invoked as the precursor to layer formation (see e.g. Thorpe (2016)), it seems appropriate to investigate the linear stability properties of the flows we are considering, in particular to identify whether they are prone to instabilities which may be identified as being of 'zig-zag' type. For the case when the forcing scale and streamwise integral scale are the same (i.e.…”

Statistical state dynamics analysis of buoyancy layer formation via the Phillips mechanism in two-dimensional stratified turbulence

“…S3T analysis predicts that, in this model system, PI requires the presence of shear. Layers have been observed in laboratory studies of rod-stirred stratified turbulence without any coherent large-scale shear (Ruddick et al 1989;Park et al 1994;Holford & Linden 1999), but layer formation in these systems has recently been attributed to a mechanism differing from PI (Thorpe 2016). The present work provides a theoretical underpinning of PI based on SSD, but is not designed to capture alternative mechanisms that may be important in the case of rod-stirred tanks.…”

“…Density layer formation has been observed in several laboratory studies in which stratified tanks were stirred by vertical rods (Ruddick, McDougall & Turner 1989;Park, Whitehead & Gnandadesikan 1994;Holford & Linden 1999). Although Ruddick et al (1989) and Park et al (1994) attributed layer formation to PI, Thorpe (2016) has recently challenged this explanation, arguing that layering in these studies, and in the study of Holford & Linden (1999), instead results from the interaction of internal shear waves with decaying wake vortices left by the moving rods. Accurate attribution of layering to PI requires the difficult diagnostic task of evaluating the flux-gradient relation in evolving turbulence.…”