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Evolution and mixing of asymmetric Holmboe instabilities Carpenter, Jeffrey Richard

Abstract

When a stably stratified density interface is embedded in a region of strong velocity shear, hydrodynamic instabilities result. These instabilities lead to the development of a turbulent flow in which vertical mixing of the density field takes place. Much previous research in the field of stratified shear instability has concentrated on what has become the canonical mode in such flows - the Kelvin-Helmholtz (KH) instability. This is one of two instabilities that are present in what is termed the symmetric case, where the centres of the shear layer and density interface coincide. The other mode is the Holmboe instability, and relies on the presence of a thin density interface centred within the shear layer. In the present study the stratified shear layer is generalized to allow an offset between the centres of the shear layer and the density interface. By including this asymmetry, and keeping the density interface thin with respect to the shear layer, the asymmetric Holmboe instability is found to emerge. The objective of the present study is to examine the evolution and mixing behavior of asymmetric Holmboe (AH) instabilities, and to compare the results to the well known KH and Holmboe instabilities. This is done by performing a series of direct numerical simulations (DNS). DNS has the advantage of directly resolving the smallest scales of variability present in the flow such that the turbulence and mixing characteristics do not require parameterization. In this way the mixing behavior is modeled without relying on a turbulence closure scheme. The simulation results show that there are two different mixing mechanisms present. The first is a feature of KH instabilities and is characterized by a significant overturning of the density interface. This leads to the mixing and production of intermediate density fluid causing a final density profile that is layered. The second mixing mechanism is found in AH and Holmboe instabilities and consists of regions of mixing and turbulence production that are located on one or both sides of the density interface. It is comprised of a cusp-like wave that periodically ejects partially mixed fluid from the top or bottom of the interface. Since the instability does not generate overturning the density interface is able to 'retain its identity' throughout the mixing event. The amount of mixing that takes place is found to be strongly dependent on the degree of asymmetry in the flow. As the asymmetry is increased the amount of mixing also increases, however, this is not necessarily an accurate representation of natural conditions as the pairing mechanism is expected to play a role in the dynamics of the flow. The development of three-dimensional secondary structure appears to agree with previous studies (e.g.: Caulfield and Peltier (2000), Peltier and Caulfield (2003), Schowalter et al. (1994)), and consists of the formation of streamwise vortices, particularly in the gravitationally unstable regions. The presence of the density interface and the periodic ejection of interfacial fluid were also found to influence the development of these vortices. The formation and breakdown of streamwise vortices appears to be an important step in the transition to turbulence. Since numerical models are hampered by difficulties in simulating the high Reynolds and Prandtl numbers found in nature, the geophysical relevance of the present work is also discussed in this context.

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