Stratified turbulent mixing in the ocean: patterns, processes, and parameterisation
Dr Jennifer MacKinnon, University of California San Diego, Scripps Institution of Oceanography, USA
Though average observed diapycnal mixing rates in the ocean interior are consistent with values required by inverse models, recent focus has been on the dramatic spatial variability of mixing rates in both the upper and deep ocean, which spans several orders of magnitude. Global ocean models have been shown to be very sensitive not only to the overall level but to the detailed distribution of mixing. Some of these patterns are driven by the geography of generation, propagation and destruction of internal waves, which are thought to supply much of the power for turbulence in the ocean interior. I will briefly review some results from the last five years of a Climate Process Team tasked with improving representations of internal-wave driven mixing in the oceanic component of climate models. Another set of recent and ongoing work has turned to the poorly understood role of mesoscale and sub-mesoscale features in stratified oceanic turbulence. In some situations, the interplay between internal waves and mesoscale vorticity can noticeably enhance turbulent mixing rates. In other situations, sub-mesoscale instabilities act to re-stratify the ocean, a counter-balance of sorts to one-dimensional vertical mixing schemes. Recent observational examples of both situations will be presented, and discussed in the broader framework of global mixing rates.
Mixing in density-stratified, free shear flows and the implications for mixing in the ocean
Professor Greg Ivey, University of Western Australia, Australia
To first order, in the interior of the ocean the mean density and horizontal velocity fields can be considered a function of the vertical coordinate z. For this simple shearing flow, we introduce a new mixing length model to describe the mixing of density and momentum. We introduce a mixing length Lp controlling mixing in the density field and a mixing length Lm controlling mixing in the momentum field. There are no undetermined coefficients in the model, and no need to make any assumptions about the value of the flux Richardson number Rif. The model determines Rif and demonstrates Rif is dependent on the relative magnitudes of three length scales: Lp, Lo, and Ls , where Lo is the Ozmidov scale and Ls the Corrsin shear scale. The model predictions are in good agreement with published laboratory observations. We discuss the implications of the model for the interpretation of oceanic turbulent microstructure measurements and the description of mixing in numerical ocean models.
Parameterising mixing in the stably stratified ocean interior
Dr Sonya Legg, Princeton University, USA
Vertical mixing is suppressed in the stable density stratification of the ocean interior, yet the vertical turbulent diffusion of heat and salt still plays a significant role in the thermohaline circulation. Ocean climate models cannot explicitly resolve the mixing processes, so must employ parameterisations relating the mixing to resolved parameters. Such mixing requires a source of energy, supplied by sheared flow; when this shear is resolved, for example in large-scale ocean currents, the parameterised turbulent diffusion can be expressed in terms of the resolved flow and stratification. However, in much of the ocean, the shear responsible for mixing is due to internal waves, which are rarely simulated in climate models. These waves are generated by the tides and wind, propagate around the ocean, and eventually lead to mixing when they break. Parameterisation of the mixing due to breaking internal waves must account for the generation, propagation and dissipation of wave energy. High resolution simulations can be used to examine the mechanisms of wave breaking, extending understanding gained from observations. Here I will describe different internal wave breaking mechanisms, including nonlinear wave-wave interactions, wave reflection from sloping and shoaling topography, and transient hydraulic jumps, as well as recent efforts to combine this understanding into a global model of the tidally-driven internal wave energy budget leading to an energetically consistent parameterisation of mixing. The impact of different geographical distributions of wave-breaking on global ocean circulation will be demonstrated using coupled climate models.
Mixing processes in the oil and gas industry
Dr Simon Bittleston, Schlumberger Gould Research, UK
Oil wells are very long and skinny (with aspect ratios of the order 10^5) and in many operations a tube sits within the wellbore with fluids pumped down the centre of this pipe, and back up the annulus between the pipe and rock. Flow rates vary significantly leading to some operations being performed in laminar flows, whilst others are turbulent. The fluids can be Newtonian or non-Newtonian. When the tube is not concentric in the wellbore, it is possible that laminar, transitional and turbulent flow can coexist in the annular space at any particular depth. The simplest case of dispersion of a tracer in a single phase flow is already of interest as the time evolution of fluid properties of the outlet of a well can give an indication of earlier events near the bottom. Taylor dispersion calculations show how sensitive the outlet distribution can be to eccentricity of the inner tube, and how rotation of the inner tube can counteract this. In some cases it is also useful to understand how a tracer distribution approaches the Taylor limit. As many of the fluids used are non-Newtonian, even these relatively simple cases exhibit unusual behaviours. More complex cases involve pumping a sequence of fluids of varying densities and rheological properties down through the tube and up the annular space. In these cases mixing process are complex, with a variety of instabilities possible. An approximate model system can be derived for certain geometrical configurations leading to realistic prediction of mixing processes. Laminar flow problems are already challenging; adding the complexity of turbulent, or partially turbulent flows, leads to a range of problems which deserve greater study. This talk will lead from the single phase to the multi-fluid and from the laminar to the turbulent, to explain the broad range of rich mixing processes that can occur in an important practical application.