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Fluid Dynamics Laboratory

John Wettlaufer, Michael Patterson and Jerome Neufeld

We are primarily interested in understanding the basic physics of mixing and transport in rotating and non-rotating geophysical flows, such as those driven by heat and salt fluxes at the sea-ice/ocean interface in a rotating system. However, our approach arises from considerations of basic fluid dynamics and hence much of what we do has broad applicability in allied physical sciences, such as astronomy and astrophysics, and engineering.
Current research projects focus on how stratification can develop in response to convection over shelf regions, entrainment in gravity currents, the circulation and mixing that exists in rapidly rotating convection in a wedge geometry, and interaction between compositional convection and shear flow during the growth of mushy layers as an analog to the growth of sea ice.
These studies form part of the larger research effort in our department of atmosphere, ocean and climate dynamics.


sea ice in the Weddell sea.


Shear flow in compositional convection  -- John Wettlaufer and Jerome Neufeld.

sea ice in the Weddell sea. On any given day one of the Polar Oceans if freezing. When the ocean freezes a hierarchy of instabilities, ranging from strictly diffusive to buoyancy driven convective, conspire to create a matrix of pure ice and highly concentrated brine-sea ice. Such processes are common among all multicomponent solidification systems and the general description of the resulting material is that is it a "mushy layer". In the case of the Polar Oceans, for very thin layers of sea ice, most of the rejected brine is trapped within the crystalline interstices. As the ice grows, a critical porous medium Rayleigh number is reached beyond which the system releases the trapped brine and drives thermohaline circulation [2]. In the presence of a strong shear flow an additional interaction driven by the Bernouli pressure difference between maxima and minima in the under-ice topography of the ice, and flow in the mushy layer can give rise to the growth of corrugations. The effect, which has been shown theoretically, could lead to a substantial increase in the under-ice roughness and hence modulate the heat and mass transfer at the ice/ocean interface [1]. We are searching for experimental evidence of this instability in a combined solidification/flume experiment and in a field effort with  Grae Worster and Dirk Notz at Cambridge University, and Jamie Morison at the University of Washington.

[1] Feltham, D.L., M.G. Worster, and J.S. Wettlaufer, The influence of ocean flow on newly-forming sea ice, J. Geophys. Res. 107, 2000JC000559 (2002).

 [2] Wettlaufer, J. S., M. G. Worster and H. E. Huppert, The solidification of leads: Theory, experiment and field observations, J. Geophys. Res., 105, 1123 (2000).



Entrainment and mixing in gravity currents  -- Michael Patterson.

Numerical simulation A gravity current is a predominantly horizontal flow where gravity drives fluid motion due to density gradients in the flow. Gravity currents occur commonly in nature (e.g. turbidity currents in the ocean and atmospheric dust storms (Haboobs)). Their large scale features have been studied extensively in a variety of different configurations, as summarized by Simpson (1997).

The figures (right) show isosurfaces of the density structure from numerical simulations for two distinct types of gravity current. The results show the effects of having a free-slip or a no-slip lower boundary on the gravity currents shape. The results highlight how no-slip boundaries induce the development of the lobe and cleft instability which in turn induces mixing at the head of the gravity current. Experimental investigation into this phenomena is underway at present.
Mixing in Kelvin-Helmholtz billows  -- Michael Patterson.

Experimental results Stratified shear flows, i.e. flows where both the fluid density and velocity vary with height, are ubiquitous in geophysics. It is well-known that under certain circumstances, such flows are susceptible to a beautiful instability, where the initial strip of vorticity in the shear layer rolls up into a quasi-periodic array of elliptical vortices, commonly referred to as Kelvin-Helmholtz (KH) billows. The properties of stratified KH billows have been widely studied in the laboratory and numerically. Of particular interest are the characteristics of the irreversible mixing associated with billows, since for flows with sufficiently high Reynolds numbers KH billows trigger turbulence. Experimental results In the atmosphere, the break down of KH billows is thought to be a major cause of clear air turbulence (a significant, and still poorly understood aviation hazard), while in the ocean, shear induced mixing plays a major role in the overall circulation and heat budget. In the figures (right) we show results from two experiments. In the first set of experimental results three KH billows form with essentially the same wavelength. The billows developed to finite amplitude, and then merged in a largely symmetric manner. In the second set of experimental results the combined effect of a variation in the initial perturbation and a variation in the imposed flow parameters result in the development of four billows. The billows that grew out of the smaller wavelength perturbation underwent rapid merger. This merger was on a smaller scale than in experiment A, and affected the larger scale billows strongly, in particular stopping the development of a large scale merger overturning late in the experiment. Instead, each billow broke down without substantial interaction with its neighbours. The consequences of different types of mixing events are looked at more fully in:

[1] M. D. Patterson, C. P. Caulfield, J. N. McElwaine and S. B. Dalziel, 'Time-dependent mixing in stratified Kelvin-Helmholtz billows: Experimental observations'. sub judice - GRL

Convection over shallow shelf regions -- Mathew Wells and John Wettlaufer.

Gravity_currents Uniform heating in a cavity with variable depth leads to horizontal density gradients. If these gradients are sufficiently vigorous then a strong gravity current will flow from the shallow region and stratify the deeper regions. This provides an interesting mechanism whereby an unstable buoyancy flux, can lead to stable stratification. If this image is turned upside down we now have a simple model for convection in a marginal sea or lake. For example about 40% of the Arctic ocean is very shallow with depths of less than 150m. In these regions the formation of winter sea ice leads to strong brine rejection and hence causes  local compositional convection. Such a process can create strong horizontal density gradients and drive  the formation of gravity currents that stratify the deep regions of the ocean.  Over the last 10,000 years  sea-level has changed by up to 150m,  so that different fractions of this region will have been exposed and the resulting formation processes of deep water will have changed as well.