Brine rejection leads to salt-fingers in seasonally ice-covered lakes

When ice forms on the surface of lakes, dissolved salts are pushed out of the ice into the liquid water below. If enough salt is rejected from the ice, the excess weight of the salt can lead to long `fingers` of salty fluid moving from the ice into the water below. We ran a series of experiments to investigate these `fingers' and conclude that this process occurs in most freshwater lakes that freeze annually. This process is important for the evolution of lakes, and how they will be different as fewer lakes freeze

Measurement of stimulated Hawking emission in an analogue system

There is a mathematical analogy between the propagation of fields in a general relativistic space-time and long (shallow water) surface waves on moving water. Hawking argued that black holes emit thermal radiation via a quantum spontaneous emission. Similar arguments predict the same effect near wave horizons in fluid flow. By placing a streamlined obstacle into an open channel flow we create a region of high velocity over the obstacle that can include wave horizons. Long waves propagating upstream towards this region are blocked and converted into short (deep water) waves. This is the analogue of the stimulated emission by a white hole (the time inverse of a black hole), and our measurements of the amplitudes of the converted waves demonstrate the thermal nature of the conversion process for this system. Given the close relationship between stimulated and spontaneous emission, our findings attest to the generality of the Hawking process.Comment: 7 pages, 5 figures. This version corrects a processing error in the final graph 5b which multiplied the vertical axis by 2. The graph, and the data used from it, have been corrected. Some minor typos have also been corrected. This version also uses TeX rather than Wor

Instability in stratified shear flow: Review of a physical interpretation based on interacting waves

Instability in homogeneous and density stratified shear flows may be interpreted in terms of the interaction of two (or more) otherwise free waves in the velocity and density profiles. These waves exist on gradients of vorticity and density, and instability results when two fundamental conditions are satisfied: (I) the phase speeds of the waves are stationary with respect to each other ("phase-locking"), and (II) the relative phase of the waves is such that a mutual growth occurs. The advantage of the wave interaction approach is that it provides a physical interpretation to shear flow instability. This paper is largely intended to purvey the basics of this physical interpretation to the reader, while both reviewing and consolidating previous work on the topic. The interpretation is shown to provide a framework for understanding many classical and nonintuitive results from the stability of stratified shear flows, such as the Rayleigh and Fjørtoft theorems, and the destabilizing effect of an otherwise stable density stratification. Finally, we describe an application of the theory to a geophysical-scale flow in the Fraser River estuary

Rotational superradiant scattering in a vortex flow

When an incident wave scatters off of an obstacle, it is partially reflected and partially transmitted. In theory, if the obstacle is rotating, waves can be amplified in the process, extracting energy from the scatterer. Here we describe in detail the first laboratory detection of this phenomenon, known as superradiance 1, 2, 3, 4. We observed that waves propagating on the surface of water can be amplified after being scattered by a draining vortex. The maximum amplification measured was 14% ± 8%, obtained for 3.70 Hz waves, in a 6.25-cm-deep fluid, consistent with the superradiant scattering caused by rapid rotation. We expect our experimental findings to be relevant to black-hole physics, since shallow water waves scattering on a draining fluid constitute an analogue of a black hole 5, 6, 7, 8, 9, 10, as well as to hydrodynamics, due to the close relation to over-reflection instabilities 11, 12, 13

Using Network Component Analysis to Dissect Regulatory Networks Mediated by Transcription Factors in Yeast

Understanding the relationship between genetic variation and gene expression is a central question in genetics. With the availability of data from high-throughput technologies such as ChIP-Chip, expression, and genotyping arrays, we can begin to not only identify associations but to understand how genetic variations perturb the underlying transcription regulatory networks to induce differential gene expression. In this study, we describe a simple model of transcription regulation where the expression of a gene is completely characterized by two properties: the concentrations and promoter affinities of active transcription factors. We devise a method that extends Network Component Analysis (NCA) to determine how genetic variations in the form of single nucleotide polymorphisms (SNPs) perturb these two properties. Applying our method to a segregating population of Saccharomyces cerevisiae, we found statistically significant examples of trans-acting SNPs located in regulatory hotspots that perturb transcription factor concentrations and affinities for target promoters to cause global differential expression and cis-acting genetic variations that perturb the promoter affinities of transcription factors on a single gene to cause local differential expression. Although many genetic variations linked to gene expressions have been identified, it is not clear how they perturb the underlying regulatory networks that govern gene expression. Our work begins to fill this void by showing that many genetic variations affect the concentrations of active transcription factors in a cell and their affinities for target promoters. Understanding the effects of these perturbations can help us to paint a more complete picture of the complex landscape of transcription regulation. The software package implementing the algorithms discussed in this work is available as a MATLAB package upon request

Laboratory, field and numerical investigations of Holmboe's instability

The instabilities that occur at a sheared density interface are investigated in the laboratory, the Fraser River estuary and with Direct Numerical Simulations (DNS). In the laboratory, symmetric Holmboe instabilities are observed during steady, maximal two-layer exchange flow in a long channel of rectangular cross section. Internal hydraulic controls at each end of the channel isolate the subcritical region within the channel from disturbances in the reservoirs. Inside the channel, the instabilities form cusp-like waves that propagate in both directions. The phase speed of the instabilities is consistent with linear theory, and increases along the length of the channel as a result of the gradual acceleration of each layer. This acceleration causes the wavelength of any given instability to increase in the direction of flow. As the instabilities are elongated new instabilities form, and as a consequence, the average wavelength is almost constant along the length of the channel. In the Fraser River estuary, a detailed stability analysis is conducted based on the Taylor-Goldstein (TG) equation, and compared to direct observations in the estuary. We find that each set of instabilities observed coincides with an unstable mode predicted by the TG equation. Each of these instabilities occurs in a region where the gradient Richardson number is less than the critical value of 1/4. Both the TG predictions and echosoundings indicate the instabilities are concentrated either above or below the density interface. These ‘one-sided’ instabilities are closer in structure to the Holmboe instability than to the Kelvin-Helmholtz instability. Although the dominant source of mixing in the estuary appears to be caused by shear instability, there is also evidence of small-scale overturning due to boundary layer turbulence when the tide produces strong near-bed velocities. Many features of the numerical simulations are consistent with linear theory and the laboratory experiments. However, inherent differences be tween the DNS and the experiments are responsible for variations in the dominant wavenumber and amplitude of the wave field. The simulations exhibit a nonlinear ‘wave coarsening’ effect, whereby the energy is shifted to lower wavenumber in discrete jumps. This process is, in part, related to the occurrence of ejections of mixed fluid away from the density interface. In the case of the laboratory experiment, energy is transferred to lower wavenumber by the ‘stretching’ of the wave field by a gradually varying mean velocity. This stretching of the waves results in a reduction in amplitude compared to the DNS. The results of the comparison show the dependence of the nonlinear evolution of a Holmboe wave field on temporal and spatial variations of the mean flow.Applied Science, Faculty ofCivil Engineering, Department ofGraduat

Exchange flow through the Burlington Ship Canal

The currents in the Burlington Ship Canal were found to be the result of a variety of driving mechanisms. Wind driven upwelling at the western end of Lake Ontario creates a horizontal density gradient through the canal driving baroclinic currents. Wind initiated standing waves and lunar tides in Lake Ontario cause water surface gradients through the canal driving barotropic currents. The barotropic currents are also strongly affected by Helmholtz or Harbour Resonance. A water balance showed that baroclinic currents contributed more flow to the harbour than stream flow and waste water treatment plant flow, particularly during periods of intense lake upwelling. The water balance also showed that velocity observations from the Acoustic Doppler Current Profiler were 19% less than predicted by the observed changes in Hamilton Harbour water level. The influence of the side wall boundary is suspected as the source of this difference.Applied Science, Faculty ofCivil Engineering, Department ofGraduat