P.I.M.S. Summer School in Fluid Dynamics

Abstracts of Invited Talks

Hydrodynamic instability and irreversible mixing
W. R. Peltier, University of Toronto

The talk will be based upon theory and numerical simulations directed towards understanding the extent to which irreversible mixing occurs in stratified fluids and the dependence of the efficiency of such mixing on stratification. Two archtypical flows will be discussed, namely those in which the initial linear inviscid bifurcations are, respectively, Kelvin-Helmholtz and Baroclinic instability. In the former case the question of interest concerns the monotonicity of the mixing efficiency with respect to the buoyancy frequency, N, and in the latter case it concerns the dependence of the efficiency on the N contrast between the troposphere and stratosphere.

11am, Monday August 16 in room 235 Central Academic Building

The upscale turbulent cascade: shear layers, cyclones and gas giant bands
W. R. Peltier, University of Toronto

This talk will discuss a range of hydrodynamic problems in which the upscale cascade of energy through subharmonic instability has a profound effect on the flow evolution. It will end with a discussion of the manner in which Rossby wave effects lead, at the largest scales, to the arrest of the cascade and to the formation of banded zonal flows on the gas giant planets.

11am, Tuesday August 17 in room 235 Central Academic Building

Nontwist Hamiltonian systems with applications in fluid mechanics and plasma physics
P. Morrison, University of Texas at Austin

The twist condition is an important condition of Hamiltonian dynamics theory that arises when the canonical momentum is a monotonic function of the velocity. However, many physically important Hamiltonian systems do not possess this condition, and consequently the structure of their phase space is dramantically different. One and a half degree-of-freedom Hamiltonian systems are described by symplectic twist maps, which may or may not possess the twist condition. I will review symplectic twist map phenomena, including the way invariant tori break-up, symmetry methods for finding periodic orbits, and Greene's residue criterion. In nontwist maps a new theory is required for tori break-up. The new theory will be described. Applications will include zonal flows in geophysical fluid dynamics and magnetic field lines.

2pm, Tuesday August 17 in room 235 Central Academic Building

The Hydraulics of Layered Flows
G. Lawrence, University of British Columbia

Many flows oceanographic, meteorological, and engineering importance can be modelled as homogeneous layers of inviscid fluid subject to a hydrostatic pressure distribution. The resulting one-dimensional (hydraulic) equations have long been used by Civil Engineers in the study of single layer flow. The extension to multi-layer flows has been pursued since the early 1950's in studies concerned with the intrusion of salt water into estuaries, the flow of air over mountains, and the exchange of fluids of slightly different densities through contractions and over sills. The results of theoretical studies will be compared with laboratory experiments and field observations.

11am, Wednesday August 18 in room 235 Central Academic Building

Hamiltonian description of shear flow
P. Morrison, University of Texas at Austin

Euler's equation linearized about a shear flow equilibrium is solved by means of a novel invertible integral transform that is a generalization of the Hilbert transform. The integral transform provides a means for describing the dynamics of the continuous spectrum that is well-known to occur in this system. The results are interpreted in the context of Hamiltonian systems theory, where it is shown that the integral transform defines a canonical transformation to action-angle variables. A means for attaching Krein signature to a continuum eigenmode is given.

2pm, Wednesday August 18 in room 235 Central Academic Building

Mixing in Density Stratified Flows
G. Lawrence, U.B.C.

The understanding of turbulence and mixing is one of the central problems in fluid mechanics. The results of laboratory studies of mixing in density stratified flows will be compared to the results of numerical and analytical studies. The emphasis will be on hydrodynamic instabilities that lead to turbulence and mixing at density interfaces in salt stratified flows.

11am, Thursday August 19 in room 235 Central Academic Building

EIFL home page

Department of Mathematical Sciences home page

Geophysical Fluid Dynamics home page

Bruce R. Sutherland, July 99.