Michael Waite - Turbulence in Stratified Fluids.
Turbulence in the atmosphere and ocean is the rule rather than the exception. It is characterized by chaotic vortices over a wide range of scales, from thousands of kilometers down to centimeters. Turbulence mixes heat, chemicals, water vapor, and salt, much more efficiently than molecular diffusion. Turbulence also dissipates kinetic energy, as large vortices break into smaller and smaller vortices, which are ultimately destroyed by viscosity. These processes often occur below the grid scale of large atmosphere and ocean models, but nevertheless can profoundly impact the large-scale flow. An improved understanding of turbulence is therefore crucial for the advancement of weather and climate modelling.
The atmosphere and ocean have stable density stratification: heavier fluid lies, on average, below lighter fluid. This decrease of density with height has a significant impact on turbulence, because vertical motions are opposed by buoyancy forces. Stratified flows tend to be predominantly horizontal, and interactions between different levels in the vertical are inhibited. This results in quasi-horizontal, layered turbulent vortices, sometimes called "pancake vortices" (figure 1). In addition, internal gravity waves propagate through stratified fluids, and three-dimensional turbulence can exist at small scales, where the effects of stratification are generally weak.
[Figure 1: A vertical cross-section of horizontal vorticity, from a
numerical simulation of stratified turbulence. The turbulence is
forced by randomly stirring vertical vortices, and so the layered
"pancake" structure emerges spontaneously. Three-dimensional vortices
at the scale of the layer thickness are visible.]
My research is focused on the dynamics and interactions of vortices, waves, and three-dimensional turbulence in stratified fluids. I study this problem with numerical simulations, i.e. by performing virtual experiments of turbulent flows on large computers. This approach compliments the work of other scientists who study data from laboratory experiments and field observations. I use different types of simulations for different aspects of the problem, such as experiments with very idealized domains ("turbulence in a box"), and atmospheric mesoscale simulations. Key quantities of interest include kinetic energy spectra, which show how energy is partitioned between vortices, waves, and turbulence of different length scales; and transfer spectra, which show how energy moves between different scales. Results are compared with theoretical predictions, laboratory findings, and field studies.
A recent project concerns the breakdown of pancake vortices into three-dimensional turbulence by a particular kind of vortex instability, called the zigzag instability. This is an interesting problem, because although stratification is often thought to be stabilizing, the zigzag instability is most active when stratification is strong. With Piotr Smolarkiewicz (MMM), I have been performing simulations of pairs of vortices in a strongly stratified fluid, and studying how they are ultimately destroyed by three-dimensional turbulence (figure 2). This appears to occur when density inside the vortices overturns, much like a breaking wave. The overturning rapidly collapses into turbulence. This process may be one way that vortices in the atmosphere and ocean dissipate energy.
[Figure 2: A horizontal cross-section of vertical vorticity in a
numerical simulation of the zigzag instability. Three times are
shown, capturing the transition of the flow to turbulence.]
ASP Spotlight September 2007
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