Instabilities in fluid dynamics

Summary

We aim to understand and control fluid instabilities like transition to turbulence and the formation of salt polygons in dry lakes.

We always think of a fluid as a substance that flows but how often do we wonder about how it flows? Open your tap a little and you will see a transparent stream of water. The flow is laminar and all the water particles gently travel in the direction of the stream. Now, open the tap to its fullest. The stream has become opaque! Water now flows in a turbulent fashion. It is full of small vortices that trap air bubbles which disturb the trajectory of light and make the stream opaque. What has happened in this experiment is an instability. At first, the flow is laminar but, at some point, a critical tap opening is reached and transition to turbulence takes place.

Fluid transport in pipes is ubiquitous in industry, from the small scale of ink jets to the large scale of pipeline transport. In most cases, we wish to increase the flow rate but this may lead to an undesirable instability. Turbulent flows in pipes are accompanied with increased wall friction and are, thus, less energetically efficient than their laminar counterparts. In addition, turbulent flow features can, in the long run, damage the pipe. We aim to understand how the instability takes place and how to control it.

Dry salt lakes can be found in many arid regions and give rise to spectacular landscapes constituted of salt polygons (google it!). What has this got to do with fluids? Well, the lake may be dry but water sits not far below the visible surface. It is salty and, when it evaporates, deposits salt into the visible surface crust, contributing to its growth and the creation of salt polygons. The surface crust is further eroded by wind and produces dust that is then transported away. At Owens Lake (California, USA), for example, the dust produced contains arsenic and is hazardous to the neighbouring populations. There, understanding the instability that produces salt polygons and controlling it may drastically increase air quality.

These are just two examples of instabilities that we aim to study. We use a combination of numerical (spectral methods, numerical continuation, etc.) and analytical (linear stability and weakly nonlinear stability analyses, etc.) techniques inspired by dynamical systems in our investigations.

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