# Network: Wave-flow interactions

Lead Research Organisation:
University of Edinburgh

Department Name: Sch of Mathematics

### Abstract

The dynamics of the fluids encountered in many environmental and industrial applications is a complicated mixture of flow motion and wave propagation. Flows and waves can interact in a variety of ways: flows can generate waves, as the familiar example of turbulence-generated noise demonstrates, but waves also generate flow motion, as in the case of along-shore currents forced by sea-surface waves. Understanding the nature of the interaction between flows and waves is a problem of central importance in fluid dynamics, with a broad range of applications. It is also a very difficult problem: for a start, the very definition of what is a wave in a moving fluid is not straighforward. Research on wave-flow interactions is currently buoyant in the UK: several groups work on different aspects of the problem, especially in the context of geophysical flows. They consider different types of flows and waves and use different techniques (analytical, numerical, experimental). However, there are many commonalities in the mathematical models underlying the problems these groups study, and it would be highly beneficial if collaborations between the groups could be initiated. This is the aim of the proposed Network. Through yearly meetings and small-scale workshops, it will stimulate interactions between researchers with complementary expertises, so that current challenges can be tackled efficiently.Four problems have been identified to start collaborative work. A first is the separation between waves and flow. Here what will be sought are both suitable mathematical definitions and practical means of identifying which components of fluid motion can be regarded as flow and as waves. A second problem concerns the spontaneous generation of waves by flow. This remains largely open when situations more complex than that of non-dispersive waves are considered. A third problem is the generation of robust mean flows by waves, of the type that controls some part of the atmospheric circulation. The challenge here will be to go beyong the current theory, often limited to symmetric mean flows, and to model both dissipative and non-dissipative interactions. A fourth problem is that of the interaction between surface waves and ocean currents, with applications to the modelling of freak waves and tsunami-wave propagation. These four problems with be complemented by others which will emerge from the interactions of the Network members.

### Publications

Connaughton C
(2011)

*Feedback of zonal flows on wave turbulence driven by small-scale instability in the Charney-Hasegawa-Mima model*in EPL (Europhysics Letters)
Cotter C
(2009)

*Variational water-wave model with accurate dispersion and vertical vorticity*in Journal of Engineering Mathematics
Ngan K
(2011)

*Scalar decay in a three-dimensional chaotic flow.*in Physical review. E, Statistical, nonlinear, and soft matter physics
Sukoriansky S
(2012)

*Rossby waves and zonons in zonostrophic turbulence*
Vanneste J
(2010)

*Streaming by leaky surface acoustic waves*in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Vanneste J
(2013)

*Balance and Spontaneous Wave Generation in Geophysical Flows*in Annual Review of Fluid Mechanics