Title:

The induced mean flow of surface, internal and interfacial gravity wave groups

Although the leadingorder motion of waves is periodic  in other words backwards and forwards  many types of waves including those driven by gravity induce a mean flow as a higherorder effect. It is the induced mean flow of three types of gravity waves that this thesis examines: surface (part I), internal (part II) and interfacial gravity waves (part III). In particular, this thesis examines wave groups. Because they transport energy, momentum and other tracers, waveinduced mean flows have important consequences for climate, environment, air traffic, fisheries, offshore oil and other industries. In this thesis perturbation methods are used to develop a simplified understanding of the physics of the induced mean flow for each of these three types of gravity wave groups. Leadingorder estimates of different transport quantities are developed. For surface gravity wave groups (part I), the induced mean flow consists of two compo nents: the Stokes drift dominant near the surface and the Eulerian return flow acting in the opposite direction and dominant at depth. By considering subsequent orders in a separation of scales expansion and by comparing to the Fourierspace solutions of LonguetHiggins and Stewart (1962), this thesis shows that the effects of frequency dis persion can be ignored for deepwater waves with realistic bandwidths. An approximate depth scale is developed and validated above which the Stokes drift is dominant and below which the return flow wins: the transition depth. Results are extended to include the effects of finite depth and directional spreading. Internal gravity wave groups (part II) do not display Stokes drift, but a quantity analogous to Stokes transport for surface gravity waves can still be developed, termed the “divergent flux induced flow” herein. The divergentflux induced flow it itself a divergent flow and induces a response. In a threedimensional geometry, the divergentflux induced flow and the return flow form a balanced circulation in the horizontal plane with the former transporting fluid through the centre of the group and the latter acting in the opposite direction around the group. In a twodimensional geometry, stratification inhibits a balanced circulation and a second type of waves are generated that travel far ahead and in the lee of the wave group. The results in the seminal work of Bretherton (1969b) are thus validated, explicit expressions for the response and return flow are developed and compared to numerical simulations in the twodimensional case. Finally, for interfacial wave groups (part III) the induced mean flow is shown to behave analogously to the surface wave problem of part I. Exploring both pure interfacial waves in a channel with a closed lid and interacting surface and interfacial waves, expressions for the Stokes drift and return flow are found for different configurations with the mean setup or setdown of the interface playing an important role.
