Abstract

A fluid is a non-rigid interconnected mass which may in general exhibit either laminar or turbulent flow. Laminar flows are characteristic of slow-moving or highly viscous flows where the fluid particles move in an ordered fashion, sliding over themselves in sheets (or laminae, hence ‘laminar’). Turbulent flows, on the other hand, are characteristic of fast-moving or low-viscosity flows, where small disturbances in the flow quickly blow up causing the fluid particles to move in an unpredictable fashion, mixing themselves up from one point in the flow to the next. Almost all real flows of interest to scientists and engineers are turbulent: the flow of water in rivers and pipelines; the flow within hydraulic machinery, e.g. turbines and pumps; atmospheric wind flows and ocean currents; and the flow or air around buildings, moving vehicles and aircraft. Turbulence manifests itself as a multiscale cascading phenomenon, where fluctuations (eddies) over a large range of scales are superimposed on a mean flow, e.g. the buffeting experienced on a windy day. Over the past decade, the wavelet transform has emerged as a particularly powerful tool for the elucidation of fluid signals (e.g. velocities, pressures and temperatures), both temporal and spatial, covering a variety of pertinent problems from the Kolmogorov scaling of high-Reynolds-number homogeneous turbulence to the nature of vortex shedding downstream of bluff bodies. Many researchers have made use of the wavelet trans-form’s ability to probe simultaneously both the spectral and temporal (or spatial) structure of turbulent fluid flows. This chapter begins with a basic outline of the wavelet-based statistical methods used extensively in the analysis of fluid flows. The chapter is then split into two main parts: the first details the wavelet analysis of jets, wakes and coherent structures in engineering flows and the second considers geophysical flows.