As already mentioned, there are several prominent features of MAV flight: (i) low Reynolds numbers (104–105), resulting in degraded aerodynamic performance, (ii) small physical dimensions, resulting in much reduced payload capabilities, as well as some favorable scaling characteristics including structural strength, reduced stall speed, and impact tolerance, (iii) low flight speed, resulting in an order one effect of the flight environment such as wind gust, and intrinsically unsteady flight characteristics. The preferred low Reynolds number airfoil shapes are different from those typically used for manned aircraft in thickness, camber, and AR. In this chapter, we discuss low Reynolds number aerodynamics and the implications of airfoil shapes, laminar–turbulent transition, and an unsteady free stream on the performance outcome.

Schmitz (1942) was among the first to investigate the aerodynamics for model airplanes in Germany, and he published his research in 1942. His work is often considered to be the first reported low-speed wind-tunnel research. However, before him, experimental investigations of low Reynolds number aerodynamics were conducted by Brown (1939) and by Weiss (1939), in the first two (and only) issues of The Journal of International Aeromodeling. Brown's experiments focused on curved-plate airfoils, made by using two circle arcs meet at maximum camber point of 8%, at varying locations. The wing test sections were all of 12.7 cm × 76.2 cm, giving an aspect ratio of 6. In all cases, the tests were conducted at a free-stream velocity of 94 cm/s.

Pioneering work on flapping-wing aerodynamics was done by Lighthill (1969) and Weis-Fogh (1973). Recent works, both in experiments and simulations, were documented by Katz (1979), Ellington (1984a), DeLaurier (1993), Smith (1996), Vest and Katz (1996), Liu and Kawachi (1998), Dickinson et al. (1999), Jones and Platzer (1999, 2003), Wang (2000), and Chasman and Chakravarthy (2001). A review of the characteristics of both flapping wings and fixed wings was given by Shyy et al. (1999a). The spectrum of animal flight with flapping wing was presented by Templin (2000). Ho et al. (2003) further reviewed the recent effort in developing flapping-wing-based MAVs. Computational and experimental studies regarding rotating-wing MAVs were made by Bohorquez et al. (2003).

The quasi-steady theory is constructed based on the instantaneous velocity, wing geometry, and AoA when the steady-state aerodynamic model is used.

My book entitled The Turbulent Ocean (referred to later as TTO) was written in 2003. It provides an account of much of the knowledge that there was then of the processes leading to turbulence in the ocean, but it was not written as a course that might be followed and used to introduce students to turbulent flow. Rather, it is a text useful for those beginning or already involved in research. It might form the basis of a number of advanced courses about ocean physics, teachers selecting material according to their needs or specialities.

I was asked to write a shorter book, an introductory course on turbulence in the ocean. Although believing that the best undergraduate and postgraduate courses are based and modelled on a teacher's own experience and enthusiasms, and that to follow a ‘set text’ may be less enjoyable for students, I became convinced that a simplified text, more directly usable in teaching students unfamiliar with fluid motion, might be of value. Turbulence is a subject of which at least a basic understanding is essential in engineering and in many of the natural sciences, but particularly for students of oceanography. Moreover, many students, whose main interests are not in oceanography and who will not later address their talents to the study of the ocean, find interest in the sea and are motivated by aspects of their studies that are related or have application to matters of public and international concern, for example those of pollution and climate change that are at present being addressed by ocean scientists.

Introduction

The properties of dispersants

The objective of this chapter is to describe some of the ideas and observations that have been devised to assess and quantify rates of turbulence dispersion in the ocean.

There are several reasons why dispersion, introduced in Section 1.5.1, is of importance in the ocean. It is dispersion that determines the distribution of the naturally occurring ‘tracers’, such as salinity, for example the area within the North Atlantic that is affected by the high salinity emanating from the Mediterranean through the Straits of Gibraltar (Fig. 5.1). The volume of the water column in the Pacific affected by the plume containing helium 3 (3He) coming from hydrothermal vents in the East Pacific Rise (Fig. 5.2) is a consequence of several processes of dispersion, notably in the initial buoyant ascent of the plume, including the entrainment of surrounding water, and the subsequent advection and spread in the stratified ocean of the water ‘labelled’ by the 3He. In many cases, especially those relating to the accidental discharge of toxic chemicals or oil into the sea or the development and spread of harmful algal blooms (HABs; Fig. 5.3), the dispersion of solutes or particles by turbulent motion may have dire consequences as the pollutants spread to sensitive regions, especially those near shore where there can be a detrimental effect on mariculture, human health and recreation. Prediction is therefore of great practical importance.

Introduction: processes, and types of boundary layers

This chapter is about turbulence in the two, very extensive, boundary layers of the ocean, the upper ocean boundary layer or region near the sea surface that is directly affected by the presence of the overlying atmosphere, and the benthic or bottom boundary layer (bbl) that lies above the underlying solid, but possibly rough and (in strong flows) mobile, seabed. Two fluxes imposed at the bounding surfaces have direct effects, those of buoyancy and momentum. The former is often dominated by a flux of heat, related by (2.8) to a flux of buoyancy. This is sometimes supplemented at the sea surface by the entry of buoyant freshwater in the form of rain or snow. The flux of momentum can be equated to the stress, as explained in Section 2.2.1. This stress, or horizontal force per unit area, may be exerted by the wind on the sea surface or, for example, by the frictional forces of an immobile sedimentary layer composed of sand or gravel on a current passing over the ocean floor.

It is useful here, as in preceding chapters, to refer to processes. By a ‘process’ is meant a physical mechanism, one that can be described in terms of its effects and its associated spatial and temporal structure, that generally involves the transfer of energy from one scale to another or from one part of the ocean to another.

Introduction

The study of ocean turbulence may be viewed as a key component in the investigation of the ocean's processes and their energetics: how the energy supplied from external sources is distributed and eventually dissipated by the external and internal processes of mixing referred to in Section 3.1. The ocean is driven mainly by forcing from the atmosphere at the sea surface and by the tidal body forces imposed by the gravitational attraction of the Moon and the Sun. Relatively insignificant are the localized, but spectacular, inputs of energy from hydrothermal vents in the deep ocean ridges, the fortunately infrequent seismic movements of the seabed that may generate devastating tsunamis, the flux of geothermal heat through the floor of the abyssal plains and the energy inputs from rivers and the break-up or melting of ice sheets. The tidal forces and atmospheric inputs are the dominant sources of energy responsible for the overall circulation of the ocean (the kinetic energy of the mean flow) and its density structure (containing potential energy), and are the principal cause of the waves and the turbulence within the ocean.

The discussion in this chapter focuses on how turbulent mixing in the deep ocean is maintained. Much of the energy provided by the atmosphere is used in driving surface waves and the processes that sustain the structure of the upper ocean boundary layer.

Measurement is at the heart of science. The measurement of turbulence in the ocean has proved difficult, and not all the technical and operational problems have been overcome. In this chapter we review the characteristics that are used to describe turbulent motion and its effects, and describe some of the methods of measuring and quantifying turbulence.

Characteristics of turbulence

Some of the characteristics of turbulence are described in general terms in Chapter 1. These can provide ways of quantifying turbulent motion as explained in this, and later, sections.

Structure

Figure 2.1 is a shadowgraph image of the development of a turbulent shear flow in a laboratory experiment. It shows large billows formed downstream of a ‘splitter plate’ dividing two streams of gases with different speeds and densities. As in the photograph of the surf zone (Fig. 1.4), Fig. 2.1 shows that the flow contains patterns or structures – the billows – that recur. Each billow extends over a finite region: the motions within are spatially coherent. Although the billows are transient, they also persist for times long enough to allow them to be identified: they are coherent for short periods of time. The structure within billows varies in detail from one to another, and consists of small-scale turbulent motions that lead to the fine ‘texture’ visible in the image.

Such patterns of relatively large-scale coherent eddies containing small-scale motions are commonly found in turbulent flows.