Introduction

Ocean wind-waves play a dominant role in air–sea interaction processes, and, despite much progress, understanding the complex underlying physical processes involved in ocean wave dynamics continues to present a substantial scientific challenge. Two tasks confront us now: first, to establish a viable theory of wind-wave generation, and second, to describe the ocean surface quantitatively. Although the emphasis of this chapter is on wind-wave spectra, a brief description of wind-wave generation theory and the concept of local equilibrium with the wind is necessary to appreciate the uncertainty and problems facing us.

There are two existing theories on wind-wave generation; both published in 1957. The first one is by Phillips (1957), who proposed resonant interaction between the waves and the pressure field associated with the wind as the generation mechanism. Lacking a feedback mechanism, the original result was only valid for the initial stage of the wave field where the growth is linear. Phillips's theory was subsequently modified by Miles (1959a, b) to include partial feedback and resulted in an exponential growth in the principal stage. The second theory is due to Miles (1957, 1959a, b, 1962, 1967), who proposed the instability of an inviscid shear flow as the main energy transfer mechanism, which causes the waves to grow exponentially. Because this model requires the existence of a wave field at the beginning, it explains more of a wind-wave interaction process rather than the actual generation phase (see, for example, Phillips 1977).

Introduction

The sea surface drag has been discussed in terms of the bulk aerodynamic coefficient parametrization, CD. There are several factors that influence stress exerted by the atmosphere on the ocean surface and these are discussed in various chapters of this book. The influence of some mesoscale phenomena is the focus here. There are, for example, the characteristic large eddies that occur in the planetary boundary layer and the sharp changes associated with storms and convective events. Finally, the sparsity of data may mean that factors contributing to ocean stress remain unmeasured, unmodelled, and even unknown.

In the context of wind stress on the sea surface we have a twofold task: first to understand processes and their influence on the stress, and second to develop parametrizations and determine the coefficients. The bulk aerodynamic method using a drag coefficient or roughness length is a local parametrization. It can be modified by local or quasi-local influences like buoyancy stratification or wave age. Atmospheric processes are typically described by numerical models with a grid-scale of 50 km or 100 km. Observations at sea are considerably more sparse. Subgridscale atmospheric variations, especially of the wind, will influence the momentum transfer and thus result in apparently unexplained variations of the drag. The present chapter deals with influence of recognized structures that are not well represented in modelled surface layer variables or local measurements.

Introduction

While the previous chapters have described the models of drag coefficient and the physics of momentum transfer at the sea surface, it is still necessary to make some direct measurement of the stress. There are unanswered questions about the value of the drag coefficient in unsteady and non-ideal conditions. One needs stress measurement to resolve these issues. In some upper ocean experiments the exact flux of momentum is important enough to justify the added work in making stress measurements rather than the simpler wind measurements needed to use with the drag coefficient. There is also the possibility that from ships and other complex structures that induce large flow distortions it may be easier to measure the stress accurately than to measure the wind speed accurately.

The Measurement of Surface Stress

Over solid surfaces the stress over a portion of the surface can be obtained by relatively straightforward methods such as measuring the force on a drag plate. The sea surface offers no such opportunity. The breaking waves that dominate the surface under conditions of strong forcing make it difficult to imagine a direct measurement technique. Thus we rely on remote observation from which we infer the drag force.

This chapter outlines the three common ways of estimating the surface stress. They are known as the Reynolds stress method, dissipation method and profile method.

Introduction

The globe of the earth is surrounded by a gaseous atmosphere which is always in motion. When in contact with the land or the water surface of the earth the flow is reduced to zero, relative to the underlying surface, and it is this boundary flow that interests us here. As well as the planetary boundary layer in the air, also known as the Ekman layer, there is an oceanic boundary layer which interacts with the air above. The thermal structure through these two regimes is shown schematically in Fig. 3.1. An adequate description of physical processes and mechanisms that determine the structure of the interacting atmospheric and oceanic boundary layers as well as a theoretical background is needed for developing parametrization schemes. The more general features of this problem are treated in the monograph by Kraus and Businger (1994).

One of the most important problems is the parametrization of the turbulent fluxes of momentum, latent and sensible heat at the sea surface. The oceans are the major source of atmospheric water and a major contributor to the heat content of the atmosphere. Most of the solar energy is absorbed by the oceans, and this energy becomes available to maintain the atmospheric circulation only through turbulent fluxes of latent and sensible heat. Radiative, sensible and latent fluxes determine the ocean surface energy flux and, consequently, the vertical structure of the upper ocean.

Effects of Boundaries

The previous discussion has focused on the manner in which momentum is exchanged across the sea surface assuming either that there are no boundaries nearby or that the wind is blowing from a long straight coastline. The ocean has been thought of as an infinite half space in the second case with a boundary perpendicular to the wind direction. What is the influence of other shore lines? What if the wind is parallel to a long straight coast? Let us restrict the problem in this chapter to where the wind is spatially uniform.

Since wind-waves have a broad spread of propagation directions, the sea surface roughness at a point is influenced by the fetch from each upstream portion of land. In this situation the wave development is not only a function of fetch in the wind direction but depends also on the cross-wind dimension of the water body. In the case of a lake or bay this will be the width. The other boundary that influences waves is the sea floor. It is through the changes in the surface roughness that we can speculate about the influence of boundaries on the drag coefficient. We will not consider effects such as wave shoaling, or the spatial changes in wind speed that result from variations in surface roughness between land and sea, as this is discussed in Chapter 11.

Introduction

The boundary layers each side of the sea surface are forced on many time and space scales. To simplify matters, the previous chapters described situations where the external forcing was constant. However the measurements presented from the natural environment were subjected to variations in forcing conditions. Observations yielded many different values of neutral atmosphere drag coefficient. While there are some trends (in Fig. 1.4 for instance), that can be attributed to different wind speed, much of the variability remains unexplained. Could some of the remaining variability result from the unsteady nature of the boundary layers each side of the air–sea interface?

The air–sea interface is a coupled system. The momentum transfer between them occurs through the sea surface which is distorted by wind-waves. These are not the idealized irrotational gravity and capillary waves but are the turbulent windsea motions induced by the sheared boundary layers. The waves play a special role in the momentum transfer between the sheared air and water boundary layers, as discussed in Section 4.5.4. The time scales typical of the air and water boundary layers need to be compared with the response time of the windsea to assess the interactions. With some understanding of these time scales, the influence of unsteadiness on the momentum flux at the sea surface can be examined. The spatial variations in the boundary layers are swept past a stationary observer who may interpret the variations as temporal change.

Exchanges at the Sea Surface

While the boundary between the ocean and the atmosphere has been extensively studied it is still not well understood. Heat, mass and momentum cross this boundary at a rate determined by many features of not only the sea surface motion but also the properties of the atmosphere and the ocean boundary layers on each side of the interface. There are some simplifications that can be made because the sharp variations are predominantly in the vertical, but there is a hierarchy of scales and processes at play which cannot be ignored in many applications. Central to understanding the processes at the boundary is gaining knowledge about the flux of momentum between the water and the air. The flux, which is the rate of transport of momentum across unit area, can be in either direction. In a frame of reference fixed to the earth, flux is mostly from the wind to the ocean currents, but less frequently, the flux is from the wind-waves or currents to the atmosphere.

The winds and currents have gradients of horizontal momentum. If we treat the sea surface as a sharp boundary between two fluids of different properties, we can model the flux of momentum from one of the fluids to the other as a drag force per unit area at the sea surface. This is the surface shear stress.

Introduction

Traditionally, the wind has been considered as the driving force for all ocean dynamics phenomena. Thus, we have the classical works on wind generated ocean circulation (Robinson 1963), and wind generated waves (Kinsman 1965). Almost half a century has elapsed, yet the prevailing thinking in the ocean community remains unchanged: Scientists engaged in ocean model development still fall into two categories – ocean circulation modellers who produce General Circulation Models (CGMs) and wind-wave modellers who have constructed, for example, Wave Modelling (WAM). In each respective endeavour, wind is considered as given and unchanged. This viewpoint is now changing. Research seems to be moving in the direction of treating the atmosphere and the oceans as a single system.

Wind-generated waves and currents are fundamental features of the world oceans. As the wind starts to blow over a resting ocean surface, it first generates small-scale wind-waves. These wind-waves extract momentum and energy from the wind field and modify the effective momentum flux into currents and also influence the wind field itself. The momentum flux will generate the drift currents, which in turn begin to influence the amplitude and directionality of the surface wind-wave field. The general ocean circulation pattern will also transport heat from one region to another to modify the global atmospheric dynamics. Thus, they form a closely knitted interacting trinity.

Introduction

Swell is formally defined as old wind sea that has been generated elsewhere. The term “old” is meant to signify that at some past time the swell energy, propagating through a given defined point, had been directly forced by the wind elsewhere. In view of the rather specific notion of “wave age” it might be better to think of swell as “escaped” wind sea. Having come from elsewhere, bearing the imprint of a different storm, swell may propagate at any speed relative to the wind or at any angle to the wind. Indeed, the vector difference in speed of the swell and peak wind sea may provide the only unambiguous criterion for identifying and separating swell from actively growing wind sea. Frequency dispersion separates the components of swell as they propagate away from the source area, and so swell tends to have a narrower spectrum than wind sea; but this provides only a qualitative selection criterion since the bandwidth of wind sea and swell may have considerable variation. For clarity we consider only two clearly defined cases of swell: (1) a distinct peak in the spectrum having peak phase speed greater than the wind component in the direction of propagation of the peak; (2) a distinct peak in the spectrum having peak phase velocity at an angle greater than 90 degrees to the wind.