Simple layered models

Pressure gradient and continuity equations in layered models

The concept of layered models

The simplest way to simulate the ocean circulation is to assume that the ocean is homogeneous in density. Such a model has no vertical structure. As discussed in Section 1.4, there is a prominent main thermocline/pycnocline in the oceans. The subsurface maximum of the vertical density gradient can be idealized as a step function, and a natural way of simulating the ocean circulation is to treat the ocean as a two-layer fluid, using the main thermocline as the interface. The lower layer lies below the main thermocline; it is very thick and water in this layer moves much slower than that above the main thermocline. As a good approximation, one can assume that fluid in the lower layer is nearly stagnant. Such a model has one active layer only; this is called a reduced-gravity model. The advantage of a reduced-gravity model is its ability to capture the first baroclinic mode of the circulation and the depth of the main thermocline. Adding one more layer to the standard reducedgravity model, one obtains a 2½-layer model, which is also discussed in this chapter. The comparison of these models is outlined in Figure 4.1.

In a sense, a reduced-gravity model is equivalent to using just two grids in the density coordinate. Similarly, multi-layer models are highly truncated models in the density coordinate.

Introduction

Energetics is one of the fundamental aspects of the climate system. Over the past decades many studies have been devoted to the energetics of the oceanic circulation. Although a more general definition of the oceanic general circulation may include wind-driven circulation, thermohaline circulation, and tides, the commonly used definition of oceanic general circulation is confined to the wind-driven circulation and thermohaline circulation.

Wind-driven circulation is a direct consequence of wind stress applied to the sea surface; therefore the energetics of wind-driven circulation must be closely linked to wind stress energy input. However, the cause of the thermohaline circulation seems complicated and remains the subject of hot debate. As explained shortly, the nature of the thermohaline circulation may depend on the viewpoint of the person who studies the problem. Therefore, research into the energetics of the oceanic circulation is often focused on the causes of the thermohaline circulation.

Energetic view of the ocean

Most previous studies on the energetics of the thermohaline circulation have been focused on the balance of thermal energy, in particular the air–sea heat fluxes and the meridional transport of thermal energy. A typical example is the book, Physics of Climate (Peixoto and Oort, 1992), in which the balance of thermal energy and its transformation have been discussed in great detail.

For a long time the importance of the mechanical energy balance, in particular energy sources from wind stress and tidal forces, failed to be recognized in the study of the thermohaline circulation.

With great progress being made in science and technology, we are becoming more interested in finding out how the climate system, including the oceanic general circulation, works on our planet. This book is written for the general reader who is searching for knowledge about oceanic circulation and its relevance to climate and the global environment on Earth.

During the process of collecting the materials for this book, I have tried to achieve a sensible balance between the physical concepts fundamental to the oceanic circulation, well-established theories, and recent developments associated with the frontiers in our field. As its title suggests, the book is about the wind-driven and thermohaline processes in the oceans. Although many theories about the oceanic general circulation have developed over recent decades, it is clear that our understanding of the circulation remains rudimentary at best. Since this book is intended as a textbook for graduate students, I have made a major effort to describe and explain the physical aspects of the circulation without relying on the sometimes complicated mathematics. To aid the reader, I have included many diagrams illustrating the physics.

In terms of the theoretical part of the book, I have made every effort to present new theories and thoughts about the energetic theory of the oceanic general circulation. Although energetics is one of the fundamental aspects of any dynamical system, the importance of examining the energetics of the oceanic general circulation has so far not been widely appreciated.

Water mass formation/erosion

The balance of water masses in the world's oceans consists of two major processes: water mass formation and erosion. Most water masses are formed near the upper surface and sink. Furthermore, through either transformation or erosion, water mass properties are continually transformed, so that a water mass gradually loses its identity. Therefore, some types of water mass are formed below the surface layers through the mixing of water masses originated from the sea surface; however, in this chapter, we primarily focus on formation/erosion of water masses in connection with surface processes.

According to the penetration depth, water-mass formation is generally separated into two major categories, those of deep water and mode water. The second category of water mass normally sinks to a relatively shallow part of the world's oceans. In this chapter, we first discuss deepwater formation and then mode water formation.

Sources of deep water in the world's oceans

In a broad sense, the balance of deep water in the world's oceans consists of two major opposing processes: the supply of newly formed water masses through deepwater formation and the removal of deep water through mixing and erosion. Deepwater formation is closely related to the downward branch of the vertical circulation, which continuously supplies the water masses, while deepwater erosion is closely related to the upward branch of the vertical circulation, which continuously removes the water masses. Both processes are essential for water mass balance and thermohaline circulation in the world's oceans.

The main focus of this book is the study of large-scale circulation in the world's oceans. As a dynamical system, the circulation in the world's oceans is controlled by the combined effects of external forcing, including wind stress, heat flux through the sea surface and seafloor, surface freshwater flux, tidal force, and gravitational force. In addition, the Coriolis force should be included, because all our theories and models are formulated in a rotating framework. In this chapter, I first describe surface forcing and the distribution of physical properties. I then discuss the classification of different kinds of motion in the world's oceans, and briefly review the historical development of theories of oceanic general circulation.

Surface forcing for the world's oceans

The ocean is forced from the upper surface, including wind stress, and heat and freshwater fluxes. In addition, tidal forces affect the whole depth of the water column, and geothermal heat flux and bottom friction also contribute to the establishment and regulation of the motions in the ocean. However, the surface forces are the primary forces for the oceanic circulation, and these are the focus of this section.

Surface wind forcing

Wind stress is probably the most crucial force acting on the upper surface of the world's oceans. The common practice in physical oceanography is to treat the effect of wind as a surface stress imposed on the upper surface of the ocean.