Sections
Book Outline Page One and Page Two
Scope and Organization
Ocean Circulation in Three Pages
Exercises
Three dimensions. The general circulation of the ocean is an important and beautiful subject, one in which significant progress has been made in the last few decades. Some of these advances have deepened (appropriately enough) our appreciation of the three-dimensional nature of the circulation. In addition to the traditional description of horizontal flow, important aspects of the circulation include
Related fields. Nonetheless, students who want to go beyond a two-dimensional picture face significant barriers. This is a shame, because the three-dimensional circulation has important implications for sibling fields, including climate, atmospheric science, and ocean chemistry and biology. Scientists in these disciplines are often most interested in how properties are transported and transformed by the ocean. Such properties include heat, carbon, and nutrients. For transport and transformation, slow vertical travel through hundreds of meters of ocean depth can be as important as faster horizontal motion over thousands of kilometers of ocean width.
Current teaching. Many students in the above-mentioned fields take a single course in physical oceanography that introduces observational and dynamical methods and results. Such courses sketch the observed circulation and may include some theoretical topics such as the western intensification of the Gulf Stream. More advanced texts on ocean circulation tend to be rather mathematical. This may deter some students, and often even physical oceanography students work hard on the equations but lose sight of the underlying concepts. Although an appropriate response to difficult material, this habit obscures the deeper links between theory and the observations. Accordingly, we emphasize conceptual explanations for the general circulation here.
Novel chapter structure. The ``Three-Dimensional'' in the title emphasizes the three dimensional nature of the ocean circulation, meaning its variations with longitude, latitude, and depth. Equally, it signals our attempt to present three dimensions of knowledge:
Numerical modeling. Another important component of physical oceanography is numerical modeling, which we integrate into the other three categories. Diagnostic models improve our observational understanding, model experiments illustrate conceptual arguments, and realistic simulations test the relevance of mathematical theories to the real ocean.
Pathways Through Book. Though aimed at readers who have already taken a course in oceanic or atmospheric dynamics and may want to skip or skim the first two chapters, the book can be the core of a two-semester graduate course. In this way, an introductory course might cover all of Chapters 1--3, most of Chapter 5, plus some topics from, say, Chapters 4, 8, and 11. An advanced second semester course might cover Chapters 6, 7, 9, and 10. Many sections of the book, particularly in Observations, are written to be accessible to undergraduates and can be supplemental reading for them.
Academic context. The book is based on notes from the General Circulation course that Klinger teaches to students in the Climate Dynamics PhD Program at George Mason University. Similarly, Haine teaches Ocean General Circulation to graduate (and some advanced undergraduate) students at Johns Hopkins University using material from the book. Our philosophy may help broaden enrollments in such classes to include students who might otherwise consider an ocean circulation theory class esoteric or inaccessible. While the book's fulcrum lies in Concepts, it includes serious treatments of Theory and presents modern Observations of the general circulation throughout.
It is convenient to group the chapters into a few themes. Here we tour both the subject and the textbook.
The Foundations chapters set the scene with material that is used extensively throughout the book. They review topics that will be familiar to students who have already studied physical oceanography.
Chapter 1 gives an overview of observational techniques, the mathematical framework for understanding the circulation, and some physical characteristics of the oceans. The ocean has variability on a broad range of time and space scales; we loosely define the large scale steady circulation to be a multiyear average of features that are at least about 100~km wide. Ship-based, satellite-based, and autonomous instruments observe ocean properties. These observations are then compiled into estimates of the steady state. Circulation is influenced by ocean density, which is calculated from measurements of temperature and salinity. Ocean dynamics is based on a handful of equations representing physical laws. Solutions to simplified versions of the equations give insight into the ocean and for realistic cases the solutions can be approximated with computers (with some caveats).
The rotation of the Earth (Chapter 2) influences every aspect of the large-scale circulation. Frictional stress from the wind drives Ekman transport at the sea surface. The circulation is generally the sum of the Ekman velocity and geostrophic velocity. We characterize two-dimensional slices of three-dimensional fluid motion with the mathematical tools divergence, vorticity, and streamfunction. The effects of density stratification can be approximated by idealizing the ocean as a stack of uniform-density layers governed by an approximation called the shallow water equations.
A primary flow structure in the ocean is the gyre: a horizontal circulation loop which spans the ocean in a roughly 2000~km latitude band (Chapter 3). The gyre circulation consists of a slow (order 1 cm/s), broad flow which concentrates into a fast (1 m/s), 100 km wide western boundary current such as the Gulf Stream. A theory of wind stress on the surface of an idealized, two-dimensional, uniform-density ocean on a rotating sphere gives reasonable predictions of the location, strength, and other characteristics of the gyres. Several topics in Chapter 3 are also discussed in introductory classes.
Geostrophic gyre flow is strongest in the top kilometer of the ocean, and to understand why, we need to also understand the distribution of small (< 1%) variations in ocean density. Chapter 4 begins this analysis by describing surface temperature, salinity, and other properties. Surface properties are strongly influenced by atmospheric interactions with the mixed layer, a vertically homogeneous region near the surface that is typically a few tens of meters thick.
The book returns several times to the question of how circulation and subsurface density variations influence each other, and how both are constrained by surface density. The pycnocline, a strong vertical density gradient, separates the mixed layer from denser abyssal water below a kilometer or so. Chapter 5 shows how linking the undersea ``hills'' and ``bowls'' of the pycnocline to the gyre circulations allows us to model the vertical variation in the horizontal circulation. In the subtropical gyres, Ekman pumping makes water slide downward along uniform-density (isopycnic) surfaces as it flows around the gyre.
Chapter 6 highlights shallow overturning cells in which meridional (northward or southward) surface Ekman transport is linked via upwelling and downwelling to geostrophic flows in the opposite direction. The cells link neighboring gyres and are strongest in the tropics. The cells are also linked to strong pairs of currents in the upwelling zones of the equator and ocean eastern boundaries. Chapter 6 demonstrates that even the idealization of a purely wind-driven, uniform density ocean can have complex three-dimensional flow involving both gyre and overturning patterns. In the real ocean, the geostrophic flow is primarily in the pycnocline.
Density variations create buoyancy forces which can drive circulation even in the absence of wind. An essential feature of a buoyancy-driven steady circulation is cross-isopycnal flow, in which a water parcel's density changes as the parcel travels. Chapter 7 describes two processes which can produce these density changes by mixing. Mesoscale eddies are horizontal current loops which typically are about 100~km wide and evolve over several weeks. Turbulent diapycnal mixing is caused by three-dimensional time-varying currents with length scales of millimeters to tens of meters and time scales of seconds to hours. The chapter explains how these processes may affect density and other properties of the steady circulation.
Chapter 8 discusses the deep meridional overturning circulation, a series of overturning cells linking the abyss to the pycnocline and mixed layer. The deep overturning is typically weaker than flow in the upper ocean, but it has important effects on climate, dominates deep water, and is especially prominent in the Atlantic Ocean. Chapter 8 discusses the processes controlling deep water formation, the strength of the meridional cells, and gyre-like horizontal circulations associated with the cells. While turbulence is often a means of dissipating energy, the deep overturning gains its strength from diapycnal mixing.
Although the entire ocean is influenced by both wind stress and buoyancy forces, the circulation concepts in the prior themes mainly concern wind-driven upper-ocean flow and buoyancy-driven deep-ocean flow. At high latitudes, this division breaks down, so we discuss the Southern Ocean (Chapter 9) and Arctic (Chapter 10) separately.
Chapter 9 discusses the Antarctic Circumpolar Current, the meridional Deacon Cell, and the deep overturning links between the Southern Ocean and the Atlantic, Indian, and Pacific Oceans. Wind-driven geostrophic flow (Chapter 3), wind-driven meridional overturning (Chapter 6), turbulence and mesoscale eddies (Chapter 7), and the deep overturning circulation (Chapter 8) all play key roles. Moreover, northward Ekman transport from wind stress in the Southern Ocean may help drive deep meridional overturning extending far into the northern hemisphere.
Similarly, a mix of topics is difficult to disentangle in the circulation within the Arctic and in the Arctic's exchange of water with the Atlantic. The cryosphere, particularly sea ice, also plays an especially big role in the Arctic. Chapters 9 and 10 are less definitive than previous parts of the book, reflecting oceanographers' less complete understanding of high latitude dynamics.
The ocean circulation is one component of the global climate system. The circulation is especially important for transporting heat around the globe, cooling the atmosphere in some places and warming it in others. Chapter 11 discusses how the circulation affects, and is affected by, heat and freshwater transport (flux). It describes the mutual influence of ocean surface properties and the atmospheric state. Geological data indicate that the Earth's climate state, including Atlantic overturning, often changed abruptly (on geological timescales), and theory shows how the circulation may fall into one of several states for given external constraints. The physical climate itself is part of the Earth System, which includes ocean and land biogeochemistry, land surface characteristics, the cryosphere, and even human intervention, but that is a subject for another book.
To deepen their understanding, students need to work through problems. Exercises at the end of each chapter attempt to guide the learning process. They are progressive and graduated in terms of difficulty. As with the layout of each chapter, they address Observations, Concepts (including quantitative estimates), and Theory. Many of them are open-ended and provide material for class discussion and term papers.
To complete some Exercises, use of high-quality data analysis, mathematical, and plotting software is essential. This reflects the nature of the field, which uses analytically unsolvable equations that to understand structures which must be characterized by data sets that are too large to process by hand. Many programming languages are adequate for the task, but MATLAB and python are two that are widely used by physical oceanographers and can be easily integrated with the TEOS-10 software package used to compute thermodynamic properties of seawater. Calculations for the exercises do not overwhelm the computing resources of a 2017 laptop, however, and none of them involve solving the equations of motion with numerical circulation models. To help students get started, several problems include oceanographic datasets, and links to sites containing them, plus simple template MATLAB scripts.
Advice applicable to all Exercises is as follows: First, each problem is associated with specific sections of the text, which are important to identify. Second, Appendix C summarizes useful datasets while Appendix B contains nomenclature and useful characteristic values of important quantities. Finally, students should make, reflect on, and clearly state, suitable approximations where necessary. The wisdom of knowing what to include, and what to neglect, shines through the conceptual explanations in our field. Cultivating that wisdom, sometimes bewildering to neophytes, is an important aim of the Exercises.
The Exercises have been field-tested by many students at George Mason, Johns Hopkins, and Oxford Universities. Comments on the Exercises and suggestions for more should be addressed to the authors. Model answers are available to instructors on the book's companion website. Last modified: 13 June 2018