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6311 results in Earth and Environmental Science: general interest

Page 33 of 316

A Brief History of Geology
  • Kieran D. O'Hara
  • Published online:
    06 April 2018
    Print publication:
    19 April 2018
  • Geology as a science has a fascinating and controversial history. Kieran D. O'Hara's book provides a brief and accessible account of the major events in the history of geology over the last two hundred years, from early theories of Earth structure during the Reformation, through major controversies over the age of the Earth during the Industrial Revolution, to the more recent twentieth-century development of plate tectonic theory, and on to current ideas concerning the Anthropocene. Most chapters include a short 'text box' providing more technical and detailed elaborations on selected topics. The book also includes a history of the geology of the Moon, a topic not normally included in books on the history of geology. The book will appeal to students of Earth science, researchers in geology who wish to learn more about the history of their subject, and general readers interested in the history of science.

  • 30 - Cooling the Earth

  • from Part VII - Silicate Flows
  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 323-333

  • Summary

    Earth cools its mantle and core by casting off heat to outer space, with the heat being transported upward through the mantle by a combination of convective motions in the interior and conduction near the top and bottom surfaces. The top thermal boundary layer is the lithosphere, and the bottom layer is called the D̋ layer. A thermal boundary layer has existed at the top of the mantle since the Earth accreted as a hot planetary body some 4.53 ×109 years ago, but a thermal layer exists at the bottom of the mantle now only because the mantle has cooled more rapidly than the core since accretion. In what follows, we will be interested in the current convective state of the mantle, and will not investigate the thermal history of the mantle.

    The mantle can directly transfer its heat to the surface, but heat from the core must be transmitted upward through the mantle. This means that the mantle is convecting in two distinct modes, with slab convection acting to cool the mantle and plume convection acting to cool the core; these two modes of cooling are investigated and discussed in Chapters 31 and 32, respectively. But before getting into that, let's briefly discuss plate tectonics (in the following section), slabs and plumes (in § 30.2), volcanism (in § 30.3) and radioactivity (in § 30.5) and quantify the heat flows within the mantle (§ 30.4), the boundary conditions at the core–mantle boundary (§ 30.6) and the temperature profile in the bulk of the mantle (§ 30.7). A comprehensive summary of the structure of the convecting mantle may be found in Davies and Richards (1992).

    Plate Tectonics

    Although it took people a long while to recognize because of the slow speeds (typically a few centimeters per year) involved, it is now clear that Earth's surface is divided into a set of nearly rigid tectonic plates that move relative to each other. The current configuration of the plates is illustrated in Figure 30.1 and the current motions of Earth's 56 lithospheric plates are given in Argus et al. (2011).

  • Part I - Introductory Material

  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 1-2

  • Summary

    In this first part, we get oriented to the general subject matter of the book and the style of approach. The orientation in Chapter 1 includes a discussion of broader aspects, such as mathematical modeling, continuum mechanics, the role of energy in the universe and the apparent need of astronomical bodies to cool as rapidly as possible. Central to our study is the concept of a continuous body, as discussed in § 1.2.

    The second chapter provides a bit more introductory detail, including the reference coordinate system, a definition of waves and flows, a summary of the scope of the book and brief introductions to a number of related issues.

  • 7 - Static State and Perturbations

  • from Part II - Kinematics, Dynamics and Rheology
  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 67-82

  • Summary

    Planetary atmospheres, oceans and interiors are dominantly in a state of hydrostatic equilibrium, with most dynamic processes being perturbations of that state. With this in mind, in this chapter, we will separate the elastic and fluid governing equations into static balance and perturbation equations. Static reference-state variables are indicated by a subscript r while perturbations have a prime. Note that reference-state variables often are functions of position – particularly spherical radius or elevation. We begin in § 7.1 with a presentation of the equations governing a static state. Next, in § 7.2 we briefly discuss the structures of the atmosphere, oceans and mantle. Then in § 7.3 we develop a set of equations quantifying small departures from the static state.

    Static State

    The static state of an elastic solid is simply the reference state with u = 0 and while the static state of a fluid body is v = 0 and again. The equation of conservation of mass is identically satisfied in the static state for both elastic and fluid bodies, while the momentum equation for both is simply the hydrostatic balance

    where and z is the upward coordinate.

    Thermodynamics tells us that the density is a function of the pressure, temperature and composition. We will ignore compositional effects for the time being and consider ρr = f (pr, T). A necessary condition for a fluid body to be in a static state is obtained by taking the curl of the momentum equation:

    Isothermal and isobaric surfaces must coincide in a static (barotropic) state. This is possible in a non-rotating, self-gravitating body, but if the body is rotating and density depends on temperature, a static state is not possible; gravity requires elliptic isobars, while thermal conduction still produces spherical isotherms. This situation occurs, for example, in stellar interiors; they are in continual Eddington-Sweet motion.

    With the functional relation between ρr and pr known, it is fairly straightforward to determine the static state of the atmosphere, oceans and Earth's interior. These structures are presented and discussed in the following section.

  • 8 - Introduction to Rotating Fluids

  • from Part II - Kinematics, Dynamics and Rheology
  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 83-100

  • Summary

    Rotation of Earth plays a dominant role in the dynamics of its atmosphere and oceans on time scales of a day or more. In a rotating (non-inertial) frame, the dynamic effect of rotation is represented a virtual force, called the Coriolis force, in the Navier–Stokes equation. A dominant effect of rotation is to produce waves and flows that are themselves rotating relative to a frame of reference fixed to Earth. This tendency is most readily observed in the atmosphere, which contains large-scale rotating air masses called “highs” and “lows” by meteorologists, and an array of smaller and often stronger rotating systems, including hurricanes (or cyclones), tornadoes, water spouts, and dust devils. As we shall see, rotation of Earth plays a direct role in large-scale systems, but only an indirect role in the smaller systems.

    In this chapter we will modify the perturbation equations given in § 7.3.2 so that they apply more specifically to the atmosphere and oceans and in doing so will encounter a number of concepts and effects that are introduced by rotation. The Coriolis force complicates the analysis of rotating fluids in several ways; apart from introducing an extra term in the Navier–Stokes equation, it couples the horizontal components of this equation, so that motions are generally not unidirectional. It will take some care and effort to decipher the dynamic constraints that rotation imposes on the flow, so we shall proceed carefully, beginning in § 8.1 with the discussion of a number of rotational concepts. Then in § 8.2, we will present the equations governing flow in a rotating fluid. The rotation of the fluid itself, represented by the vorticity, is an important quantity of interest; the vorticity equation is presented and discussed in § 8.3. Often horizontal motions in a thin layer of fluid are independent of the vertical coordinate and can be quantified by vertically averaged equations; the vertically averaged continuity equation is developed in § 8.4. Large-scale motions in the atmosphere and oceans may be categorized as geostrophic or quasi-geostrophic. Geostrophic flows result from a balance between the Coriolis and pressure terms, as described in § 8.5, while quasi-geostrophic flows result from a balance between the inertial, Coriolis and pressure terms, as described in § 8.6.

  • Appendix B - Dimensions and Units

  • from Part VIII - Fundaments
  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 405-411

  • Summary

    The fundaments of kinematics presented include:

  • • B.1: an introduction to dimensional analysis;

  • • B.2: an introduction to the international system of units; and

  • • B.3: a table of parameters relevant to waves and flows on Earth and their estimated magnitudes.

    • Dimensional Analysis

    This fundament provides an orientation to the process of dimensional analysis, whereby a problem is simplified by analyzing the dimensions of its variables and parameters. The theoretical basis for this process is provided by the Buckingham Pi theorem. An essential part of the process is the formation of a minimal number of dimensionless parameters, typically denoted by ∏, each of which is an algebraic combination of the dimensional parameters in the problem. One advantage of dimensional analysis is that we do not need a set of governing equations (though that is, of course, quite helpful). All that is needed is a “grocery list” of relevant parameters.

    A related procedure is non-dimensionalization, whereby a set of governing equations and the parameters within it are made dimensionless. Often the equations are significantly simplified by this procedure, making them more amenable to analysis and solution.

    Dimensional analysis employs the seven base dimensions (length, mass, time, temperature, electric current, amount of substance and luminous intensity) of the SI system. Mechanical systems involve only the first three (length, mass and time), denoted by L, M and T:

    L = length M= mass T = time.

    Commonly the dimensions of a variable are identified using square brackets; for example, [g] = L·T−2 means that the dimensions of acceleration are length divided by time squared.

    In addition to the seven base dimensions, the SI system contains two supplemental units: plane and solid angle. These do not play a direct role in dimensional analysis and non-dimensionalization, but they do affect the numerical relationships among the dimensionless variables. The number of dimensionless parameters involved in a physical problem can easily be determined by use of the Buckingham Pi theorem which states that

    N∏ = Np −Nd,

    where N∏ is the number of dimensionless parameters, Np is the number of dimensional

    parameters and Nd is the number of base dimensions contained in all parameters.

  • 27 - Oceanic Currents

  • from Part VI - Flows in Rotating Fluids
  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 277-291

  • Summary

    As we have previously noted, a major dynamic feature of the oceans is the thermocline, which separates a thin well-mixed top layer from a deep stably stratified layer beneath. The oceans have three types of large-scale motion that involve one or both of these layers, as summarized in Table 27.1.We have previously investigated the tides; in this chapter we will look into barotropic currents in the upper ocean (above the thermocline) driven by wind stress at the ocean surface and deep currents driven by subtle differences in temperature and salt content, beginning with the former.

    Figure 27.1 shows the major oceanic currents in the upper ocean, consisting primarily of gyres having ﹛clockwise, counterclockwise﹜ flow in the ﹛northern, southern﹜ hemisphere. There are five main gyres, occurring in the five major ocean basins: the northern Pacific, southern Pacific, northern Atlantic, southern Atlantic and (southern) Indian Oceans. In addition there are several minor gyres and currents near the equator and at high latitudes.

    The near-surface flows within an ocean basin are driven by the prevailing winds illustrated in Figure 26.1, but in a somewhat indirect manner. The prevailing winds are predominantly along lines of constant latitude, being easterly (from west to east) in the tropics and westerly (from east to west) in mid-latitudes. As we saw in § 25.5.4, these winds drive near-surface flows (Ekman transport) in the normal direction: north-south, along lines of constant longitude. These potential north-south flows have no dynamic outlet and instead the wind stresses result in deformation of the ocean surface which sets up a counterbalancing north-south pressure gradient. Near-surface flows arise due to a latitudinal variation of this dynamic balance, quantified by the curl of the wind stress, forming the great oceanic gyres illustrated in Figure 27.1. These flows are predominantly in the east-west direction in the open oceans. With the exception of the southern ocean surrounding Antarctica, these east-west flows are blocked by continents and are diverted in the north-south direction in thin boundary layers, predominantly on the western boundaries of the oceans, forming the western boundary currents.

Page 33 of 316