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31496 results in Solid Earth Geophysics

Page 93 of 1575

  • Appendix E - Thermodynamics

  • 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 445-476

  • Summary

    Thermodynamics is concerned with the amounts of energy stored in – and transferred to and from – a thermodynamic system (i.e., a specified portion of the Universe). The behavior of energy is codified in three laws:

  • • The zeroth law defines the concept of temperature. Temperature is an intensive thermodynamic state variable.1

  • • The first law quantifies conservation of energy; it is entirely bookkeeping – keeping track of the types and amounts of energy stored in a system and transferred into or from it.

  • • The second law restricts the possible changes of forms of energy. In a nutshell, changes of energy from organized to disorganized are unconstrained, but transfers of energy from disorganized to organized are severely limited2 and are quantified by the thermodynamic efficiency; see Appendix E.11. An unavoidable consequence of the second law is the degradation of the kinetic energy of a flowing fluid to heat due to the action of viscous forces.

    • A thermodynamic system consists of any clearly defined portion of the universe. A system is assumed to be composed of a vast number3 of massive particles (i.e., particles having a rest mass). These particles may be atoms, electrons, ions, molecules and/or larger aggregations of matter, provided that the system consists of a vast number of them. (It is simplest to think of the particles as atoms.) A system may be categorized as closed or open; transfers of energy and matter into or out of a closed system are not permitted, while these transfers are permitted if the system is open.

    The following fundaments of thermodynamics include:

  • • E.1: a discussion of storage and transfers of energy;

  • • E.2: an introduction to the mole, which is a way to count atoms or molecules;

  • • E.3: an introduction to the first law of thermodynamics;

  • • E.4: a discussion and categorization of thermodynamic potentials, variables and parameters;

  • • E.5: the equations of state for density and entropy, including an alternate form for the first law and the equation of state for sea water;

  • • E.6: an introduction to ideal mixtures;

  • • E.7: development of the energy equation;

  • • E.8: a brief introduction to the thermodynamic behavior of ideal gases;

  • • E.9: a summary of the thermodynamics of the atmosphere;

  • • E.10: a discussion of phase equilibrium; and

  • • E.11: quantification of thermodynamic efficiency.

  • 23 - A Simple Model of Turbulent Flow

  • from Part V - Non-Rotating Flows
  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 227-241

  • Summary

    In this chapter we address one of the most difficult problems in physical science: turbulence. Nearly all geophysical flows are turbulent.Much of our knowledge of turbulent flows is based on observation; a first-principle theory of turbulence does not exist, though there are a number of heuristic theories. We will consider turbulence in the context of channel flow of water (think of rivers and streams), but the concepts and models considered apply to many other geophysical flows, including motions of the atmosphere and oceans, as well as engineered flows, such as flows over airplanes and flows over and within turbines and rockets.

    As water flows down a sloping channel, the downslope gravitational force imparts momentum and kinetic energy to the fluid. The force is balance by a drag force exerted by the bottom and the kinetic energy is dissipated as heat by viscosity. This requires the action of molecular viscosity. The trouble is, the viscosity of water is very small: ν ≈10−6 m2·s−1. We have seen in § 22.2.2 that the speed of flow predicted by laminar-flow theory is very large; such speeds do not occur in natural settings. Turbulence invariably develops if a given flow is large or rapid enough and acts to retard the flow. In § 23.1 we discuss when and how turbulence arises and investigate the transition from laminar to turbulent flow. Then in § 23.2 we present and discuss the engineering approach to the quantification of turbulence.

    Models of turbulent flow invariably characterize it as the sum of a “macroscopic” mean and a set of “microscopic” perturbations, though in practice this division is not very clean. The equations governing the mean flow, developed in § 23.3, contain perturbation terms which must be determined. While man-made channels can have relatively smooth bottoms, we will see in § 23.4 that natural channels are invariably hydraulically rough. The approach which is the best combination of simplicity and accuracy is mixing-length theory, coupled with a rough bottom; this is introduced in § 23.5. The resulting turbulent velocity profile for flow of water in a channel is investigated in § 23.6. This chapter concludes in § 23.7 and § 23.8 with some comments on the drag coefficient and the turbulent diffusion of heat.

  • 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 379-380

  • Summary

    The fundaments contain material that is underpins the main text. They are intended to “fill the gaps” in a reader's background or else to provide generalizations of simplified presentations in the main text. The 47 fundaments are grouped into seven appendices according to general topic, including:

  • • A: mathematics;

  • • B: dimensions and units;

  • • C: kinematics;

  • • D: dynamics;

  • • E: thermodynamics;

  • • F: waves; and

  • • G: flows.

    • These fundaments are not meant to be read in sequence, but rather to be read or referred to as the need arises; most have pointers from the main text provided via footnotes. Most of the fundaments are “stand-alone” summaries, with the exception of those dealing with thermodynamics, which are necessarily somewhat interdependent.

  • 32 - Cooling the Core

  • 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 339-353

  • Summary

    In this chapter we investigate the flows within the mantle that convey heat from Earth's metallic core upward to the surface. Heat is drawn out of the core by a thermal boundary layer (the D ̋ layer) at the base of the mantle, having a temperature contrast of roughly 800 K (see Figure 7.3). The large change in temperature within the D ̋ layer alters the properties of seismic waves and is believed to be the primary cause of subtle seismic anomalies at the base of the mantle. Also, this large temperature increase causes a large decrease in viscosity (by as much as a factor of 1000; see § 6.2.4), making this layer very mobile compared with the adjacent mantle material. This mobility permits hot material within the D ̋ layer to migrate horizontally to the base of a set of plumes, where it feeds upward flow within the plumes, which act as chimneys to convey this hot material to the surface. Flow within the D ̋ layer is investigated in § 32.1 and plume flow is studied in § 32.2.

    D̋ Layer

    The D̋ layer is both a thermal and dynamic feature of the lower-most mantle. It draws heat from the core via thermal conduction and advects heated mantle material toward the bases of plumes. This layer is maintained in a steady state with thermal diffusive thickening being balanced by a slow downward flow of mantle material into the layer to replace the heated material that is advected away. Since the viscosity of mantle material decreases strongly with temperature, the D ̋ layer has a double-layer structure, with the temperature adjusting across a thicker outer layer (roughly 150 km depth) and the viscosity and velocity adjusting in a thinner inner layer (roughly 20 km depth). In the following these two scales will be denoted by h with a suitable subscript: η for viscosity and T for temperature. In addition, we will encounter a third vertical scale, representing the temperature gradient at the core–mantle boundary.

  • Part IV - Waves 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 167-168

  • Summary

    Waves exist due to the presence of a restoring force. In Part III, we investigated a variety of waves that occur in the atmosphere, oceans and Earth's mantle due to the action of:

  • • compressibility (sound waves in § 9.3 and elastic compressive waves in § 10.1 and § 10.3);

  • • elastic rigidity (elastic transverse waves in § 10.2 and § 10.4);

  • • gravitation:

  • – at a single sharp interface (deep-water waves in Chapter 11 and shallow-water waves in Chapters 12 and 13);

  • – at two sharp interfaces (interfacial waves in § 14.2); and

  • – in a continuously stratified fluid (internal gravity waves in § 14.3); and

  • • surface tension (capillary waves in § 14.1).

    • If the fluid is rotating relative to an inertial frame of reference, the Coriolis force also acts as a restoring force and, as we shall see in this part, plays a crucial role in a number of types of waves. In fact, there is a bewildering array of waves because the Coriolis force comes in two flavors: f -plane and β-plane (see § 8.1.5) and can act alone or in conjunction with other effects, such as coastlines or bottom topography. In addition, the Coriolis force can modify the forms of some non-rotating waves, in effect creating new types of waves. So how can we make sense of all these? Let's begin our survey in Chapter 15 with an analysis of three “pure” rotating waves: geostrophic (f -plane), inertial and quasi-geostrophic (β-plane) waves.

    Following this introduction, we will investigate the effect of the Coriolis force on several of the waves we previously studied. Rotation affects those waves that persist for a day or more, while shorter-period (higher frequency) waves are unaffected. Those waves having compressibility, elasticity or surface tension as the restoring force have high frequency and are unaffected by rotation. However, interfacial, stratified and (occasionally) deep-water waves have sufficiently low frequencies to be affected by rotation; these modified waves are considered in Chapter 16.

  • 31 - Cooling the Mantle

  • 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 334-338

  • Summary

    Earth's mantle is cooled by the introduction of cold slabs. This plate-tectonic mode of cooling is somewhat unusual, as mantle convection in the other large terrestrial bodies in our solar system operates differently, as explained in § 31.1. Mantle convection acts to convey heat toward the surface at a rate greater than can be achieved by conduction alone. This rate is parameterized in § 31.3. This chapter concludes in § 31.4 with a simple model of the mantle thermal structure and a discussion in § 31.4.1 of slab divergence.

    Modes of Mantle Convection

    All planetary bodies in our solar system (and likely elsewhere) formed by accretion relatively quickly (≈ 10 million years or possibly less) and the associated gravitational energy released by this process led to a set of hot young planets. Ever since, these planets have been doing their best to cast this heat off to outer space as fast as they can. Convection of molten silicate is an efficient mode of cooling for a terrestrial planet; upwelling brings hot molten silicate material to the surface, where its heat can readily be radiated to outer space. Young planets with this mode of convection are in the magma-ocean phase. This state is fairly short-lived (several million years), as the surface temperature soon falls below the solidus temperature, and the mode of convection that ensues depend whether there is significant amounts of liquid water present or not. If little or no water is present, the planet transitions through three cooling modes having progressively weaker convection, weaker heat flow and lower temperatures. Fortuitously, since the rate of transitioning varying inversely with the size of the planet, we have good examples of each of these three modes within our own solar system:

  • • sluggish-lid convection (Venus): the surface is hot enough and convective motions are sufficiently vigorous to cause the surface to deform;

  • • rigid-lid convection (Mercury): the surface is sufficiently cold that convective motions are unable to cause it to deform and convection must occur beneath this rigid lid; and

  • • conduction (Moon): The rate of internal heating and global cooling are sufficiently small that heat is transferred entirely by conduction.

  • Part V - Non-Rotating Flows

  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 193-194

  • Summary

    We now shift our attention from rotating waves to simple, non-rotating one-dimensional flows.We begin the next phase of our journey in the following chapter with an orientation to one-dimensional flows. Following this orientation, the appropriate forms of the continuity and momentum equations that governing these flows are developed in § 19.1. These equations are applied to steady and un-steady flows in a horizontal channel in Chapters 20 and 21, respectively. In these preliminary studies the channel is horizontal, so gravity has no effect (other than to keep the fluid in the channel). In Chapter 22 we allow the channel to slope downward and investigate how this affects the flow of simple materials. Virtually all natural flows of water and air are turbulent; we develop a simple model of turbulent flows in Chapter 23 and then conclude this part by applying this model to some simple flows in Chapter 24.

  • Preface

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

  • Summary

    This monograph is the outgrowth of a set of notes that were prepared some years ago for a course that in fact never was taught. The notes lay fallow until the occasion of my 75th birthday, which inspired me to try to clean up my computer files. Upon discovering these notes, I consulted David Furbish regarding using these as the basis of a monograph on geophysical waves and flows. His encouraging response gave me the confidence to attempt to do so. This is the outcome of that endeavor.

    The goal of that course was – and of the current monograph is – to present a unified approach to geophysical waves and flows, starting from the simplest case and progressively adding complicating factors in a systematic manner. Simplest are sound waves that occur in air and water. Similar, but somewhat more complicated, are compressive body waves (P waves), transverse waves (S waves) and edge waves (Rayleigh and Love waves) in Earth's mantle. Seemingly similar, but dynamically distinct, is the fluid edge wave (think of ocean waves), occurring in both deep and shallow water. It is a short step from shallow-water waves to flows in a horizontal channel. Next, if the channel is sloping, we encounter gravitationally driven flow and this leads naturally to the study of turbulent flows. These topics are found in Chapters 9–13 and 19–23 of this monograph.

    In order to approach the analysis of waves and flows properly with a sound theoretical basis, we need to begin from square one, quantifying the manner in which a continuous body can move (kinematics), the nature of the forces that make it do so (dynamics) and the form of its response (rheology). These essential topics are covered in Chapters 3–7. Of course, rotation of Earth affects many types of waves and flows, so this subject is introduced in Chapter 8, with waves affected by rotation investigated in Chapters 15–18 and flows affected by rotation investigated in Chapters 25–28. It is interesting to compare and contrast the readily visible flows within the atmosphere and oceans to silicate flows occurring within Earth's mantle and in volcanoes; these latter flows are investigated in Chapters 29–35.

  • 3 - Kinematics of Deformation and Flow

  • 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 23-34

  • Summary

    We now turn our attention to the deformation and flow of a continuous body and in this chapter develop the concepts and mathematical expressions necessary for their quantification. We will be considering two types of body, elastic and fluid, depending on its behavior when subject to a non-hydrostatic or deviatoric stress (which we haven't defined yet). The displacement of an elastic body remains finite, while the displacement of a fluid body increases without bound. Whether a body behaves elastically and fluidly depends on several factors, including its composition, temperature and the state of stress. As a material is heated it tends to behave more like a fluid. And if the applied stresses are sufficiently great, a body will either begin to flow or break. Once a body has broken, it no longer is a continuous body and we would need a different mathematical formalism to describe its behavior.

    Deformation is used primarily in reference to elastic bodies, while flow typically refers to fluid bodies, but they are closely related. Deformation is quantified by the relative change of position, i.e., strain, while flow is quantified by the time rate of change of position, i.e., the rate of strain. Equations governing strain and rate of strain are developed in the following sections.

    Orientation to Kinematics

    The form of the kinematic constraint on deformation and flow depends whether the body is elastic or fluid. An elastic body is one that can resist applied forces without continuing displacement (that is, x can be independent of t), while a fluid body experiences continuous displacement unless the internal (contact) forces are of a particular form (hydrostatic). In either case, these bodies must deform such that the amount of mass is conserved, and no voids form. The constraints on the deformation of elastic bodies and the flow of fluid bodies are developed in § 3.3 and § 3.4, respectively, leading to separate versions of the equation of conservation of mass for elastic and fluid bodies. Two versions of the equation of conservation of mass arise in part because elastic and fluid bodies are observed differently.

  • 22 - Gravitationally Forced Flows

  • from Part V - Non-Rotating Flows
  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 218-226

  • Summary

    In the previous two chapters, we investigated the nature of flow in a horizontal channel assuming (except for the study of flash floods in § 21.4) resistance to flow is negligibly small, and we were able to classify flows as either sub- or super-critical and to investigate the smooth transition from sub- to super-critical and the abrupt transition from super- to sub-critical. We focused on the flow of water (as opposed to other fluids) because it has a very low value of viscosity and in many cases may be treated as inviscid. However, all real flows involve resistance which tends to degrade the mechanical energy. Typically channeled flows are maintained by the release of gravitational potential energy as the material moves downslope.

    In this chapter we consider the one-dimensional flow of a continuous material down a slope. The material might be water in a river, ice in a glacier, snow in an avalanche, debris in a rock slide, molten rock in a lava stream, mud in a landslide, muddy water in a turbidity current, etc. We will formulate the problem fairly generally in § 22.1, then specialize it to specific types of material in § 22.2.

    Formulation

    Most natural downslope flows, exemplified by rivers and glaciers, are much wider than they are deep and move along beds that are relatively flat. Typically a river is wider than deep by a factor of 100 (e.g., see Yalin, 1992). Also, rivers, glaciers and like flows typically are contained by banks that are raised and relatively steep. It follows that a first approximation of the flow bed is a shallow rectangle and that the velocity is independent of the cross-stream direction to dominant order.

    Let's consider flow of material in a straight, flat-bottomed channel (at z=0) of constant width; as previously, the downstream direction is x, the (unimportant) cross-stream direction is y and the (nearly) vertical direction is z. The height of the surface is represented by z = h(x, t). In this chapter we will focus on flows that are steady and invariant in the x direction, having h constant and v = u(z)1x. Our goal is to determine the vertical structure of the flow, u(z), driven by a down-gradient component of gravity.

  • 1 - Introduction

  • from 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 3-8

  • Summary

    This monograph is a survey of – and introduction to – the ways in which the atmosphere, oceans and various parts of the so-called solid Earth can deform and move. The most common type of deformation is a wave and the most common type of motion is flow. Our goals are to quantify and understand these deformations and motions. In order to achieve these goals, we will need to develop an appropriate set of procedures and tools.

    An appropriate procedure is mathematical modeling, which consists of three steps:

  • • Formulation of a mathematical model of a physical system. This is the crucial element in the procedure. If the model does not mimic the relevant physical processes, it will fail to yield useful results.

  • • Solution of the mathematical problem. This is the part stressed in most mathematics courses, but in fact is the most routine aspect of the procedure.

  • • Interpretation of the solution. This is the payoff; solution of a well-conceived model should yield new physical insight and make testable predictions.

    • We won't be following these steps formally, instead they will come naturally as we investigate each type of wave and flow.

    Our mathematical models will treat the physical system (that is, the portion of Earth under consideration) as a continuous body, using the mathematical apparatus of continuum mechanics. The concept of a continuous body is discussed in § 1.2. Continuum mechanics consists of three fundamental elements:

  • • Kinematics describes how bodies can move and deform. For example, it limits the types of deformation which leave a body competent (i.e., unfractured).

  • • Dynamics explains why bodies move and deform. They do so in response to external and internal forces, within the context of Newton's second law.

  • • Rheology quantifies the kinematic response to dynamic forces, taking into account the material properties of the body under investigation. Two identically shaped bodies, composed of water and of steel, respond quite differently to the same applied forces. Rheology encompasses the change of volume of a body induced by a change in pressure (compressive rheology) and the change of shape caused by a change in deviatoric stresses (shear rheology).

  • 11 - Deep-Water Waves

  • from Part III - Waves in Non-Rotating Fluids
  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 119-133

  • Summary

    Water waves are fluid edge waves; they also are called surface waves or gravity waves. These waves arise from a much different mechanism than do edge waves in elastic bodies. This is evident from the fact that water waves travel much more slowly than do sound waves. However, they do have the same basic structure as elastic edge waves: harmonic variation in the horizontal direction and exponential decay with depth. Water waves occur on and near the free surface; they cannot occur in a closed container. These waves occur because gravity acts to pull down the water that stands higher than average and push aside water lying beneath, as illustrated in Figure 11.1. This figure is a “snapshot”; the wave might be progressive (moving either to the left or right) or standing (with fixed nodes) or some combination of these two limiting cases.

    The adiabatic incompressibility and kinematic viscosity of water are K ≈2×109 Pa and ν ≈ 10-6 m2 ·s-1. The pressure at the bottom of a typical ocean, which is 4200 m deep, is about 4 ×107 Pa. This compresses water by about 2%. Since we are interested in surface waves, it is safe to treat water as completely incompressible. Viscous effects are important only near solid boundaries (and then only within thin boundary layers) or if the water is turbulent (as it is in breakers and whitecaps). So it is safe to treat water as inviscid in the study of non-breaking waves.

    Waves on open water are almost always progressive (i.e., moving in a certain direction). Standing waves occur when two progressive waves travel past each other in opposite directions, such as commonly occurs near a vertical breakwater. We will consider progressive waves in this chapter, with standing waves considered in § 12.3.

    We will find in § 11.1 that the equation governing motions within water is not the wave equation, but Laplace's equation.1 The wave character of the solution comes from the boundary conditions at the surface. These conditions are developed in § 11.2.

    Water Wave Equation

    As with sound and seismic waves, let's focus our attention on plane waves traveling in the x direction, with motion and variation in both the horizontal (x) and vertical (z) directions.

  • 24 - Some Non-Rotating Turbulent Flows

  • from Part V - Non-Rotating Flows
  • David E. Loper, Florida State University
  • Book:
    Geophysical Waves and Flows
    Published online:
    26 October 2017
    Print publication:
    26 October 2017, pp 242-250

  • Summary

    In this chapter we consider some non-rotating turbulent flows that are a bit more complicated than the flow of water down a slope considered in § 23.6. These include turbulent katabatic winds driven by thermal buoyancy (§ 24.1), avalanches driven by snow suspended in air (§ 24.2) and cumulonimbus clouds driven by the release of latent heat as water vapor condenses (§ 24.3).

    Turbulent Katabatic Winds

    In § 22.2.5, we investigate the katabatic wind down a slope in the case that the flow is laminar and, using typical parameter values, found that the flow is very likely turbulent rather than laminar. When flow is turbulent, the diffusivity coefficients for momentum and heat are not constant, but instead vary linearly with elevation. In this section, we will revisit the problem formulated in § 22.2.5, but with variable diffusivities, using Reynolds analogy to set the turbulent thermal diffusivity equal to the turbulent diffusivity of momentum.1

    The governing equations now are

    where z is elevation above the ground, u is the downslope speed, is the dimensionless perturbation temperature, is the reduced gravity, s the down-slope thermal gradient, is the temperature contrast, is the turbulent diffusivity, is a small dimensionless parameter is the velocity scale and is the roughness scale. As before, these equations are to be solved on the domain subject to the conditions u And as before, we can combine the two equations into a single complex equation, although the scalings are somewhat different. In the present case

    while the complex equation for W= T ∗ −iu/U is

    where is the dimensionless vertical distance and is the scaled boundary roughness, subject to conditions W(0) = 1 and W(∞) = 0.

    The problem for the turbulent katabatic winds is a bit more challenging than for the laminar winds because our complex ordinary differential equation now has a variable coefficient. We can get this equation in “standard” form by introducing a new independent variable; let

  • Guadalupian cool versus warm water deposits in central Iran: a record of the Capitanian Kamura event

  • SAKINEH AREFIFARD
  • Journal:
    Geological Magazine / Volume 156 / Issue 3 / March 2019
    Published online by Cambridge University Press:
    26 October 2017, pp. 430-446

  • An integration of geochemical and grain association studies were carried out on Middle Permian deposits in central Iran where both cool and warm water carbonates are found. The recrystallization of most bioclasts, lime-mud matrix and ooids along with high Sr contents suggests a probable original aragonite mineralogy for carbonates of the Middle Permian Jamal Formation at the Shotori section. Low bulk carbonate δ18O values imply pervasive diagenetic alteration in this section. Conversely, Middle Permian deposits at the correlative Bagh-e Vang section have a probable calcite precursor supported by low Sr contents and no evidence of recrystallization. This mineralogical variation in these coeval carbonates is considered to be due to the change in depth and temperature of the depositional palaeoenvironment. δ13C values started to rise over 2 ‰ PDB and reached a maximum of 4.3 ‰ PDB at the Wordian–Capitanian boundary at the Bagh-e Vang section. This δ13C rise is attributed to high primary productivity as previously reported in the Capitanian Abadeh Formation in central Iran. The positive δ13C excursion in these sections is correlated with the Capitanian ‘Kamura event’ identified from the mid-Panthalassian sections in Japan. No noticeable positive excursion occurs in the δ13C plot at the Shotori section making the interpretation of palaeo-productivity difficult. It is suggested that an active oceanic upwelling was the probable driver of the Middle Permian oceanic productivity in central Iran. Remarkable negative δ13C excursions around 3.7 and 4.2 ‰ PDB in Capitanian carbonates close to the Guadalupian–Lopingian boundary at the Bagh-e Vang and Abadeh sections, respectively are recorded, which are a proxy for low palaeo-productivity and a transition from a cool to warm climate, consistent with an early Lopingian sea level rise.

  • 35 - Lava Flows

  • 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 367-378

  • Summary

    Commonly andesitic and rhyolitic magmas rise up discrete conduits, whereas basaltic magma often – at least during the early stages of an eruption phase – rises to the surface through a magmatic dike (also called a rift or fissure): a linear crack extending from a magma chamber at depth to the surface. Typically as magma erupts from a dike, outgassed volatiles (mainly water) produce a linear fire fountain composed of incandescent blobs of lava.

    After magma reaches the surface, its subsequent behavior depends largely whether the eruption is effusive or explosive. A discussion of the possible styles of lava flow is found in Griffiths (2000). Effusive eruptions lead to the production of lava which flows relatively gently downslope, initially in the form of a planar sheet. We will consider a simple model of lava sheet flow in the following section.

    On the other hand, explosive eruptions display a variety of behaviors depending on the speed, mass flow and composition of the erupting magma. Some of these behaviors are explored in § 35.2.

    Lava Sheet Flow

    In this section we will develop a simple model of subaerial (that is, on land, as opposed to under the sea) lava sheet flow: a sheet of hot basaltic lava flowing steadily down a slope (in the x direction) from a magmatic dike.

    Our simple model will ignore

  • • variations in topography;

  • • horizontal variations in the lava surface;

  • • fluid inertia;

  • • loss of heat to the ground;

  • • radiative cooling;

  • • variations in the ambient temperature;

  • • effects of rain;

  • • the dynamic effect of crystals suspended in the liquid lava;

  • • buoyancy effects; and

  • • variations of thermal conductivity with temperature.

    • In order to simplify the analysis further, we will assume that the cool upper layer of lava is rafted along with the flow, rather than being anchored to the ground at the sides. The weight of this rafted layer is borne by the liquid beneath, so that there is a vertical hydrostatic balance. This rafted layer may deform as needed in order to adjust to the flow of the liquid beneath.

Page 93 of 1575