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8124 results in Fluid dynamics and solid mechanics

Page 86 of 407

  • 7 - Long-Wave Theories, 1: Lubrication Theory and Related Techniques

  • Neil M. Ribe, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book:
    Theoretical Mantle Dynamics
    Published online:
    20 September 2018
    Print publication:
    04 October 2018, pp 121-146

  • Summary

    Chapter 7 is the first of two chapters on long-wave theories for flow in thin layers. The focus is on lubrication theory and related techniques. The examples treated include the spread of viscous gravity currents, plume-plate and plume-ridge interaction, thermal boundary layer instability, effective boundary conditions from thin-layer flows, and conduit solitary waves.

  • 10 - Hydrodynamic Stability and Thermal Convection

  • Neil M. Ribe, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book:
    Theoretical Mantle Dynamics
    Published online:
    20 September 2018
    Print publication:
    04 October 2018, pp 192-218

  • Summary

    Chapter 10 discusses the broad field of hydrodynamic stability using two examples: the Rayleigh-Taylor instability, and Rayleigh-Benard convection. Linear stability analyses of both are performed, followed by derivations of several types of order-parameter equations for finite-amplitude Rayleigh-Benard convection. Finally, convection at high Rayleigh number is studied using scaling analysis and boundary-layer theory.

  • 4 - Slow Viscous Flow

  • Neil M. Ribe, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book:
    Theoretical Mantle Dynamics
    Published online:
    20 September 2018
    Print publication:
    04 October 2018, pp 33-85

  • Summary

    Chapter 4 treats the broad field of slow (creeping) viscous flow, with emphasis on the special case of Stokes flow (= linearized slow viscous flow). Topics include reversibility and dissipation theorems; potential representations; classical exact solutions including corner flow; superposition and eigenfunction expansion methods; singular solutions and the boundary-integral representation; slender-body theory; and flow in a spherical annulus due to internal loads.

  • 6 - Boundary-Layer Theory

  • Neil M. Ribe, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book:
    Theoretical Mantle Dynamics
    Published online:
    20 September 2018
    Print publication:
    04 October 2018, pp 96-120

  • Summary

    Chapter 6 introduces the theory of thermal boundary layers. Different methods for solving the boundary-layer equations are discussed, including variable transformations and the method of matched asymptotic expansions. The problem of a plume from a point source of heat is treated both for constant viscosity and temperature-dependent viscosity.

  • 2 - Dimensional and Scaling Analysis

  • Neil M. Ribe, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book:
    Theoretical Mantle Dynamics
    Published online:
    20 September 2018
    Print publication:
    04 October 2018, pp 9-21

  • Summary

    Chapter 2 introduces dimensional analysis and scaling analysis, two general techniques for obtaining insight into how some parameter of interest depends on the other parameters defining the problem at hand. Two methods of dimensional analysis are discussed: Buckingham's Pi-theorem, and nondimensionalisation of the governing equations. Scaling analysis is illustrated using the example of heat transfer from a hot sphere moving in a viscous fluid.

  • 9 - Theory of Two-Phase Flow

  • Neil M. Ribe, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book:
    Theoretical Mantle Dynamics
    Published online:
    20 September 2018
    Print publication:
    04 October 2018, pp 175-191

  • Summary

    Chapter 9 presents the theory of flow in media comprising two rheologically distinct phases, with particular application to partially molten rocks. The equations for conservation of mass, momentum and energy in partially molten systems are derived, and solved for two simple one-dimensional model problems (gravitational compaction and magma solitary waves).

  • 8 - Long-Wave Theories, 2: Shells, Plates and Sheets

  • Neil M. Ribe, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book:
    Theoretical Mantle Dynamics
    Published online:
    20 September 2018
    Print publication:
    04 October 2018, pp 147-174

  • Summary

    Chapter 8 introduces the theories of thin viscous sheets and elastic shells. These objects differ from the thin layers of Chapter 7 in being freely deformable and capable of large changes of shape. The theory of thin viscous sheets with arbitrary curvature is first developed in general nonorthogonal coordinates, after which the theory of elastic shells in lines-of-curvature coordinates is presented and several geodynamical applications discussed. The chapter closes with a discussion of immersed viscous sheets with application to subduction.

Gas Turbines
  • Internal Flow Systems Modeling
  • Bijay Sultanian
  • Published online:
    25 September 2018
    Print publication:
    13 September 2018
  • This long-awaited, physics-first and design-oriented text describes and explains the underlying flow and heat transfer theory of secondary air systems. An applications-oriented focus throughout the book provides the reader with robust solution techniques, state-of-the-art three-dimensional computational fluid dynamics (CFD) methodologies, and examples of compressible flow network modeling. It clearly explains elusive concepts of windage, non-isentropic generalized vortex, Ekman boundary layer, rotor disk pumping, and centrifugally-driven buoyant convection associated with gas turbine secondary flow systems featuring rotation. The book employs physics-based, design-oriented methodology to compute windage and swirl distributions in a complex rotor cavity formed by surfaces with arbitrary rotation, counter-rotation, and no rotation. This text will be a valuable tool for aircraft engine and industrial gas turbine design engineers as well as graduate students enrolled in advanced special topics courses.

  • THE CONTROLLER DESIGN FOR SINGULAR FRACTIONAL-ORDER SYSTEMS WITH FRACTIONAL ORDER 0 <α< 1

  • Part of
  • T. ZHAN, S. P. MA
  • Journal:
    The ANZIAM Journal / Volume 60 / Issue 2 / October 2018
    Published online by Cambridge University Press:
    25 September 2018, pp. 230-248
    • Article
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  • We study the problem of pseudostate and static output feedback stabilization for singular fractional-order linear systems with fractional order $\unicode[STIX]{x1D6FC}$ when $0<\unicode[STIX]{x1D6FC}<1$. All the results are given by linear matrix inequalities. First, a new sufficient and necessary condition for the admissibility of singular fractional-order systems is presented. Then based on the admissible result, not only are sufficient conditions for designing pseudostate and static output feedback controllers obtained, but also sufficient and necessary conditions are presented by using different methods that guarantee the admissibility of the closed-loop systems. Finally, the effectiveness of the proposed approach is demonstrated by numerical simulations and a real-world example.

Theoretical Mantle Dynamics
  • Neil M. Ribe
  • Published online:
    20 September 2018
    Print publication:
    04 October 2018
  • Geodynamics is the study of the deformation and flow of the solid Earth and other planetary interiors. Focusing on the Earth's mantle, this book provides a comprehensive, mathematically advanced treatment of the continuum mechanics of mantle processes and the craft of formulating geodynamical models to approximate them. Topics covered include slow viscous flow, elasticity and viscoelasticity, boundary-layer theory, long-wave theories including lubrication theory and shell theory, two-phase flow, and hydrodynamic stability and thermal convection. A unifying theme is the utility of powerful general methods (dimensional analysis, scaling analysis, and asymptotic analysis) that can be applied in many specific contexts. Featuring abundant exercises with worked solutions for graduate students and researchers, this book will make a useful resource for Earth scientists and applied mathematicians with an interest in mantle dynamics and geodynamics more broadly.

Page 86 of 407