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1737 results in Nonlinear Science and Fluid Dynamics

Page 10 of 87

  • 2 - Ideal Fluid Flow

  • from Part I - Inviscid Flow
  • Frank H. Berkshire, Imperial College of Science, Technology and Medicine, London, Simon J. A. Malham, Heriot-Watt University, Edinburgh, J. Trevor Stuart, Imperial College of Science, Technology and Medicine, London
  • Book:
    Introductory Incompressible Fluid Mechanics
    Published online:
    05 January 2022
    Print publication:
    02 December 2021, pp 27-99

  • Summary

    Let us consider the forces that act on a small parcel of fluid in a fluid flow. There are two types:

    1. 1. External or body forces, these may be due to gravity or external electromagnetic fields. They exert a force per unit volume on the continuum.

    2. 2. Surface or stress forces, these are forces, molecular in origin, that are applied by the neighbouring fluid across the surface of the fluid parcel.

    The surface or stress forces are normal stresses and tangential or shear stresses. In this chapter we only include the stress forces across the fluid parcels due to pressure differentials, representing a specific component of the normal stresses, and we entirely ignore the shear stresses. In other words, we leave out the stress components essentially resulting from molecular diffusion. This is what defines ideal fluid flow.

  • 6 - Boundary-Layer Theory

  • from Part II - Viscous Flow
  • Frank H. Berkshire, Imperial College of Science, Technology and Medicine, London, Simon J. A. Malham, Heriot-Watt University, Edinburgh, J. Trevor Stuart, Imperial College of Science, Technology and Medicine, London
  • Book:
    Introductory Incompressible Fluid Mechanics
    Published online:
    05 January 2022
    Print publication:
    02 December 2021, pp 223-252

  • Summary

    The Reynolds numbers associated with flows past aircraft or ships are typically large, indeed of the order of 108 of 109; recall Remark 4.36 and . For individual wings or fins, the Reynolds number may be an order of magnitude or two smaller. However, such Reynolds numbers are still large and the flow around a wing for example is well approximated by Euler flow. We can imagine the flow over the top of the wing of an aircraft has a high relative velocity tangential to the surface wing directed towards the rear edge of the wing.

  • 1 - Flow and Transport

  • from Part I - Inviscid Flow
  • Frank H. Berkshire, Imperial College of Science, Technology and Medicine, London, Simon J. A. Malham, Heriot-Watt University, Edinburgh, J. Trevor Stuart, Imperial College of Science, Technology and Medicine, London
  • Book:
    Introductory Incompressible Fluid Mechanics
    Published online:
    05 January 2022
    Print publication:
    02 December 2021, pp 3-26

  • Summary

    A material exhibits flow if shear forces, however small, lead to a deformation which is unbounded – we could use this as a definition of a fluid. A solid has a fixed shape, or at least a strong limitation on its deformation when force is applied to it. Within the category of ‘fluids’, we include liquids and gases. The main distinguishing feature between these two fluids is the notion of compressibility. Gases are usually compressible – as we know from everyday aerosols. Liquids are generally incompressible – a feature essential to all modern car brakes. However, some gas flows can also be incompressible, particularly at low speeds.

Introduction to Turbulent Transport of Particles, Temperature and Magnetic Fields
  • Analytical Methods for Physicists and Engineers
  • Igor Rogachevskii
  • Published online:
    10 September 2021
    Print publication:
    05 August 2021
  • Turbulence and the associated turbulent transport of scalar and vector fields is a classical physics problem that has dazzled scientists for over a century, yet many fundamental questions remain. Igor Rogachevskii, in this concise book, systematically applies various analytical methods to the turbulent transfer of temperature, particles and magnetic field. Introducing key concepts in turbulent transport including essential physics principles and statistical tools, this interdisciplinary book is suitable for a range of readers such as theoretical physicists, astrophysicists, geophysicists, plasma physicists, and researchers in fluid mechanics and related topics in engineering. With an overview to various analytical methods such as mean-field approach, dimensional analysis, multi-scale approach, quasi-linear approach, spectral tau approach, path-integral approach and analysis based on budget equations, it is also an accessible reference tool for advanced graduates, PhD students and researchers.

Page 10 of 87