*Anatoly I. Ruban*

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780199681754
- eISBN:
- 9780191761621
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199681754.003.0006
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Chapter 5 discusses the ‘short separation bubble’ that forms at the leading edge of an aerofoil when the angle of attack reaches a certain value. It then suggests that the process of the formation of ...
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Chapter 5 discusses the ‘short separation bubble’ that forms at the leading edge of an aerofoil when the angle of attack reaches a certain value. It then suggests that the process of the formation of the bubble is described by the Marginal Separation theory, which represents a special version of the triple-deck theory. It then covers how, in this case, the viscous-inviscid interaction problem may be reduced to an integro-differential equation for the skin friction. It discusses how by solving this equation not only the transition from attached to separated flow in the boundary layer be predicted, but also the well-known phenomenon of the ‘bubble bursting’ that leads to a sudden loss of the lift produced by an aerofoil.Less

Chapter 5 discusses the ‘short separation bubble’ that forms at the leading edge of an aerofoil when the angle of attack reaches a certain value. It then suggests that the process of the formation of the bubble is described by the Marginal Separation theory, which represents a special version of the triple-deck theory. It then covers how, in this case, the viscous-inviscid interaction problem may be reduced to an integro-differential equation for the skin friction. It discusses how by solving this equation not only the transition from attached to separated flow in the boundary layer be predicted, but also the well-known phenomenon of the ‘bubble bursting’ that leads to a sudden loss of the lift produced by an aerofoil.

*Bahram Mashhoon*

- Published in print:
- 2017
- Published Online:
- July 2017
- ISBN:
- 9780198803805
- eISBN:
- 9780191842313
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198803805.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

In extended general relativity (GR), Einstein’s field equation of GR can be expressed in terms of torsion and this leads to the teleparallel equivalent of GR, namely, GR||, which turns out to be the ...
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In extended general relativity (GR), Einstein’s field equation of GR can be expressed in terms of torsion and this leads to the teleparallel equivalent of GR, namely, GR||, which turns out to be the gauge theory of the Abelian group of spacetime translations. The structure of this theory resembles Maxwell’s electrodynamics. We use this analogy and the world function to develop a nonlocal GR|| via the introduction of a causal scalar constitutive kernel. It is possible to express the nonlocal gravitational field equation as modified Einstein’s equation. In this nonlocal gravity (NLG) theory, the gravitational field is local, but satisfies a partial integro-differential field equation. The field equation of NLG can be expressed as Einstein’s field equation with an extra source that has the interpretation of the effective dark matter. It is possible that the kernel of NLG, which is largely undetermined, could be derived from a more general future theory.Less

In extended general relativity (GR), Einstein’s field equation of GR can be expressed in terms of torsion and this leads to the teleparallel equivalent of GR, namely, GR||, which turns out to be the gauge theory of the Abelian group of spacetime translations. The structure of this theory resembles Maxwell’s electrodynamics. We use this analogy and the *world function* to develop a nonlocal GR|| via the introduction of a causal scalar constitutive kernel. It is possible to express the nonlocal gravitational field equation as modified Einstein’s equation. In this *nonlocal gravity* (NLG) theory, the gravitational field is local, but satisfies a partial integro-differential field equation. The field equation of NLG can be expressed as Einstein’s field equation with an extra source that has the interpretation of the *effective dark matter*. It is possible that the kernel of NLG, which is largely undetermined, could be derived from a more general future theory.