William McFadden Orr

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William McFadden Orr (born May 2, 1866 in Ballystockhart , County Down , † August 14, 1934 in Douglas , Isle of Man ) was a Northern Irish-British applied mathematician .

Orr, the son of a farmer and Protestant, attended the Methodist College in Belfast and studied at the Queen's College with the completion in 1885 and at St John's College of the University of Cambridge , where he student of Joseph Larmor was, with whom he was friends afterwards. In 1888 he received a bachelor's degree. In the second part of the Tripos exams , he became Senior Wrangler in 1889 (i.e. best of his class) and in 1891 became a Fellow of his college in Cambridge after working on Feuerbach circles . In 1892 he became Professor of Mathematics at the Royal College of Science for Ireland in Dublin and Professor of Mathematics and Applied Mathematics when the Royal College of Science was merged with Trinity College to form University College Dublin in 1926 . Orr was heavily involved in teaching there, about which he complained in a letter to Larmor. In 1933 he retired.

He is known for linear stability studies on hydrodynamics in linear approximation, such as the Orr-Sommerfeld equations named after him and Arnold Sommerfeld . It describes the flow of a viscous liquid (described by the non-linear Navier-Stokes equation ) near a wall. In addition, the two-dimensional case and the case of small perturbations in a linear approximation ( linear stability theory ) are considered. Orr and Sommerfeld investigated the stability for different velocity profiles of the flow near a wall or in pipes. For example, Couette flow, where the velocity increases linearly from zero at the wall and where the linear stability analysis gives stability for all Reynolds numbers , or a profile like the Hagen-Poiseuille flow , where the linear stability analysis shows instability above a certain level, are investigated Reynolds number. The analysis is only valid in a linear approximation, and so, for example, with the Couette flow in the experiment, although it should actually be stable according to Orr-Sommerfeld, it collapses above a certain amplitude.

In addition, he published about special functions in analysis and various mechanical problems, such as the precession and nutation (i.e. the rotational movements as a rigid body) of a sphere filled with a frictionless liquid (whereby in applications, for example, the earth's body was thought of) Lord Kelvin had treated. Orr discovered errors in treatment at Kelvin in 1898 (as did Henri Poincaré in 1901). Orr also published on thermodynamics.

Orr was a Fellow of the Royal Society from 1909 . In 1892 he married Elizabeth Campbell and had three daughters with her.

Fonts

  • The stability or instability of the steady motions of a liquid, 2 parts, Proceedings of the Royal Irish Academy, Series A, Volume. 27, 1927, pp. 9-68, 69-138

Web links

Individual evidence

  1. ↑ Sommerfeld, A Contribution to the Hydrodynamic Explanation of Turbulent Fluid Movements, Proceedings of the 4th International Congress of Mathematicians, Rome, 1908, Volume 3, pp. 116-124
personal data
SURNAME Orr, William McFadden
BRIEF DESCRIPTION Irish-British mathematician
DATE OF BIRTH May 2, 1866
PLACE OF BIRTH Ballystockhart , County Down
DATE OF DEATH August 14, 1934
Place of death Douglas , Isle of Man