Brooke Benjamin

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Thomas Brooke Benjamin (born April 15, 1929 in Wallasey , † August 16, 1995 in Oxford ) was a British applied mathematician who deals with nonlinear partial differential equations, especially hydrodynamics .

The son of a lawyer, he went to school in Wallasey and in Wales during World War II, interrupted by diabetes. From 1947 he studied engineering in Liverpool, where he was also active in various orchestras (including co-founder and often conductor of the Liverpool Mozart Orchestra). After graduation in 1950, he studied at Yale University with a master's degree in 1952 and at Cambridge University (King's College), where he studied electronics and hydraulics (he was fascinated by the hydraulics laboratory under Alfred Maurice Binnie ). He received his PhD with a dissertation examining cavitation using high-speed photography and became a fellow of his college in 1955. He also published with Michael James Lighthill on surface acoustic waves (where they achieved the same results independently and then jointly published). In it they formulated a hypothesis named after them about surface waves in liquids (Benjamin Lighthill Hypothesis). In 1958 he became deputy research director (a post created especially for him at the interface between the engineering faculty and applied mathematics), helped set up the hydrodynamics laboratory in Cambridge in 1964 and became a reader in 1967 . In 1970 he became director of the Fluid Mechanics Research Institute at the University of Essex . There he also directed the university choir. In 1979 he became Sedleian Professor at Oxford University and Fellow of Queen's College. In 1995 he retired.

With his post-doctoral student Jerry Bona , he developed the Benjamin – Bona – Mahony equation (BBM) in 1972 as a model for long-range gravity waves of small amplitude. The Benjamin-Ono equation is named after him and H. Ono . Other special hydrodynamic problems he dealt with were cavitation with application to damage to ship propellers, avalanche-like internal waves in oceans, swirling flow, Taylor-Couette flow , vortex formation and interaction with airplane wings, flow in channels with rigid obstacles and dynamic interaction of the Skin of dolphins and submarines with turbulence and how this increases their speed and silence. He later went on to general questions about the existence of certain forms of flow, which he treated with abstract mathematical methods, on which the Russian school also did fundamentals at that time, and also used numerical calculations on the computer early on. At Cambridge he was part of the group of theorists in hydrodynamics led by Geoffrey Ingram Taylor and George Keith Batchelor . But he also undertook experimental work.

In 1964 he and his student Jim Feir investigated the most sinusoidal water waves in a tank and discovered their instability against the generation of higher harmonics (Benjamin Feir sideband instability of steep water waves).

He was a frequent visiting professor at the University of Pennsylvania.

He was a Fellow of the Royal Society (1966), was its Vice President in 1990/91 and gave the Bakerian Lecture in 1992 . In 1992 he became a member of the Académie des Sciences . He has received honorary degrees from Bath University, Brunel University and Liverpool University. Benjamin was President of the UK National Conference of University Professors and supported international cooperation with developing countries such as the International Center for Theoretical Physics in Trieste, founded by Abdus Salam .

Fonts

  • with MJ Lighthill: On cnoidal waves and bores. Proc. R. Soc. Lond. A 224, 1954, pp. 448-460 (Benjamin-Lighthill conjecture).
  • On the flow in channels when rigid obstacles are placed in the stream, Journal of Fluid Mechanics, Volume 1, 1956, pp. 227-248
  • Shearing flow over a wavy boundary, J. Fluid Mechanics, Volume 6, 1959, pp. 161-205
  • Instability of periodic wavetrains in nonlinear dispersive systems, Proc. Roy. Soc. A, Vol. 299, 1967, pp. 59-75
  • with JE Feir: The disintegration of wave trains on deep water, Part 1 (Theory), J. Fluid Mech., Volume 27, 1967, pp. 417-430
  • Internal waves of permanent form in fluids of great depth. J. Fluid Mech, Volume 29, 1967, pp. 559-562 (Benjamin-Ono equation)
  • with J. Bona, JJ Mahony: Model Equations for Long Waves in Nonlinear Dispersive Systems, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 272, 1972, pp. 47-78 (BBM equation)
  • Verification of the Benjamin-Lighthill conjecture about steady water waves, J. Fluid Mech., Vol. 295, 1995, pp. 337-356.

Web links

Individual evidence

  1. ↑ Consider a uniform flow in a channel of finite depth and free surface (rotation-free, incompressible). The movement of the liquid can be described by a flow function that satisfies the Laplace equation and the Bernoulli equation with Bernoulli's constant R (with the boundary condition that it disappears at the bottom of the channel). Let Q be the volume flow and S the flow force. Then, according to Benjamin and Lighthill's conjecture, the uniform wave train is determined by Q, R, S.
  2. ↑ Benjamin-Feir instability , Encyclopedia of Mathematics, Springer
personal data
SURNAME Benjamin, Brooke
ALTERNATIVE NAMES Benjamin, Thomas Brooke
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH April 15, 1929
PLACE OF BIRTH Wallasey
DATE OF DEATH August 16, 1995
Place of death Oxford