Posts Tagged 'Fluid Dynamics'

Inertial Oscillations and Phugoid Flight

The English aviation pioneer Frederick Lanchester (1868–1946) introduced many important contributions to aerodynamics. He analysed the motion of an aircraft under various consitions of lift and drag. He introduced the term “phugoid” to describe aircraft motion in which the aircraft alternately climbs and descends, varying about straight and level flight. This is one of the basic modes of aircraft dynamics, and is clearly illustrated by the flight of gliders.


Glider in phugoid loop [photograph by Dave Jones on website of Dave Harrison]

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The Water is Rising Fast

Seventy percent of the Earth is covered by water and three quarters of the world’s great cities are on the coast. Ever-rising sea levels pose a real threat to more than a billion people living beside the sea. As the climate warms, this is becoming a greater threat every year [TM113 or search for “thatsmaths” at].


Mean Sea level in Seattle from 1900 to 2013

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Thank Heaven for Turbulence

The chaotic flow of water cascading down a mountainside is known as turbulence. It is complex, irregular and unpredictable, but we should count our blessings that it exists. Without turbulence, we would gasp for breath, struggling to absorb oxygen or be asphyxiated by the noxious fumes belching from motorcars, since pollutants would not be dispersed through the atmosphere [TM101, or search for “thatsmaths” at].


Turbulent flow behind a cylindrical obstacle [image from “An Album of Fluid Motion”, Milton Van Dyke, 1982].

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Modelling Rogue Waves


Rogue wave [image from BBC Horizons, 2002]

There are many eyewitness accounts by mariners of gigantic waves – almost vertical walls of water towering over ocean-going ships – that appear from nowhere and do great damage, sometimes destroying large vessels completely. Oceanographers, who have had no way of explaining these ‘rogue waves’, have in the past been dismissive of these reports [TM090, or search for “thatsmaths” at].

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Richardson’s Fantastic Forecast Factory

Modern weather forecasts are made by calculating solutions of the mathematical equations that express the fundamental physical principles governing the atmosphere  [TM083, or search for “thatsmaths” at]

The solutions are generated by complex simulation models with millions of lines of code, implemented on powerful computer equipment. The meteorologist uses the computer predictions to produce localised forecasts and guidance for specialised applications.


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The Flight of a Golf Ball

Golf balls fly further today, thanks to new materials and mathematical design. They are a triumph of chemical engineering and aerodynamics. They are also big business, and close to a billion balls are sold every year. [TM081: search for “thatsmaths” at Irish Times ].


Simulation of flow around the dimples of a golf ball. Image from

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Life’s a Drag Crisis

The character of fluid flow depends on a dimensionless quantity, the Reynolds number. Named for Belfast-born scientist Osborne Reynolds, it determines whether the flow is laminar (smooth) or turbulent (rough). Normally the drag force increases with speed.

The Reynolds number is defined as Re = VL/ν where V is the flow speed, L the length scale and ν the viscosity coefficient. The transition from laminar to turbulent flow occurs at a critical value of Re which depends on details of the system, such as surface roughness.

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