In this article we take a look at group velocity and at the extraction of the envelope of a wave packet using the ideas of the Hilbert transform.
Posts Tagged 'Geophysics'
Waves Packed in Envelopes
Published April 26, 2018 Occasional Leave a CommentTags: Fluid Dynamics, Geophysics, Wave Motion
Geodesics on the Spheroidal Earth-II
Published April 19, 2018 Irish Times Leave a CommentTags: Geometry, Geophysics, Navigation, Pythagoras
Geodesy is the study of the shape and size of the Earth, and of variations in its gravitational field. The Earth was originally believed to be flat, but many clues, such as the manner in which ships appear and disappear at the horizon, and the changed perspective from an elevated vantage point, as well as astronomical phenomena, convinced savants of its spherical shape. In the third century BC, Eratosthenes accurately estimated the circumference of the Earth [TM137 or search for “thatsmaths” at irishtimes.com].
Geodesic at bearing of 60 degrees from Singapore. Passes close to Quito, Ecuador. Note that it is not a closed curve: it does not return to Singapore.
Geodesics on the Spheroidal Earth – I
Published April 12, 2018 Occasional Leave a CommentTags: Geometry, Geophysics, Navigation, Pythagoras
Both Quito in Ecuador and Singapore are on the Equator. One can fly due eastward from Singapore and reach Quito in due course. However, this is not the shortest route. The equatorial trans-Pacific route from Singapore to Quito is not a geodesic on Earth! Why not?
A drastically flattened spheroid. Clearly, the equatorial route between the blue and red points is not the shortest path.
Staying Put or Going with the Flow
Published February 1, 2018 Irish Times Leave a CommentTags: Algorithms, Geophysics, Numerical Analysis
The atmospheric temperature at a fixed spot may change in two ways. First, heat sources or sinks may increase or decrease the thermal energy; for example, sunshine may warm the air or radiation at night may cool it. Second, warmer or cooler air may be transported to the spot by the air flow in a process called advection. Normally, the two mechanisms act together, sometimes negating and sometimes reinforcing each other. What is true for temperature is also true for other quantities: pressure, density, humidity and even the flow velocity itself. This last effect may be described by saying that “the wind blows the wind” [TM132 or search for “thatsmaths” at irishtimes.com].
Hurricane Ophelia approaching Ireland, 16 October 2017, 1200Z. Image from https://earth.nullschool.net/
Energy Cascades in Van Gogh’s Starry Night
Published January 4, 2018 Irish Times Leave a CommentTags: Fluid Dynamics, Geophysics
“Big whirls have little whirls that feed on their velocity,
And little whirls have lesser whirls, and so on to viscosity.“
We are all familiar with the measurement of speed, the distance travelled in a given time. Allowing for the direction as well as the magnitude of movement, we get velocity, a vector quantity. In the flow of a viscous fluid, such as treacle pouring off a spoon, the velocity is smooth and steady. Such flow is called laminar, and variations of velocity from place to place are small. By contrast, the motion of the atmosphere, a fluid with low viscosity, can be irregular and rapidly fluctuating. We experience this when out and about on a gusty day. Such chaotic fluid flow is called turbulence, and this topic continues to challenge the most brilliant scientists [TM130 or search for “thatsmaths” at irishtimes.com].
Vincent Van Gogh’s Starry Night.
Continue reading ‘Energy Cascades in Van Gogh’s Starry Night’
Inertial Oscillations and Phugoid Flight
Published July 13, 2017 Occasional Leave a CommentTags: Applied Maths, Fluid Dynamics, Geophysics
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].
The Water is Rising Fast
Published April 20, 2017 Irish Times Leave a CommentTags: Fluid Dynamics, Geophysics
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 irishtimes.com].
Mean Sea level in Seattle from 1900 to 2013
