In fluid dynamics, Luke's variational principle is a Lagrangian variational description of the motion of surface waves on a fluid with a free surface, under the action of gravity. This principle is named after J.C. Luke, who published it in 1967. This variational principle is for incompressible and inviscid potential flows, and is used to derive approximate wave models like the so-called mild-slope equation, or using the average-Lagrangian approach for wave propagation in inhomogeneous media.
Luke's Lagrangian formulation can also be recast into a Hamiltonian formulation in terms of the surface elevation and velocity potential at the free surface. This is often used when modelling the spectral density evolution of the free-surface in a sea state, sometimes called wave turbulence.
Both the Lagrangian and Hamiltonian formulations can be extended to include surface tension effects.
Read more about Luke's Variational Principle: Luke's Lagrangian, Hamiltonian Formulation
Famous quotes containing the words luke and/or principle:
“Then the owner of the house became angry and said to his slave, Go out at once into the streets and lanes of the town and bring in the poor, the crippled, the blind, and the lame.’”
—Bible: New Testament, Luke 14:21.
“Well, you Yankees and your holy principle about savin’ the Union. You’re plunderin’ pirates that’s what. Well, you think there’s no Confederate army where you’re goin’. You think our boys are asleep down here. Well, they’ll catch up to you and they’ll cut you to pieces you, you nameless, fatherless scum. I wish I could be there to see it.”
—John Lee Mahin (1902–1984)