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:
“Return to your home, and declare how much God has done for you.”
—Bible: New Testament, Luke 8:39.
Jesus to one healed of demons.
“As in an icicle the agnostic abides alone. The vital principle is taken out of all endeavor for improving himself or bettering his fellows. All hope in the grand possibilities of life are blasted.”
—Anna Julia Cooper (1859–1964)