Luke's Variational Principle

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:

    But they had no children, because Elizabeth was barren, and both were getting on in years.
    Bible: New Testament, Luke 1:7.

    The mode of founding a college is, commonly, to get up a subscription of dollars and cents, and then, following blindly the principles of a division of labor to its extreme,—a principle which should never be followed but with circumspection,—to call in a contractor who makes this a subject of speculation,... and for these oversights successive generations have to pay.
    Henry David Thoreau (1817–1862)