In continuum mechanics, Whitham's averaged Lagrangian method – or in short Whitham's method – is used to study the Lagrangian dynamics of slowly-varying wave trains in an inhomogeneous (moving) medium. The method is applicable to both linear and non-linear systems. As a direct consequence of the averaging used in the method, wave action is a conserved property of the wave motion. In contrast, the wave energy is not necessarily conserved, due to the exchange of energy with the mean motion. However the total energy, the sum of the energies in the wave motion and the mean motion, will be conserved for a time-invariant Lagrangian. Further, the averaged Lagrangian has a strong relation to the dispersion relation of the system.
The method is due to Gerald Whitham, who developed it in the 1960s. It is for instance used in the modelling of surface gravity waves on fluid interfaces,[1][2] and in plasma physics.[3][4]
- ^ Grimshaw (1984)
- ^ Janssen (2004, pp. 16–24)
- ^ Dewar (1970)
- ^ Craik (1988, p. 17)