Stokes drift: Difference between revisions

For the Eulerian velocity as a monochromatic wave of any nature in a continuous medium: <math>u=\hat{u}\sin\left( kx - \omega t \right),</math> one readily obtains by the [[perturbation theory]] – with <math>k\hat{u}/\omega</math> as a small parameter – for the particle position <math>x=\xi(\xi_0,t):</math>

\xi(\xi_0,t)\approx\xi_0+(\frac{\hat{u}/}{\omega)}\cos(k\xi_0-\omega t)+(\tfrac12 frac{k\hat{u}^2/}{2\omega^2)}\sin2(k\xi_0-\omega t)+\frac{k\hat{u}^2t/2}{2\omega\} t.