What leads to Stokes drift?
Dr Anirban Guha (University of Dundee)
Friday 29th September 14:30-15:30 Maths 311B/ ZOOM (ID: 858 8205 0218)
Waves existing at the water surface cause net transport of floating particles in the direction of wave propagation - the Stokes drift. However, what is the fundamental mechanism that leads to Stokes drift? Although overwhelmingly understood for water waves, Stokes drift is a generic mechanism occurring in any non-transverse wave in fluids. To further clarify this point, we undertake a fully Lagrangian approach and put the pathline equation of sound (1D) and water (2D) waves into perspective. We show that the 2D pathline equation of water waves is reducible to 1D when expressed in terms of the Lagrangian phase θ. Therefore we posit that the pathline equation is essentially 1D for all kinds of waves in fluids. We solve the respective pathline equation for sound and water waves using asymptotic methods to obtain a parametric representation of particle position x(θ) and elapsed time t(θ). The parametric description has allowed us to show that Stokes drift is a consequence of wave kinematics and arises because a particle in a linear wave field spends more time, undergoes greater horizontal displacement,and travels at a faster average horizontal velocity in the crest phase in comparison to the trough phase. Finite amplitude waves may add nuances, however, the above-mentioned understanding is generally valid. We substantiate all our arguments with second-order-accurate quantitative estimates.