Understanding Stokes drift mechanism via crest and trough phase estimates

Anirban Guha (Lead / Corresponding author), Akanksha Gupta

Research output: Contribution to journalArticlepeer-review


By providing mathematical estimates, this paper answers a fundamental question – “what leads to Stokes drift”? Although overwhelmingly understood for water waves, Stokes drift is a generic mechanism that stems from kinematics and occurs in any non-transverse wave in fluids. To showcase its generality, we undertake a comparative study of the pathline equation of sound (1D) and intermediate-depth water (2D) waves. Although we obtain a closed-form solution x(𝑡) for the specific case of linear sound waves, a more generic and meaningful approach involves the application of asymptotic methods and expressing variables in terms of the Lagrangian phase 𝜃. We show that the latter reduces the 2D pathline equation of water waves to 1D. Using asymptotic methods, we solve the respective pathline equation for sound and water waves, and for each case, we obtain a parametric representation of particle position x(𝜃) and elapsed time 𝑡(𝜃). Such a parametric description has allowed us to obtain second-order-accurate expressions for the time duration, horizontal displacement, and average horizontal velocity of a particle in the crest and trough phases. All these quantities are of higher magnitude in the crest phase in comparison to the trough, leading to a forward drift, i.e. Stokes drift. We also explore particle trajectory due to second-order Stokes waves and compare it with linear waves. While finite amplitude waves modify the estimates obtained from linear waves, the understanding acquired from linear waves is generally found to be valid.
Original languageEnglish
Number of pages23
JournalJournal of Physical Oceanography
Early online date22 Feb 2024
Publication statusE-pub ahead of print - 22 Feb 2024


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