**Theoretical Expression of Stokes drift:**

The Stokes drift of a single-frequency deep-water gravity wave can be expressed as

$$\mathbf{U}\_s = \mathbf{U}\_{ss} \mathbf{e}^{\frac{8\pi^2 \kappa}{\mathfrak{g}\Gamma^2}} \mathbf{k} \tag{A16}$$

$$\mathbf{U}\_{\rm ss} = \frac{2\pi^3 \mathbf{H}\_{\rm s}^2}{\mathbf{g} \mathbf{T}^3},\tag{A17}$$

where Us is the Stokes drift rate on the ocean surface, **k** is the unit wavenumber vector of the fluctuation, Hs is significant wave height, T is mean wave period, g = 9.8 m/s2, and z is the water depth (z = 0 at the sea surface;z>0 above the water surface).
