non-dimensionalization we will perform the non-dimensionalization of the parameters

prerequisite conditions put velocity potential function as follow \[ \begin{equation} \phi=U x+\varphi-\frac{1}{2} U^2 tz \en...

In dispersive water waves (e.g., surface gravity waves on deep or shallow water), several concepts describe how waves travel,...

paper core

Pressure to the surface to a stream notation \(\varpi\): -> r ///////p439 (22) \(\sigma\): -> \(\omega\) \(c\): -> \...

wave patterns 📄P411, Sec 12.4 For a point source \(P\), the characteristics carrying disturbances pass through \(P\) and we...

Solution Explanation show that, under the (zeroth-order) Hankel transform in the radial variable, \[ \mathcal{H}_0\left[\nabl...

This part mainly focus on ship wave with the infinite depth water, also mainly use Fourier transform method.

Continuity equation: Current density:[1] \[ \boldsymbol{j}=\rho \boldsymbol{v}\quad(1) \] where the direction of \(\boldsymbo...

This note primarily delves into incompressible flow momentum equation and Surface of water waves and boundary condition and Variational Formulation.