linear and nonlinear waves note 2
how to obtain \(p=a \cos ^2 \theta\) Question: \(p=a \cos ^2 \theta,\) In this context, \(a\) is simply the constant of int...
one dimension ship wave with surface tension
Consider 1-D gravity-capillary waves, the surface displacement is described by: \[ \begin{equation} \frac{2 \pi \eta}{P}=\lim...
relations among Rays, Group Velocity, Phase Velocity, and the Wave Number Vector in Water Waves
In dispersive water waves (e.g., surface gravity waves on deep or shallow water), several concepts describe how waves travel,...
Paper Capillary Gravity wave in different Froude number and different surface tension
paper core
Hydronamics note 1
Pressure to the surface to a stream notation \(\varpi\): -> r ///////p439 (22) \(\sigma\): -> \(\omega\) \(c\): -> \...
linear and nonlinear waves note 1
wave patterns 📄P411, Sec 12.4 For a point source \(P\), the characteristics carrying disturbances pass through \(P\) and we...
The Kelvin Wave Patterns in in High-Froude-Number Capillary Flows - Note I
Solution Explanation show that, under the (zeroth-order) Hankel transform in the radial variable, \[ \mathcal{H}_0\left[\nabl...
Lagrangian and Eulerian description
Continuity equation: Current density:[1] \[ \boldsymbol{j}=\rho \boldsymbol{v}\quad(1) \] where the direction of \(\boldsymbo...
The Equations for Water Waves
This note primarily delves into incompressible flow momentum equation and Surface of water waves and boundary condition and Variational Formulation.