Kelvin WedgeFourier Coefficients of Quadratic Forms in $\cos \gamma$ for Steady Capillary-Gravity Waves

The math is sound. The method is not. We factor the quadratic denominator \(a+b \cos \gamma+c \cos ^2 \gamma\) and reduce the computation of its Fourier coefficients to those of…

fluid mechanics

Kelvin WedgeDiagonalizing Azimuthal Mode Coupling via a Discrete Fourier Transform

The math is sound. The method is not. We recast the azimuthal mode-coupled surface equations as a block-Toeplitz convolution in the mode index and diagonalize this coupling via…

fluid mechanics