====== Diagram Linear Superposition of Linear Waves and Spectral Analysis ======
The up to six basic components to be entered generate one wave each according to the linear wave theory of //Airy/Laplace//.\\
The equations of the different basic components therefore follow the equation \( \eta_i (t) = \frac{H_i}{2} \cdot \cos(- \omega_i \cdot t + \varphi_i)\), with \( \omega_i = \frac{2 \cdot \pi}{T_i} \).\\
The amplitude \( a_i = \frac{H_i}{2} \) and the frequency \( f_i = \frac{1}{T_i} \) are displayed for each of the basic components.\\ \\
The displayed time series of the water surface elevation results from linear superposition (i.e. summation) of all entered basic components.\\ \\
The spectral energy density of the individual components is calculated as \( S(f) = \frac{{a_i}^2(f)}{2 \cdot \Delta f} \).\\
The zero-order moment is given by \( m_0 = \int S(f) \cdot \mathrm{d}f \), the spectral wave height follows \( H_{m0} = 4 \cdot \sqrt{m_0} \).
Lernplattform des Leichtweiß-Institut für Wasserbau
The field of Sea State is part of the module **[[https://www.tu-braunschweig.de/en/lwi/hyku/teaching/master/basic-coastal-engineering|Basic Coastal Engineering]]** within the specialization Coastal and Ocean Engineering of the master programmes Civil and Environmental Engineering.