Diagram Wave Reflection at a Structure

The displayed wave profiles are calculated according to the linear wave theory of Airy/Laplace.
Therefore, the water surface elevation follows the equation \( \eta (x,t) = \frac{H}{2} \cdot \cos(k \cdot x - \omega \cdot t)\).

The wave energy is calculated as \( E = \frac{1}{8} \cdot \rho_w \cdot g \cdot H^2 \), while the coefficients presented are as follows: \( K_r = \frac{H_r}{H_i} \), \( K_t = \frac{H_t}{H_i} \), \( K_d = \frac{H_d}{H_i} \). Furthermore: Sea water density \( \rho_w = 1025 \frac{kg}{m^3} \), as well as acceleration due to gravity \( g = 9.81 \frac{m}{s^2} \).

Since the wave energy of the incoming wave is maintained according to \( E_i = E_r + E_t + E_d \), follows: \( {K_r}^2 + {K_t}^2 + {K_d}^2 = 1 \).

Lernplattform des Leichtweiß-Institut für Wasserbau

___ Incoming wave
___ Reflected wave
___ Resulting water surface elevation
___ Transmitted wave

Dissipation coefficient K_d = 0

Calculation example for the set coefficients at a wave height of

Incoming wave: Wave height H = 00.0 m, Wave energy E = 00.0 kJ/m²

Reflected wave: Wave height H_r = 00.0 m, Wave energy E_r = 00.0 kJ/m²

Resulting water surface elevation (stationary wave): Wave height H_stationary = 00.0 m

Transmitted wave: Wave height H_t = 00.0 m, Wave energy E_t = 00.0 kJ/m²

Dissipated wave energy E_d = 00.0 kJ/m²

The field of Wave Transformation is part of the module Basic Coastal Engineering within the specialization Coastal and Ocean Engineering of the master programmes Civil and Environmental Engineering.