====== Diagram Loads on Pile Structures ======
The wave length \( L \), the maximum horizontal orbital velocity \( u_{max} \), the maximum horizontal orbital acceleration \( \left( \frac{\delta u}{\delta t} \right)_{max} \), as well as the displayed wave profile are calculated according to the linear wave theory of //Airy/Laplace// and follow the equations given in the lower part of the page for the purpose of clarity.\\ \\
The force coefficients \( C_D \) and \( C_M \) are determined according to //Shore Protection Manual (SPM)//, the formulae for this are also given in the lower part of the page.\\ \\
Drag force \( f_D \), inertia force \( f_M \), and the total force \( f_{tot} \) are determined according to //Morison (1950)//.\\
They thus follow the equation \( f_{tot} = f_D + f_M = \frac{1}{2} \cdot C_D \cdot \rho_w \cdot D \cdot |u| \cdot u + C_M \cdot \rho_w \cdot \frac{\pi \cdot D^2}{4} \cdot \frac{\delta u}{\delta t} \).\\ \\
The following also applies: Reynolds number \( Re = \frac{u_{max} \cdot D}{\nu} \), sea water density \( \rho_w = 1025 \frac{kg}{m^3} \), acceleration due to gravity \( g = 9.81 \frac{m}{s^2} \) and kinematic viscosity \( \nu = 10^{-6} \frac{m^2}{s} \).
Lernplattform des Leichtweiß-Institut für Wasserbau
Wave length L = 0
D/L: 4
fges: 4; at the time t: 4
__ Wave profile __ Drag force fD __ Inertia force fM__ Total force ftot
\\ \\ \\
According to the linear wave theory of //Airy/Laplace//:\\
Wave length \( L = \frac{g \cdot T^2}{2 \cdot \pi} \cdot \tanh( \frac{2 \cdot \pi}{L} \cdot d) \),\\
Maximum horizontal orbital velocity \( u_{max} = \frac{H \cdot \pi}{T} \cdot \frac{\cosh \left(\frac{2 \pi}{L} \cdot (z+d) \right)}{\sinh \left(\frac{2 \pi}{L} \cdot d \right)} \),\\
Maximum horizontal orbital acceleration \( \left( \frac{\delta u}{\delta t} \right)_{max} = \frac{2 \cdot H \cdot \pi^2}{T^2} \cdot \frac{\cosh \left(\frac{2 \pi}{L} \cdot (z+d) \right)}{\sinh \left(\frac{2 \pi}{L} \cdot d \right)} \),\\
Wave profile \( \eta (t) = \frac{H}{2} \cdot \cos(- \frac{2 \cdot \pi}{T} \cdot t)\).\\ \\
Force coefficients for the Morison equation according to //Shore Protection Manual (SPM)//:\\
Drag force coefficient \( C_D = \begin{cases} 1.2 & \text{ for } Re < 2.0 \cdot 10^5 \\ \frac{23}{15} - \frac{Re}{6 \cdot 10^5} & \text{ for } 2.0 \cdot 10^5 < Re < 5.0 \cdot 10^5 \\ 0.7 & \text{ for } Re > 5.0 \cdot 10^5 \end{cases}\) \\ \\
Inertia force coefficient \( C_M = \begin{cases} 2.0 & \text{ for } Re < 2.5 \cdot 10^5 \\ 2.5 - \frac{Re}{5 \cdot 10^5} & \text{ for } 2.5 \cdot 10^5 < Re < 5.0 \cdot 10^5 \\ 1.5 & \text{ for } Re > 5.0 \cdot 10^5 \end{cases}\)
The field of Loads on Structures is part of the module **[[https://www.tu-braunschweig.de/en/lwi/hyku/teaching/master/coastal-dynamics-and-engineering-design|Coastal Dynamics and Engineering Design]]** within the specialization Coastal and Ocean Engineering of the master programmes Civil and Environmental Engineering.