Lernplattform des Leichtweiß-Institut für Wasserbau

====== Diagram Ranges of Water Depth and Water Particle Orbits ====== The displayed water particle orbits are calculated according to the linear wave theory of //Airy/Laplace//. \\ Therefore, the horizontal axis \(a\) as well as the vertical axis \(b\) of the elliptical water particle orbits are represented by the equation \\ \( a (z) = H \cdot \frac{\cosh(\frac{2 \pi}{L} \cdot (z+d))}{\sinh(\frac{2 \pi}{L} \cdot d)} \) and \( b (z) = H \cdot \frac{\sinh(\frac{2 \pi}{L} \cdot (z+d))}{\sinh(\frac{2 \pi}{L} \cdot d)} \) . \\ \\ The applicability of the linear wave theory for the set parameters is not verified! For any parameter sets that according to the breaker criterion of //McCowan// ( \( \frac{H}{d} = 0.78 \) ) or the criterion of limiting steepness for deep water ( \( \frac{H}{L} = \frac{1}{7} \) ) are not affected by wave breaking, water particle orbits are displayed. The displayed water particle orbit can therefore in most cases only be understood as a basic outline and do not necessarily reflect the actual conditions for the set parameters. \\ \\ The division into the different water depth ranges is based on the relative water depth \( \frac{d}{L} \): \\ Deep water: \( \frac{d}{L} \geq 0.5 \) \\ Transitional water: \( 0.5 > \frac{d}{L} > 0.05 \) \\ Shallow water: \( \frac{d}{L} \leq 0.05 \) Lernplattform des Leichtweiß-Institut für Wasserbau

Wave height H [m]: Wave length L [m]:

Calculation example for the set coefficients at a depth of

Horizontal axis of the water particle orbits: a = 22.2 m

Vertical axis of the water particle orbits: b = 55.5 m

The field of Wave Theories 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.