Waves II.pdf

OCEAN UNIVERSITY OF SRI LANKA Aspects of Coastal Engineering CRM 4022 Waves in the Ocean -ii Eng. Nilupul Senarathne M.Eng (Moratuwa), M.A (Financial Econ).(Colombo), Bsc Eng. (Hons) (Moratuwa)...

OCEAN UNIVERSITY OF SRI LANKA Aspects of Coastal Engineering CRM 4022 Waves in the Ocean -ii Eng. Nilupul Senarathne M.Eng (Moratuwa), M.A (Financial Econ).(Colombo), Bsc Eng. (Hons) (Moratuwa), AMIE(SL) SMALL AMPLITUDE/FIRST ORDER/AIRY WAVE THEORY 1. Fluid is homogenous and incompressible, therefore, the density is a constant. 2. Surface tension is neglected. 3. Coriolis effect is neglected. 4. Pressure at the free surface is uniform and constant. 5. Fluid is ideal (lacks viscosity). SMALL AMPLITUDE/FIRST ORDER/AIRY WAVE THEORY 6. The wave does not interact with any other water motion. 7. The bed is a horizontal, fixed, impermeable boundary which implies that the vertical velocity at the bed is zero. 8. The wave amplitude is small and the wave form is invariant in time and space. 9. Waves are plane or low crested (two dimensional). Can accept 1, 2, and 3 and relax assumptions 4-9 for most practical solutions. 1. Longer waves travel faster than shorter waves. 2. Small increases in T are associated with large increases in L. Long waves (swell) move fast and lose little energy. Short wave moves slower and loses most energy before reaching a distant coast. k = 0.016 Kp = 0.791 P max = 179 kPa MOTION IN A SURFACE WAVE Local Fluid Velocities and Accelerations (HORIZONTAL) (VERTICAL) Tc Irregular Waves Tz  Probability Distribution H Intervals No of % of Occurrence Occurrence s 0-1 50 0.15 1-2 80 0.24 2-3 100 0.29 3-4 70 0.21 4-5 30 0.09 5-6 10 0.03 Fourier Transformation – Linear Superposition  Energy Density Function – Wave Spectrum ∞ Total Energy = ρg ‫׬‬0 𝑆(𝜔). 𝑑𝜔 1 𝐴2 S(ω)= 2 ∆𝜔 ω Rock Manual 34.9 Years – Hourly data Weibull Distribution