WAVE TRANSFORMATION II (REFLECTION, BREAKING, REFORMING)

25/10/2014 WAVE TRANSFORMATION II (REFLECTION, BREAKING, REFORMING) Wave Transformation • reflection • breaking • reforming Wave Reflection 25/10/2014 Wave Reflection Incident and reflected wave: Hi  2x 2t  cos    T   L Hr  x  t   r  cos    T   L i  Resulting wave (Hr=Hi):   i  r  Hi   2x 2t   2x 2t   cos      cos    T  T    L  L   Hi cos 2x 2t cos L T Water Surface and Particle Motion Partial Wave Reflection 25/10/2014 Partial Wave Reflection Modes in Closed and Open-Ended Basins Period of Oscillation: Closed Basin L gT  2d    2  L  1/  2  L T    g tanh(2d / L)  1/ 1st harmonic: lB  L / jth harmonic: lB  j L  4  lB T    g tanh( d / lB )  1/  4  lB Tj     jg tanh( jd / lB )  j  1,2, 25/10/2014 Shallow Water Bodies  jd  jd    lB  lB Alternative: Tj  2lB j gd L  gdT lB  j L j  1,2, Period of Oscillation: Open-Ended Basin 1st harmonic: lB  L jth harmonic: lB   j  1 T 4lb gd Tj  4lB j 1 gd L Reflection from Sloping Surfaces  Hr Hi Surf similarity parameter:  tan  Hi / Lo 25/10/2014 Wave Reflection Coefficient Correction Factors Multiple layers Slope roughness Breaking Waves 25/10/2014 Incipient Wave Breaking Wave Breaking Criteria Deep water: Ho  0.142  Lo Hb  0.78 db Shallow water: Intermediate water: H  2d     0.142    L max  L  Breaker Height Index Hb  H o' 3.3( H o' / Lo )1/3 25/10/2014 Breaker Depth Index Hb/db is a function of wave steepness and slope Types of Wave Breaking Breaker Types Spilling o < 0.5 Plunging 0.5 < o < 3.3 Surging/collapsing o  o > 3.3 tan  H o / Lo 25/10/2014 Wave Reforming Horikawa and Kuo Experiment Stable wave height H s  d   0.4 ... parameter:  tan  Hi / Lo 25/10/2014 Wave Reflection Coefficient Correction Factors Multiple layers Slope roughness Breaking Waves 25/10/2014 Incipient Wave Breaking Wave Breaking Criteria Deep water:...25/10/2014 Wave Reflection Incident and reflected wave: Hi  2x 2t  cos    T   L Hr  x  t   r  cos    T   L i  Resulting wave (Hr=Hi):   i  r  Hi... a function of wave steepness and slope Types of Wave Breaking Breaker Types Spilling o < 0.5 Plunging 0.5 < o < 3.3 Surging/collapsing o  o > 3.3 tan  H o / Lo 25/10/2014 Wave Reforming