“Bilingual Course”,ZHENG Jinhai March 2009,Coastal Hydrodynamics,HOHAI UNIVERSITY,Chapter 3 WAVE TRANSFORMATIONS,Stating ocean wave characteristics,Stating transformations of waves entering shallow water,2/34,Wave conservation,Chapter 3,3.2 Wave transformations in shallow water,2. Wave shoaling,3. Wave refraction,4. Wave reflection,5. Wave diffraction,6. Wave breaking,3/34,Chapter 3,The conservation of wave equation can be expressed as,1. Conservation of wave equations,This equation states that any temporal variation of the wave number vector must be balanced by spatial changes of the wave angular frequency.,4/34,Chapter 3,2. Wave transformation in shoaling water,Assuming that the energy flux is conserved in the process of wave propagation, the wave height at a given water depth can be determined by:,5/34,Chapter 3,3. Wave refraction,6/34,Chapter 3,Wave convergence and/or divergence,7/34,Chapter 3,4. Wave reflection,The reflection coefficient is defined as,which varies with the angle of the slope, the incident wave steepness and the characteristics of the slope.,8/34,Chapter 3,5. Wave diffraction,9/34,Chapter 3,6. Wave Breaking,Critical wave conditions Limiting wave steepness Breaker criterion Breaker angle Breaker types,10/34,Chapter 3,When waves reach the beach and enter water approximately as deep as the waves are high, they break, the crest throwing itself forward or breaking up into bubbles and foam.,11/34,Chapter 3,Critical wave conditions,The most basic of the criteria is that the velocity of the water in the very peak of the crest is equal to wave celerity. If waves were any larger so that the crest water particle velocity exceeded the wave celerity, the waves would topple forward and break.,12/34,Chapter 3,Limiting wave steepness,For any given water depth and wave period, there is an upper limit to the wave height at which the wave becomes unstable and breaks. The limiting steepness （极限波陡） is,13/34,Chapter 3,Breaker criterion,The ratio of the height of wave breaker to the water depth of wave breaking is regarded as the breaker criterion （破波指标）.A widely accepted breaker criterion is,14/34,Chapter 3,Breaker angle,The breaker angle （破波角） can be calculated with the following formula,15/34,Chapter 3,Breaker types,Three types of breakers are : spilling（崩破波）, plunging（卷破波）, surging （激破波）.,16/34,Chapter 3,Spilling breakers tend to occur on beaches of very low slope (gentle slope) with waves of high steepness values. In spilling breakers the wave gradually peaks until the crest becomes unstable and cascades down as “white water” (bubbles and foam).,17/34,Chapter 3,Numerical Modeling of Spilling Breaker,18/34,Chapter 3,Plunging breakers occur on steeper beaches and are characterized by the crest of the wave curling over forward and impinging onto part of the wave trough. In plunging beakers the shoreward face of the wave becomes vertical, curls over, and plunges downward as an intact mass of water.,19/34,Chapter 3,Experimental Modeling of Plunging Breaker,20/34,Chapter 3,Surging breakers occur on very steep beaches and are characterized by narrow or nonexistent surf zones and high reflection.Surging breakers peak up as if to plunge, but then the base of the wave surges up the beach face so that the crest collapses and disappears.,21/34,Chapter 3,Numerical Modeling of Surging Breaker,22/34,Chapter 3,7. Case studies,Damage of Langtongmen Breakwater Caused by No.9119 Typhoon Three-dimensional Experimental Study on Wave Characteristics in Front of Concave Breakwater Wave Height Prediction for Sea Dike Re-construction in Nanri Island,23/34,Chapter 3,Case study (I),TOPOGRAPHY: The breakwater lies in a valley between two small hills northeast of the island and faces open sea. Beyond 150 m away from the breakwater is flat shoreland but close to the structure within about 100 m there exists a nearshore bottom slope of 1:10.,24/34,Chapter 3,25/34,Chapter 3,CAUSES: The topographic configuration contributes to a concentration of wave energy during the wave spreading from open sea toward the breakwater, which enhances the wave height rapidly and results in wave breaking severely in front of the structure.,26/34,Chapter 3,Case study (II),27/34,Chapter 3,28/34,Chapter 3,29/34,Chapter 3,A complex short-crested wave system may occur in front of a concave breakwater due to the superposition of incident waves upon oblique reflected waves or the crossing of reflected waves from two breakwater sections, and the concentration of wave energy may result in amplification of wave height.,30/34,Chapter 3,In summary, because of their importance to beach processes in general, the properties of waves in shallow water have been extensively studied. The determination of characteristics of shallow water wave is one of the most important engineering subjects, and it is still an area of active research.,