Wave Breaking The release of energy derived from the wind, along a narrow coastal zone - geomorphic work done by wind, really, translated through medium of water. Wave Breaking Wave breaking is responsible for the processes which control beach morphology: (1) nearshore current generation (2) sediment transport 1
Wave Breaking Show videos of Wave Break Vilano beach movie Steamer s Lane movie 2
Condition for Wave Breaking As waves shoal into shallow water, wave height increases and wave length decreases: " 1 H = H 0 $ # 2n L = T gh c 0 c % ' & 1/ 2 " gt = H 0 $ # 4π 1 % ' gh & 1/ 2 Wave steepness: H L = H 0 # gt % $ 4π T 1 & ( gh ' gh 1/ 2 ~ h 3 4 Something has to give! Wave Breaking When it occurs?. Common misconception breaking is a result of waves dragging on the bottom, then trip forward due to friction NO! Friction plays a very small role computer simulations that completely neglect friction can still produce breaking waves. A wave breaks when it becomes overly steep, because the velocity of water particles in the wave crest exceed the velocity of the wave form! 3
Style of Breaking Schematic and traces of high-speed photos illustrating different types of wave breaking behavior. But what causes each one of the different breaking styles? Style of Breaking - Illustrated Spilling waves (flat beaches) Plunging waves (moderate beaches) First observations recognized that beach slope and wave steepness had something to do with this... Surging waves (steep beaches) 4
Breaker Types Examples from Davidson-Arnott text Iribarren Number ξ ξ = $ & % S H L ' ξ = 1/ 2 b ) $ & ( % S H b L ' ) ( 1/ 2 This ratio of beach steepness to wave steepness has a deep-water form and a nearshore form. ξ < 0.5 0.5 < ξ < 3.3 ξ b < 0.4 0.4 < ξ b < 2.0 ξ > 3.3 ξ b > 2.0 From Battjes, 1974 5
Wave Break Style vs. Ir. # Lab Results from a Wave Tank Early Numerical Models 6
Early Numerical Models More Recent Numerical Models 7
More Recent Numerical Models Solitary Wave Runup on a beach More Recent Numerical Models 3-D Weakly Plunging Breaking Wave on a Beach 8
More Recent Numerical Models 3-D Weakly Plunging Breaking Wave on a Beach Wave Breaking Condition γ (gamma) - ratio of H b to h b γ b = H b h b Is this a constant? some disagreement = 0.73 --> 1.03, from lab studies of monochromatic waves For a given wave steepness, the higher the beach slope, the greater the value of γ b 9
Breaker Height Prediction - various forms H b 1 = H 3.3(H /L ) 1/ 3 H b 0.563 = H (H /L ) 1/ 5 H b 0.46 = H (H /L ) 0.28 Munk (1949) - based on Solitary Wave Theory Komar and Gaughan (1972) - based on Airy Wave Theory Kaminsky and Kraus (1993) - based on Lab Measurements Breaker Height Prediction - reconfigured Data span 3 orders of magnitude of breaker heights Remarkably well-behaved data H b 0.563 = -----> H H (H /L ) 1/ 5 b = 0.39g 1/ 5 (TH 2 ) 2 / 5 10
Surf Zone Wave Decay and Energy Dissipation Steep, reflective beaches - Wave breaking (and energy dissipation) is concentrated through plunging breakers. Broken wave surges up the beach as runup. Low-slope, dissipative beaches - Extensive, wide surf zone over which spilling breakers dissipate energy. At any time, several broken wave bores, and smaller unbroken waves, are visible. Villano Beach Anastasia Island Wave energy dissipation pattern depends on morphology of the beach Reasons for understanding surf zone wave decay Understanding the patterns of wave decay in the surf zone is important for two significant reasons: 1. Wave energy dissipation is inversely related to the alongshore pattern of wave energy delivery -- so it can help identify relative vulnerability of coastal property. 2. Wave energy expenditure is partially transformed into nearshore currents, which are responsible for sediment transport and beach morphologic modification. 11
Waves in the Surf Zone Thornton & Guza (1982) - Torrey Pines Beach Torrey Pines Beach fine sand with minimal bars and troughs. Wave staffs and current meters - measurements from 10 m water depth to inner surf zone. Published the distributions of wave breaking within the surf zone on a natural beach The Surface Roller vs. The Main Part of the Breaking Wave 12
Wave Height in the Inner Surf Zone or The Height of Surf Bores Broken wave height is controlled primarily by water depth Surf wave heights after initial breaking 13
Waves over a barred beach profile Bar (induces breaking) Trough (breaking ceases) Beach (breaking resumes) Dissipation Models - Depth-controlled Random Wave Breaking Beach Profile ( EC g ) = ε f ε b x Wave Heights ε f 1 & 2π f H # rms = ρc f $! 16 π $ % sinh kh!" 3 Energy Flux Profile Energy Dissipation ' ε b = 3 π 16 ρgb3 f H 5 rms ) γ 2 h 1 1 3 ) () 1+ H rms γh ( ( ) 2 ) 5 2 *,, +, Thornton and Guza (1982, JGR) 14
Modeling Wave Energy Dissipation - Homer, Alaska Move locus of wave break seaward 15