Surf Zone Hydrodynamics PDF

Outline where breaking take place, q The surf zone q Wave breaking and breaker types SURF ZONE HYDRODYNAMICS the main driver of surfzone dynamics q Energy and momentum transport q Radiation stress developed by Longuet-Higgins --> waves are inducing forces make up sea level component, Iñigo Lo...

Outline where breaking take place, q The surf zone q Wave breaking and breaker types SURF ZONE HYDRODYNAMICS the main driver of surfzone dynamics q Energy and momentum transport q Radiation stress developed by Longuet-Higgins --> waves are inducing forces make up sea level component, Iñigo Losada q Cross-shore balance: set-down and set-up Master Coastal Hazards-Risks, Cimate Change Impacts and Adaptation (COASTHazar) q Nearshore currents q Longshore currents q Undertow q Rip currents q 3-D effects in the surf zone The surf zone The surf zone the opposite of off-shore The surf zone is the part of the nearshore where incident waves break and breaking-induced processes dominate the fluid motion and consequently sediment transport processes. This zone is located between the zone of wave shoaling and the swash zone and can be subdivided into outer surf zone and inner surf zone. The surf zone is also characterized by complex hydrodynamic processes generated by wave breaking including: wave set-up, infragravity waves and surf zone currents (surf zone circulation). also wave set-down The interaction of said processes with sediment transport and dynamics is the main driver of nearshore morphology changes. Dimensions may vary depending on the beach The surf zone The surf zone still water level + wave shoaling transformation: H +++ positive mean water level T = ctc L --c --- Fig. 12. The high intensity bands in each image are due to persistent wave breaking on the inner and outer bars of the beach.(Source. Pape et al. ) bore prapagating mean water level is negative (compared to swl) in shoaling region no more bore, only run-up 'swash zone' The surf zone The surf zone mild slope, energetic wave in dissipative beach typical in winter lots of sediment in motion, transported A turbulent bore containing entrained suspended sediment just prior to reaching the swash zone. (Source: Coastal Wiki.) The swash zone Wave breaking and breaker types huge gradient of wave height decrease wave envelope, also related to wave celerity Photo shows the inner surf zone and a bore reaching the swash zone in the background and a swash uprush reaching the top of a beach berm in the foreground visualizing shoaling process, H ++ bore advancing towards the shoreline Wave breaking and breaker types Energy and momentum transport when u > c, (particle speed is faster than wave celerity) Shoaling waves increase in wave height and decrease in celerity until the water particle velocity at the crest exceeds the wave celerity. This limit is associated with a limiting wave steepness, which is given �⁄�)_��� = 0.142 �� ℎ( ℎ Using shallow-water approximations, γ = Hb/hb = 0.88, (use 0.78) Hb breaking wave height, influenced by D50, hb breaker depth for coarse sediment, the Ir is influenced by wave components γ breaker criterion more for fine sediment, Ir is governed by The wave energy E is given by: = 1 8 � ρ is the density of water g is the gravitational acceleration. mass transport (3- dimension) Momentum equals mass multiplied by velocity, that is, a mass being transported or a mass flux. Thus, momentum q can be expressed as q = ρū, where ū = (cross-shore, alongshore, vertical) velocity vector. beach profile In the deep water In the breaking zone Spilling Plunging Collapsing Surging Waves transport energy and momentum as they propagate. � < 0.5 0.5 < � < 2.5 2.5 < � < 3.0 � > 3.0 � < 0.4 0.4 < � < 1.5 1.5 < � < 2.0 � > 2.0 (���� = beach slope) � = ����/ �/ Momentum is therefore a vector quantity of which the direction is the same as that of the velocity vector in deep water the net momentum transport and net mass transport is zero. It's a closed circular pathline Radiation stress Radiation stress As waves propagate, the momentum of a fluid element can change, resulting in a wave-induced momentum flux, which is given by ρu2. Radiation stress is a vector quantity with both normal and shear components. For an oblique wave approaching an alongshore-uniform coast at an angle of θ to the shore normal, these components can be expressed n relates celerity with group (using linear wave theory) as: celerity Newton’s second law: any change of momentum results in a force acting upon the fluid element. Hence, wave-induced momentum flux results in a wave force acting in the opposite direction. if wave producing momentum flux --> generate an additional extra force -- momentum flux changes The wave-induced momentum flux is referred to as ‘radiation stress’, which is conventionally defined as ‘the excess momentum flux due to the presence of waves” radiation stress • transfer of momentum q = ρū, through that plane with the particle velocity normal to that plane momentum transport, only within the surfzone Horizontal transport of wave-induced momentum through a vertical plane of unit width perpendicular to the wave propagation direction. Radiation stress associated with momentum flux • wave-induced pressure force acting on the plane due to the wave induced pressure wave in the water. is a force representing the excess of momentum flux due to presence of wave Normal component in the cross-shore (x) direction = Normal component in the along-shore (y) direction = Shear components = n is the ratio between the wave speed and the wave group speed, and n = 0.5 in deep water and n = 1 in shallow water. 1 − + cos 2 − = 1 + sin 2 cos sin The shear components act in the direction of the axis given by the first subscript, but exert themselves on a plane normal to the direction of the axis given by the second subscript. Radiation stress For shore-normal waves, θ = 0 and thus: = 2 − associated with pressure = = which in shallow water − 1 2 1 2 =0 = 1 reduces to = 1.5 and = 0.5 . Cross-shore balance: set-down and set-up Fy compensates/balance for Syy (remember Newton's 2nd law) it's acting in opposite direction Cross-shore balance: set-down and set-up In intermediate water depths prior to wave breaking the value of n increases in the direction of wave travel. Therefore, Sxx increases in the shoreward direction (prior to breaking), resulting in an equal and opposite wave force acting in the seaward direction. This offshore-directed force is balanced by a small hydrostatic pressure gradient, resulting in a slightly lower (than the still water level, SWL) surface elevation at the shoreward end of the shoaling zone (prior to wave breaking). This small lowering of the surface elevation just prior to the breaker location is referred to as wave set-down increase of water level, the way of nature compensates for Fx, more water column -> more pressure assume delta x is very small, how to obtain value for the next series? Taylor ... Wave-induced forces. An increase of momentum transport (increase in radiation stress) in � - or direction is equivalent to a loss of momentum, hence, to exerting an opposite force on the water body Cross-shore balance: set-down and set-up the way nature compensates of force of momentum flux: drop of water level --> less hydrostatic pressure Cross-shore balance eq. and simplified solutions The opposite phenomenon occurs in the surf zone (after waves break). When waves break, energy is dissipated rapidly, resulting in a shoreward decrease in Sxx. This results in an onshore-directed wave force, which must then be balanced by a hydrostatic pressure gradient such that the water level is higher (than the SWL) at the shoreline. This raising of the water level in the surf zone is referred to as =− � = (ℎ + ) At the breakpoint: Inside the surf zone: � The same Set-up mechanism also happen in infragravity wave due to wave group propagation =− 3⁄8 1 + 3⁄ 8 set-up is much larger than the set-down � mean water level, average over time =− 1 � 16 ℎ � with a maximum wave set-up ηmax (relative to SWL) of 5/16γ Hb at the shoreline. With γ = 0.5 (for irregular waves) this returns a maximum shoreline set-up of what is the value of set-up about 0.16Hb. of 1 meter Hb? 3 meter? What's the significant Cross-shore balance eq. and simplified solutions Nearshore currents due to excess of mass transport, (a) longshore current due to oblique wave incidence; (b) cross-shore mass flux and undertow (bed return flow); (c) rip currents due to onshore flow over bars and alongshore setup gradients resulting from alongshore non-uniform morphology variations in x, y components are generated Longshore currents =− + � Longshore currents (longshore uniform coast) Wave-induced force Fy due to horizontal gradients in radiation stresses in the longshore direction For a longshore uniform coast ∂/∂y=0 =− � This alongshore force is balanced by the bed shear stresses resulting from the generation of an alongshore current. Note that for shore-normal waves Syx = 0, and hence there is no wave-driven longshore current under shore-normal waves. oblique incident wave, inducing changes in radiation stresse -> inducing force paralel to the shoreline -> shear stress is produced to compensate the inbalance --> current generation =− = � =− = cos sin cos From Snell’s law (wave refraction) sinθ/C = cte � in the nearshore zone, it is reasonable to assume that θ is small (usually < 10o), and thus cosθ ≈ 1 and that the celerity can be expressed in terms of its shallow water asymptote =− 5 16 ( ℎ) ⁄ ℎ � By equating the above wave force to a quadratic bed shear stress, an expression for the cross-shore varying longshore current can be obtained as: � =− 5 16 ℎ sin ℎ � where cf is a friction factor and 0 < x < xb (xb is the surf-zone width) Longshore currents (longshore uniform coast) Cross-shore currents: Undertow if there's no oblique incident --> no longshore current This cross-shore distribution is only valid from the breaker line to the shoreline, and predicts that the longshore current is zero just outside the breaker line, suddenly increases to its maximum value at the breaker line, and then gradually decreases to zero across the surf zone offshore direction Cross-shore distribution of the alongshore current on a planar beach Mass flux Lateral dispersion of momentum takes place in nature via horizontal eddies = Each line represents a different level of lateral mixing (indicated by the P-value), with P = 0 representing no lateral mixing locations of maximum alongshore-current velocity q is the mass flux (unbroken or breaking waves), ω = 2π/T (T is the wave period), and ht is the water depth below trough level, k is the wave number. = ℎ = ℎ Depth-averaged undertow velocity Cross-shore currents: Rip currents As the mass flux for unbroken waves is relatively small, the undertow is very small outside the surf zone. However, for breaking waves the mass flux increases by about two orders of magnitude due to the influence of the surface roller; typical undertow velocities are about 0.2–0.3 m/s. Cross-shore currents: Rip currents Rip currents are usually associated with relatively deep, cross-shore oriented channels from the shoreline to beyond the breakpoint. These channels are separated alongshore by shallow alongshore bars or transverse bars. Offshore-directed rip currents are a component of the horizontal cellcirculation patterns that are generated due to a combination of onshore flow over shallow bars and alongshore set-up gradients variations of set-up presences paralel to the shoreline, induce by the bathymetry Cross-shore currents: Rip currents Cross-shore currents: Rip currents full circulationn Nearshore currents for different angles of incidence 3-D Effects in the surf zone Longshore current and undertow https://www.weather.gov/safety/ripcurrent-surviving SURF ZONE HYDRODYNAMICS Iñigo Losada Master en Ingeniería de Caminos, Canales y Puertos ETS de Ingenieros de Caminos, Canales y Puertos