WAVE DRIVEN CURRENTS D.R. BascoPrinciples of radiation stressWaves breaking at angle create time-averaged longshore currentLongshore current profile across the shoreWaves breaking create mean water-level set down and set up Undertow is time-averaged cross-shore currentRip currents and nearshore current systemsLongshore currents cause sediment transport

Idealized environment for longshore current theoryWave FieldSimple, monochromatic gravity wave trainsSteady-state, incident wave fieldTwo-dimensional, horizontally propagatingLinearized theory and radiation stressesOblique angle of incidence, long wave crestsSpilling-type breakersConstant breaker ratio in surf zone

Idealized environment for longshore current theoryBeachInfinite length, straight and parallel contoursPlane bottom slopeGentle slopeImpermeable bottomFluidIncompressibleHomogeneous (no air entrainment)CurrentDepth-integrated, parallel to coastlineTime-average (one wave period)

Idealized environment for longshore current theoryNeglected Stresses and AccelerationsNo surface wind stressNo atmospheric pressure gradientNo Coriolis accelerationNo tidesNo local (time-average acceleration, I.e., steady flowNo wave-turbulence interaction stressesNo bed shear stress outside of surf zoneNo rip currents presentNo wave-current interaction stresses

WAVE DRIVEN CURRENTS SummaryPrinciples of radiation stressWaves breaking at angle create time-averaged longshore currentLongshore current profile across the shoreWaves breaking create mean water-level set down and set up Undertow is time-averaged cross-shore currentRip currents and nearshore current systemsLongshore currents cause sediment transport

*Title slide showing outline of presentation on wave driven currents.*Schematic plan view of coastal waves illustrating how waves shoal,refract(bend) diffract behind structures,reflect off structures, breaks near the coast in the surf-zone and create a longshore current. This topic is called Coastal Hydrodynamics and are crudely depicted here from old course notes and a transparency.*Definition sketch for radiation stress or the excess horziontal momentum flux by the time-averaged and depth-integrated presence of the water waves. Top is plan view, middle is section view and bottom is formula to calculate the X-directed component Sxx. *Schematic of the key parameters to calculate the longshore current profile as shown in the bottom picture. Top is the wave height variation across the surf-zone that is the key variable. Cross-section shows wave set-down and set-up of the mean water level. Middle plan form shows the refracting wave crests and the bottom shows the current profile .*The original theory of longshore current profile variation and the influence of the P parameter on the profile shape. When P=0 there is no lateral turbulent mixing and the profile is unrealistically triangular. The larger the P value the more mixing and the flatter the profile.*An example with one meter breaker at 10 degree angel and P=0.1 versus P=0.4*Some examples of the theory ( modified slightly) versus measurements.*Another example of theory versus experiment and the theory of the wave height versus the measured wave height.*A plot of actual measurements of the average longshore current across the surf-zone versus the wave energy flux factor that includes Hb and breaking wave angle . Note the range of V is from 10 cm/sec to over 1 m/sec.*Schematic depiction of the surf-zone. Some water mass is trapped in the surface roller of the broken wave and this mass of water is transported onshore and must return by flowing back out to sea.

*The undertow is defined as the time-averaged, mean return flow out to sea. Theory versus measurement.*Self-explanatory*Illustration of the longshore current (blue) and cross-shore current (green) combining vectorially from top to bottom over the water depth to produce a three-dimensional current profile. Thus longshore sediment transport and cross-shore sediment transport that are the products of the sediment in suspension and the time-averaged currents are really idealized efforts to first understand a 3-D process.*What is a rip current? How is it different than the undertow? What are nearshore circulation patterns of the wave induced currents? Do you have rip currents on your beaches in the Caribbean ?*Same as previous slide but for waves approaching the shoreline at an angle.*An example of nearshore circulations patterns at La Jolla California at the Scripps Inst of Oceanography research pier. Plan view showing rip currents and nearshore current directions.*An example of nearshore circulations patterns at La Jolla California at the Scripps Inst of Oceanography research pier. Plan view showing rip currents and nearshore current directions.