Surf Zone Hydrodynamics

Question 1

motivation

Answer 1

mean water movements and surface elevations are useful for
- sediment and contaminant transfer
- storm damage due to mean water super elevation
- rip tides

Question 2

radiator stresses

Answer 2

hard to quantify mean wave velocity
-linear has u_w bar = 0 but u_w.u_w bar non zero and this appears from the nonlinear moment equation
* leads to time integrated wave induced stress tensors which contribute to motion

on the way shorewaord wave momentum produces a force in the wave direction and perpendicular to it as well as changes in in MWS and longinitudinal currents

S = radiator stress
-work done by wave that causes a change in mean flow or water elevation
-stress tensor
-sum of Sm (due to moment) and Sp (due to pressure)
*comes from momentum flux and excess pressure F compared to still water

Sxx = mean flux of horizontal moment in x axcross a vertical plane of constant x minus the same without waves
-also Syy

Sxy = mean flux of horizontal moment in x across vertical plane y

Question 3

Equations of motion

Answer 3

-required for wave induced mean flow and mean water surface
-Navier-stokes equation used to get the time averaged, depth integrated momentum equations
* Rayleigh decomosition applied + nonlinear terms replaced with stress components
* tau0 bar is the mean shear stress @ the bed
*Sij are radiator stresses - momentum flux due to waves
*Sij’ are depth integrated Reynolds stresses - momentum flux due to turbulence

Question 4

Wave influence on eta bar

Answer 4

-use cross shore time average momentum equation
-assumptions
*Sxx&raquo_space; S’xx
*no longshore velocity or gradents
*tau0 bar neglected since its < 5% of the other terms
*U = 0, continuity

Reduces to:

partial deta_bar/dx = -1/rho.g(eta bar + d) . partial dSxx/dx
-change in radiator stress is balanced by a slope in the water surface in the opposite direction
-shoaling: increased H therefore increased Sxx and decreasing eta bar, leads to a set down
-surf zone: decreasing H therefore decreasing Sxx and increasing eta bar, leads to set up

Question 5

Longshore currents

Answer 5

created by wave breaking at an angle to the shore
-also due to tides and winds
-V bar max at the breaking location, assumed as decreasing linearly to shore and zero before by its more like a normal
-Equation is from the balance between waves momentum flux and friction
*assumes no cross shore velocity or gradients
*uniform current
*uniform longitudinal beach slope