45 Questions
What dominates the fluid motion in the surf zone?
Wave breaking-induced processes
Which hydrodynamic process is a main driver of nearshore morphology changes?
Surf zone circulation
Where is the surf zone located in relation to the swash zone?
Between the zone of wave shoaling and the swash zone
What are the two subdivisions of the surf zone?
Outer surf zone and inner surf zone
What is the opposite of off-shore?
Onshore
What does the surf zone fluid motion mainly consist of?
Breaking-induced processes
What characterizes the surf zone hydrodynamic processes generated by wave breaking?
Wave set-up, infragravity waves, and surf zone currents
What is the main driver of nearshore morphology changes?
Interaction of wave breaking-induced processes with sediment transport
What is the equation for the wave set-up at the shoreline?
$\eta = -\frac{5}{16}\gamma H_b$
What is the maximum shoreline set-up relative to SWL for irregular waves with $H_b = 3$ meters?
0.16 meters
What is the expression for the cross-shore varying longshore current?
$U = -\frac{5}{16}H\sin(\theta)$
What is the typical undertow velocity for breaking waves?
0.2–0.3 m/s
What type of currents are associated with relatively deep, cross-shore oriented channels from the shoreline to beyond the breakpoint?
Rip currents
What does the equation $\omega = 2\pi/T$ represent?
Angular frequency
What is the equation for the lateral dispersion of momentum via horizontal eddies?
$q = \frac{\omega}{2\pi}H_b$
What does the P-value represent in the lateral mixing diagram?
Lateral mixing level
What is the equation for wave energy?
E=1/8 ρgH^2
What is the shallow-water approximation for wave steepness?
The limiting wave steepness equation
What characterizes the momentum transport when particle speed exceeds wave celerity?
Momentum and energy transport occur
What is the equation for the wave-induced momentum flux, known as radiation stress?
q=ρū
What is the result of energy dissipation when waves break?
A shoreward decrease in Sxx
What type of balance involves set-down and set-up in the surf zone?
Cross-shore balance
What are the different types of wave breaking mentioned in the text?
Spilling, plunging, collapsing, and surging waves
What is the equation for the wave energy dissipation in the surf zone?
Not explicitly mentioned in the text
What is the equation for wave energy?
$E=\frac{1}{8} \rho g H^2$
What is the shallow-water approximation for wave steepness?
It is given by the limiting wave steepness equation
What is the expression for momentum transport?
$q=\rho \bar{u}$
What does radiation stress represent?
A wave-induced momentum flux
What is the result of energy dissipation when waves break?
A shoreward decrease in $S_{xx}$
What are the types of wave breaking mentioned in the text?
Spilling, plunging, collapsing, and surging waves
What is the relationship between particle speed and wave celerity for momentum and energy transport?
Particle speed exceeds wave celerity
What does the cross-shore balance involve?
Set-down and set-up, compensating for wave-induced forces
What is the total radiation stress in the wave propagation direction ( extit{x}-direction) according to the given information?
$(n -1/2) E + nE$
In the case of wave propagation in the extit{x}-direction, what are the values of $S_{xx}$ and $S_{yy}$ when $n = 1/2$?
$S_{xx} = 1/2 E$, $S_{yy} = 0$
What are the expressions for $S_{xx}$ and $S_{yy}$ for waves propagating at an angle $\theta$ relative to the positive extit{x}-direction?
$S_{xx} = (n - \frac{1}{2} + n \cos^2 \theta) E$, $S_{yy} = (n - \frac{1}{2} + n \sin^2 \theta) E$
What characterizes the radiation stress components for waves traveling in a direction $\theta$ relative to the positive extit{x}-direction?
The pressure part of the radiation stress is equal to $(n - \frac{1}{2}) E$
What is the total wave-averaged transport of $x$-momentum in the $x$-direction?
$S_{xx}$
What is the shear component of the radiation stress defined as?
Transport of $x$-momentum in the $y$-direction
For the special case of normally incident waves, what is the value of $u_y$ and $S_{xy}$?
$u_y = 0$ and $S_{xy} = 0$
What is the name given to the depth-integrated and wave-averaged flow (or flux) of momentum due to waves?
Radiation stress
What are the components of the wave-induced horizontal flux of momentum through a vertical plane at a given location?
The transfer of momentum $\rho \vec{u}$ through that plane with the particle velocity normal to that plane; the wave-induced pressure force acting on the plane due to the wave induced pressure $p_{\text{wave}}$ in the water
What was the definition of radiation stress given by Longuet-Higgins and Stewart (1964)?
The excess momentum flux due to the presence of waves
What is the name given to the depth-integrated and wave-averaged flow of momentum due to waves?
Radiation stress
What does the wave-induced horizontal flux of momentum through a vertical plane consist of?
Transfer of momentum $\rho \vec{u}$ through that plane with the particle velocity normal to that plane
What are the wave forces responsible for, according to the text?
Impacting mean water motion and levels
Study Notes
Coastal Wave Dynamics and Radiation Stress
- High intensity bands in images are due to persistent wave breaking on inner and outer bars of the beach
- The surf zone has a mild slope and energetic waves, typical in winter with lots of sediment in motion
- Wave breaking and breaker types include spilling, plunging, collapsing, and surging waves
- Momentum and energy transport occur when particle speed exceeds wave celerity
- Shallow-water approximations for wave steepness are given by the limiting wave steepness equation
- Wave energy is given by the equation E=1/8 ρgH^2
- Momentum is a vector quantity, with mass transport expressed as q=ρū
- Radiation stress is a wave-induced momentum flux, resulting in a wave force acting in the opposite direction
- Radiation stress transfer of momentum through a vertical plane is associated with wave-induced pressure force
- Cross-shore balance involves set-down and set-up, compensating for wave-induced forces
- In intermediate water depths prior to wave breaking, the value of n increases in the direction of wave travel, resulting in an equal and opposite wave force acting in the seaward direction
- When waves break, energy dissipation results in a shoreward decrease in Sxx
Radiation Stress and Momentum Transport in Waves
- The particle velocity (u) transports momentum (\rho u) through a plane at every height above the bed (per unit crest length).
- Figure 5.28 and Figure 5.29 illustrate the momentum transport and radiation stress components at a certain point in (x,y)-space for obliquely incident waves.
- A coordinate system is considered according to Fig. 5.28, with the wave propagating at an angle with the (x)-axis and the particle velocity having (u_x) and (u_y) components.
- The total wave-averaged transport of (x)-momentum in the (x)-direction or the radiation stress (S_{xx}) is obtained by integrating over the depth from bottom to instantaneous water surface and time-averaging.
- (S_{xx}) acts normal to the considered plane and is equivalent to a normal stress acting in the (x)-direction.
- The shear component of the radiation stress, (S_{xy}), is defined as the transport of (x)-momentum in the (y)-direction and acts as a shear stress on the plane.
- For the special case of normally incident waves, the (x)-direction is the wave propagation direction, resulting in (u_y) and (S_{xy}) being zero.
- When considering a plane normal to the (y)-direction, the momentum fluxes in the (y)-direction are given by (S_{yy}) and (S_{yx}).
- By using linear wave theory, expressions for the radiation stress can be obtained that are valid to second order.
- The radiation stress in the wave propagation direction due to advection of momentum by the horizontal orbital motion is represented by (S_{xx, \text{hor, part, vel.}}) and depends on the wave energy in the water column.
- In the case of irregular waves, the equation for radiation stress can be applied using the wave energy in the water column.
- There are contributions to the radiation stress due to pressure fluctuations between wave trough and crest level and the vertical oscillatory fluid motion helping carry the weight of the water column.
Test your knowledge of coastal wave dynamics and radiation stress with this quiz. Explore wave breaking types, energy and momentum transport, radiation stress, and cross-shore balance in coastal environments.
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