Wave Mechanics Assignment – Example Solution

ERROR by ME!Do you know what it was?

Other questions with the problem set?

Field Trip – You be the judge…

Field Trip – You be the judge…

Show of hands… who has a problem with pushing the field trip back, yet again, by a week to April 13th?

Could work nicely schedule-wise…

Next week: Apr. 6 & 8 – last of the “new material”

Tues. Apr. 13th – Field Trip

Thurs. Apr. 15th – In class work session on field trip data

Tues. Apr. 20th – Turn in results of field trip data analysis – last day of class

Field Trip – Planned Data Collection Area

Beach Morphology – Examples from Field and Lab

Useful to use extreme vertical exaggeration to visualize features

Be careful not to be misled about the relief of these subtle features.

Examples show usual components of beach profiles – sloping beach face, presence of a berm, bars and troughs.

Depth of Closure

Envelope of Beach Profiles collected over years of profiling - thins and pinches seaward

Depth at which no appreciable seasonal change occurs = Depth of Closure (hc)

Depth of Closure not absolute! Remember the extreme events and inconsistency of nearshore wave climate.

Coefficients are often adjusted depending on the data for a particular site

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hc = 2.28He − 68.5 He2

gTe2

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Equilibrium Beach ProfileBeach appearance, in general, is steep at the shore and decreasing slope with increasing water depth.

Regularity in shape has inspired an attempt to derive mathematical expressions to describe profiles.

Very well known (most common) is the Bruun-Dean “x to the two-thirds” profile.

Originally, used by Per Bruun to represent profile shape seaward of the breaker line, but, as shown by Bob Dean, the relationship maintains accuracy through the surf-zone if the exponent is allowed to vary over a range (0.2 to 1.2) – verified with 504 profiles from U.S. Atlantic and Gulf Coasts.

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h = Ax 2 / 3

Exploring the Bruun-Dean ProfileAn increase in the coefficient, A, or a decrease in the exponent, b, results in an increase in profile concavity.

Increasing concavity changes the beach from dissipative to more reflective.

b=2/3 corresponds to a uniform energy dissipation per volume of incoming broken wave bore.

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h = Ax b

What’s “A” in the Bruun-Dean Eq. Profile Eqn?

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h = Ax 2 / 3

Related to mean grain diameter of sediment on the beach; A increases with sediment diameter or settling velocity.

This brings up an interesting relationship between beach material and morphology.

A governs the overall beach profile slope.

But beach slope also depends on wave conditions, steepness, and wave height/energy, implying a relationship between A and wave conditions.

What are the units on A? Do they make intuitive sense?

Theoretical Justification for “A”

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h = Ax 2 / 3

Dean (1977) theorized that there is a uniform dissipation of wave energy flux per unit volume within the surf zone, written mathematically

Where De is equilibrium wave energy flux dissipation, and h is local depth. By using Airy-theory and depth-controlled wave height, Dean was able to express the profile shape factor as

Compound Profile - two regimes

Inman et al. (1993) compound - conjoined profile.

Accounts for different processes that dominate in the “shore-rise” and “bar-berm” portions of the profile.

What might they be?

Beach Face Slope and Closure Depth – Komar and McDougal (1994) exponential relationship

In general, beach face slope depends on sed. grain size and ~daily wave conditions, while closure depth depends on ~annual wave climate…

Forced through a closure depth of hc=1.57He