Single wave overtopping volumes and their travel distance

SINGLE WAVE OVERTOPPING VOLUMES AND THEIR TRAVEL DISTANCELykke Andersen, Burcharth & Gironella

Coastal Structures 2007, Venice, July, 2007 1 of 17

Single wave overtopping volumes and their travel distance

Coastal Structures 2007, Venice

Lykke Andersen, T., Aalborg University, DenmarkBurcharth, H. F., Aalborg University, Denmark

Gironella, X., UPC, Barcelona, Spain



Introduction• The critical overtopping is typically given as an average discharge and not as single wave overtopping volume and velocity, which are expected to be more directly associated to hazards.

x

1

Qpass / Qtot• The landward distribution of overtopping in combination with the single wave overtopping volume can be used to give an idea of the damage/forces exerted on a structure.

• The landward distance the overtopping water travel put restrictions to the use of these areas and their drainage.



Methodology

Methodology for single wave overtopping estimations:

1. Estimate mean overtopping discharge (e.g. CLASH Neural Network or conventional overtopping formulae)

2. Estimate number of overtopping waves

3. Estimate maximum single wave overtopping volume (use results from 1 and 2)

4. Estimate travel distance of maximum single wave overtopping volume

The present work deals with step 2, 3 and 4 for rubble mound breakwaters.



Experimental set-up (main tests)Lykke Andersen, 2006 (PhD thesis - includes both large and small scale data)

1:2 1:1.5

Water levels

Cross Section 1 - Low wall

Seeward Landward

Cross Section 2 - Normal wall

Cross Section 3 - High wall

Cross Section 4 - High wall with recurved face

1:2 1:1.5CORE

OVERTOPPING TANK

• Chambers more narrow at the bottom for good accuracy also for small overtopping discharges.

• Chambers equipped with surface elevation gauges and pumps configured to start and stop automatically during tests.

• Wave steepness s0p: 0.02 – 0.045



Experimental set-up (additional tests) Burcharth et. al, 2007 (Puerto de la Cruiz, small scale tests)

Long waves (s0p = 0.01)



Data analysis

• Controlling of pumps in overtopping chambers from data acquisition software (e.g. WaveLab2 software package from Aalborg University).

• Select water levels for start and stop of each pump.

• Measure levels in chambers and state of pumps.



Methodology








Number of overtopping wavesFormula by Van der Meer & Janssen (1995)

Non-breaking waves:

2/exp

cHR

NN sc

w

ow

fhc 62.1

Gives in most cases values in the correct order of magnitude. Large difference between the two data sets.

f = 0.4 used• Armour crest freeboard

used (Ac) for all four cross-sections

Burchart et. al, 2007(f = 0.55)



Number of overtopping wavesFormula by Besley (1999)

Number of overtopping waves related to the dimensionless overtopping discharge:

Gives a very good estimate for all tested cases!

sm HgTqQ

2

24199.0

4634.0

101Qfor 1

101Q108for 50.2

108Qfor 4.55

w

ow

w

ow

w

ow

NN

QNN

QNN



Methodology








Single wave overtopping volumeFranco et al. (1994), Van der Meer and Janssen (1995):

B

AVVVF /exp1 A = 0.84, B = 0.75

BowNLnA

VV /1max 1

1

1

ow

i NiVF

Weibulls plotting position formula is used:

Similar to the equation used by Franco et al. (1994) and van der Meer and Janssen (1995) except that they used Now instead of Now +1 in the logarithm.

Bow

B

ow

i iLnNLnANiLnA

VV /1

/1

11

Combining the two equations leads to:

i = 1 =>

Bow

owtotalNLn

NA

VV /1max 1

ow

total

NV

V



Single wave overtopping volume

Bow

owtotalNLn

NA

VV /1max 1

Upper envelope: A = 1.63, B = 0.75

Lower envelope: A = 0.60, B = 0.75

Central: A = 1.12, B = 0.75

Franco + VdM: A = 0.84, B = 0.75Large Now: Franco + VdM is close to a

central estimate

Small Now: Franco + VdM is close to a lower limit (unsafe prediction of Vmax)



Methodology








Landward distribution of mean discharge Formula by Lykke Andersen & Burcharth, 2006

pL0

0.150plevel1.05-

0ptotal

xpassing 0,sh2.7-cos / xmaxs1.1-exp=qq

Ratio of overtopping passing travel distance x at splash down level hlevel:

where is the angle of incidence

x(hlevel=H)

x(hlevel=0)

x

hlevelH

More than 1000 tests



Landward distribution of max single wave overtopping volume

Distribution of large single wave overtopping volumes seems not to be very different from the distribution of the mean discharge

Application of formula for distribution of mean discharge on max single wave overtopping volume.

pL0

0.150plevel1.05-

0ptotalmax,

xpassingmax, 0,sh2.7-cosx / maxs1.1-exp=

VV



Influence of wind & scale effects

• In the EU-CLASH project differences between prototype and small scale overtopping results have been observed.

• The differences might be due to model effects (e.g. wind) or scale effects.

• Wind and scale effects are expected to be most pronounced for relatively small overtopping discharges (q < 1 l/sm).

• The presented formula for landward distribution of overtopping is limited to green water overtopping and cannot predict travel distance of wind carried spray.

• The influence of scale effects on the landward distribution is expected to be quite small as indicated by the test results in large and small scale.



Conclusions• Experimental results on overtopping of individual waves

have been analysed.• A calculation procedure for calculating single wave

overtopping volumes and their travel distance has been presented.

• The formula by Besley (1999) estimate the number of waves overtopping with great accuracy in all of the tested cases.

• The existing formula for single wave overtopping volume has been slightly modified to account for cases with few overtopping waves. Upper and lower envelope curves has been given for single wave overtopping volume.

• The travel distance of maximum single wave overtopping volumes is quite similar to that found for the mean discharge.

Thank you for your attention!

Single wave overtopping volumes and their travel distance

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