IAHR 2015, The Hague, The Netherlands, 2 July 2015

Joint IAHR-COPRI Symposium on Long Waves and Relevant Extremes

SWAN’s Underestimation of Long Wave

Penetration into Coastal Systems

Jacco Groeneweg and Joana van Nieuwkoop

Deltares, The Netherlands

Context

1. Primary motivation

2. Conclusions from previous studies

3. Goal of present study

4. Reanalysis of hindcast studies

5. Conclusions and recommendations

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Safety assessment of primary sea and flood defenses

Hydraulic Boundary Conditions (HBC)

Numerical modelling (SWAN)

Motivation (1)

• Various improvements in SWAN (journal publications, conference presentations)

• Penetrated North Sea wave energy underestimated by SWAN

Bed Level

[m NAP]

UHW1

Measured SWAN

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Motivation (2)

Primary goal: Provide an explanation for SWAN’s underestimation

of swell wave penetration in tidal inlet systems and, if possible,

improve SWAN.

No conclusive explanation for underestimation from several studies

in the past, until

• Groeneweg et al. (JWPCE, 2015): hypothesis that 2D nonlinear

interactions play an important role

• Groeneweg et al. (ICCE2014): theoretical explanation and

further verification

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TRITON SWAN Observed

Numerical analysis (1) – JWPCE 2015

Case 2 (Hm0 = 0.082m; T = 1.87s;

short-crested)

TRITON

SWAN

Hm0 [m]

1. Waves refract on channel edge.

2. Under oblique angles SWAN is not sufficiently able to transport

the energy into and across the channel.

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D

B

TRITON SWAN

B B

D

NONLINEAR

Hm0 = 0.082 m

LINEAR

Hm0 = 0.00082 m

B

D

Simplified geometry depth [m]

Hypothesis:

(2D) Nonlinear interactions

play an important role in the

transmission of energy from

flats into navigation channels.

Case 3 (T = 1.45 s; long-crested)

Numerical analysis (2)

Through nonlinear shoaling

energy is transferred to

larger incident angles!

φ2,-2 φ2,2

φ1,3φ1,1φ1,-1 φ1,-3

φ2,0

φ3,3φ3,1φ3,-1φ3,-3

f [H

z]

ky [rad/m]

Theoretical explanation – ICCE 2014

White arrows: super-harmonic interactions

Red / purple arrows: sub-harmonic interactions

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[]

Courtesy: Toledo (JFM, 2013)

deep

d = 0.4 m

Further verification – ICCE2014

• Overestimation of second harmonic

with SWAN over transitional slope.

TRITON SWAN SWAN, no LTA

B B

D

• Spectrum TRITON in deep part

broader at primary frequency D

• 2D nonlinear interactions broaden the

spectra in directional space, so

components are generated that can

enter the channel.

• Mechanism not in SWAN (only 1D) !!!

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Goal of the present study

• Determine under which conditions SWAN underestimates the low frequency wave energy when propagating into complex tidal inlet systems.

• Special attention is paid to the role of nonlinear interactions and refraction.

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Method

• Re-analysis of existing wave hindcasts of

storm periods in three regions (buoys; radar)

• SWAN with atmospheric and hydrodynamic

forcing from the same sources

• Numerical and physical settings similar

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Eastern Wadden Sea

19 cases

Western Scheldt

30 cases

Ameland tidal inlet

29 cases

radar

H1

0 [

m]

Depth

[m

]

Peak wave dir [degN]

Results – Ameland tidal inlet (1)

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Strong correlation between l-f energy

underestimation and geometry, and thus

channel orientation, location of tidal flats,

water depth, wind/wave direction.

AZB21

AZB21

Depth [m]

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Results – Ameland tidal inlet (2)

AZB32

observed

SWAN

Observed waves enter or cross the channel, whereas the computed waves are refractively trapped to the channel edges.

White arrow:

dominant wave direction (radar)

Purple arrow:

peak wave direction (SWAN)

Conclusions and discussion

• For many instances a mismatch between measured and computed l-f energy is observed in the tidal inlet gorge, to a large extent determined by the local geometry relative to water depth, incident wave direction (wind direction).

• For all three areas, cases were found where differences could be explained by the hypothesis of Groeneweg et al. (2014, 2015):

• The observed waves could enter or cross the channel, whereas the computed waves were refractively trapped to the channel edges.

• L-f part of observed spectra directionally broader than the computed spectra, due to 2D nonlinear interactions.

• But not for all cases: differences already at offshore boundary, strong currents may be effective, other inaccuracies in SWAN may play a role.

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• Since there are many factors that determine the reliability of SWAN results in the considered complex areas, do not derive a generic concept to correct SWAN results for the observed underestimation of low-frequency wave energy.

• Develop a 2D alternative for the presently implemented 1D three-wave interaction formulation (LTA) in SWAN.

• Make use of simultaneously measured 2D wave spectra and radar data.

• While storms are rare, the information they provide is very valuable. Continuation of the measurement programs in the Wadden Sea and Zeeland estuaries is recommended.

Recommendations

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Acknowledgements

The presented work is part of the WTI 2017 project (“Research

and development of safety assessment tools of Dutch flood

defences”), commissioned by the department WVL of

Rijkswaterstaat in the Netherlands.

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