Engineering Task
Geoge
GuidePart2.pdf
Example: Fetch-limited Wave Growth in a Lake
The purpose of this simple application is to study fetch-limited wind-
wave growth in a 40 km long and 40 km wide lake having a constant
water depth of 15 m. The fully spectral formulation is used. The results
can readily be compared to well-known fetch-limited growth
relationships in the literature.
◼ The wind is blowing from West (270 °N) for 15 hours. The wind
speed is constant U10= 13 m/s.
Estimate the wave charateristic parameters.
1
22019/5/16
Simulation completed
Run completed successfully
Post-process and presentation
◼ Points: time series, .dfs0
◼ Lines: time series for a line .dfs1
◼ Areas: for a domain .dfsu or .dfs2
View .dfs0 files directly ◼ Wave parameters at the middle of the lake (Point 1: x = 38 km, y = 20 km
Point 2: x = 20 km, y = 20 km) and at the middle of the east boundary
◼ Time series – “Waves_x20km_y20km.dfs0”
Use Plot Composer to generate
figure for a repot
1
2
3. Select ‘Time Series Plot’
“File”->”New”->”MIKE ZERO”->”Plot Composer”
Use “Plot Composer” – “Time series Plot”
Present the wave height variation at Points 1 and 2
East Point: Sign. Wave Height [m] Middle Point: Sign. Wave Height [m]
00:00 2002-01-01
04:00 08:00 12:00 0.0
0.5
1.0
1.5
Empirical formula
Fetch-limited JONSWAP formulae
◼ The non-dimensional (*) fetch limited, JONSWAP wave parameters for deep water are,
◼ where the non-dimensional (*) JONSWAP parameters are
g is the acceleration due to gravity
F is the fetch length
U10 is the wind speed 10m above the water surface (international convention)
Hmo is the significant wave height derived from the zeroth moment (mo) of the spectrum (ie the area under the spectrum)
Tp is the period corresponding to the peak of the spectrum
the superscript * denotes a dimensionless parameter
9
( ) 1/ 2
* * 0.0016
mo H F= ( )
1/ 3 * *
0.286 p
T F=
* * *
2 2
10 10 10
; ; pmo
mo p
gTgHgF F H T
U U U = = =
Duration limited JONSWAP formulae
◼ In cases where the wind duration limits the growth of waves, the fetch length (F) is replaced by an effective fetch length (Feff) defined as the (shorter) “fetch length” that produces the same duration limited wave height.
where the dimensionless wind duration is,
◼ If F* > F*eff then conditions are duration limited and so F*eff is used in place of F* in the fetch limited JONSWAP formulae on the previous slide.
10
3 / 2 *
*
68.8 eff
t F
=
*
10
gt t
U =
JONSWAP computation
procedure 1. Determine U10, td, and F
2. Compute F*, t* and F*eff 1. if F* < F*eff waves are fetch limited
use F* in JONSWAP formulae
2. if F* > F*eff waves are duration limited
use F*eff in JONSWAP formulae
3. Compute JONSWAP wave parameters for the following cases: 1. deep water
2. fully developed sea
4. Compare all values and the smallest is the correct (limiting) result.
11
Comparison between models
Hs (m) Tp (s)
JONSWAP 1.33 5.02
MIKE 21 SW 1.34 4.54
View .dfs1 files directly ◼ Wave parameters along the line across the lake
◼ Profile file- dfs1 - Waves_line.dfs1
Set up each item on the menu bar according to your
Use “Plot Composer” – “Profile Plot”
Present the wave height distribution along a line
“File”->”New”->”MIKE ZERO”->”Plot Composer”
Sign. Wave Height [m]
1/01/2002 3:00:00 PM
0 10000 20000 30000 40000 0.0
0.5
1.0
1.5
View .dfsu files directly ◼ Wave parameters at the whole domain
◼ dfsu - Waves_parameters.dfsu
Set up each item on the menu bar according to your
Use “Plot Composer” – “Dfsu Plot”
Present the wave height distribution in the whole domain
“File”->”New”->”MIKE ZERO”->”Plot Composer”
View spectrum at a point ◼ Wave spectrum at a point
◼ dfsu - spectra.dfsu (unstructured mesh)
.dfsu direct view – (unit is not correct)
Set up each item on the menu bar according to your
Use “Plot Composer” – “Dfsu Plot”
Present the wave spectrum distribution
“File”->”New”->”MIKE ZERO”->”Plot Composer”
View spectrum at a point ◼ Wave spectrum at a point
◼ dfs2 - spectra.dfs2 (regular grid)
To generate Polar Plot – the spectrum file is .dfs2 Set up each item on the menu bar according to your
Use “Plot Composer” – “Polar Plot”
Present the wave spectrum distribution
“File”->”New”->”MIKE ZERO”->”Plot Composer”
N
N E
E
S E
S
S W
W
N W
3 s
6 s
9 s
12 s
15 s
18 s
Spectrum in a point
East Point: Energy
density
Above 0.0225
0.0210 - 0.0225
0.0195 - 0.0210
0.0180 - 0.0195
0.0165 - 0.0180
0.0150 - 0.0165
0.0135 - 0.0150
0.0120 - 0.0135
0.0105 - 0.0120
0.0090 - 0.0105
0.0075 - 0.0090
0.0060 - 0.0075
0.0045 - 0.0060
0.0030 - 0.0045
0.0015 - 0.0030
Below 0.0015
1/01/2002 15:00:00, Time step: 45 of 45
Example: Fetch-limited Wave Growth in a Lake
The purpose of this simple application is to study fetch-limited wind-
wave growth in a 40 km long and 40 km wide lake having a constant
water depth of 15 m. The fully spectral formulation is used. The results
can readily be compared to well-known fetch-limited growth
relationships in the literature.
◼ The wind is blowing from West (270 °N) in 6 hours. Then the wind
direction turns to a south direction (180 °N) from where it blows for 8
hours. The wind speed is constant U10= 13 m/s.
Estimate the wave charateristic parameters.
29
wind conditions - .dfs0
Spectral variation
Slope lake example ◼ East side deep 30 m
◼ West side: shallow (< 2m)
◼ The wind is blowing from East for 15 hours. The wind speed is constant
U10= 25 m/s.
◼ Estimate the wave charateristic parameters.
Eastly wind
Impact of breaking
No breaking With breaking
Sign. Wave Height [m]
1/01/2002 3:00:00 PM
0 10000 20000 30000 0.0
1.0
2.0
3.0
4.0
Sign. Wave Height [m]
1/01/2002 3:00:00 PM
0 10000 20000 30000 0.0
1.0
2.0
3.0
4.0
5.0
Water depth [m]
1/01/2002 3:00:00 PM
0 10000 20000 30000
5
10
15
20
25
30
With breaking
No breaking
How about bottom friction?
Wave study on the Coast
Questions on Assignment 2?
