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2005
• #
2009 – $ %
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2003:
-
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2009 :
#
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* # (1996 – 2003)
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Directional Waverider Buoy DATAWELL, 7 90 . .
20 !"
1.28 ".
#
$
%
Storm in Blue Bay. Black Sea, Gelendzhik. Photo Igor Podymov
& + / .
2'
2003. ( 5 .+
5
.)
* *21 / ,
12 . 15
+ 2%
$
Hmax Hmean
12
Hmax, Hmean,
2003
9
6
0 0
5
10
)
,
15
20
25
01.02.2003
Time, hour, 02.02.2003 0.16
Spectra. m2 s
3
Fmax, "
0.14
Fmax, Hz
0.12
Frequency, Hz Time, hour, 02.02.2003
0.1
0.08
0.06 0
5
10
)
,
15
20
01.02.2003
Time, hour, 02.02.2003
Changes of wave height and frequency of spectrum maximum
25
#
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)
15
/degrees
5
x 10
Spectrum, m 2 s
0.195 0.185 0.175 0.165 0.155 0.145 0.135 0.125 0.115 0.105 0.095 0.085 0.075 0.065 0.055 0.045 0.035 0.025 220
x 10
6
10
5
0 240
260
280 300 Direction, degrees
320
340
0
0.05
0.1 Frequency, Hz
0.15
6
4
Spectrum, m
2
Frequency, Hz
02011316.MEM Spectrum, m 2 s/degr
3
2
13
1
0 220
240
260
280 300 Direction, degrees
320
340
360
2'
2003 .
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2003 .
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Spavlet, s2
Spectra. m2s
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Frequency, Hz Pseudofrequency, Hz Frequency, Hz
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02.02.2003 10:25 AM
600
Height, cm
400 200 0 -200 -400 -600
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Time, s 520
540
560
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0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
1
1.5
2
2
spectra, cm s
waves, cm
0.04 0.05 20 Wave series 23 0.02 0 10 -0.05 0 0.05 20 40 60 80 100 120 140 160 0 0 10 0 -0.05 0 0.05 20 40 -0.0260 80 100 120 140 160 10 0 0 -0.05 0 -0.04 0.05 20 40 60 80 100 120 140 160 10180 0 145 150 155 160 0 -0.05 0 0.0520 40 60 80 100 120 140 160 180 40 0 -0.05 0 0.04 40 60 80 100 120 140 160 180 3 0 0 -0.04 0 0.04 40 60 80 100 120 140 160 180 3 0 0 -0.04 0 0.0440 60 80 100 120 140 160 180 0 2200 0 -0.04 0 100 150 200 20 0.02 50 0 -0.02 0 100 150 200 2 0 0.0250 0 -0.02 0 80 100 120 140 160 180 200 2 0 0.02 60 0 -0.02 0 80 100 120 140 160 180 200 2220 0 0.0260 0 -0.02 0 0.02 120 80 100 140 160 180 200 220 20 0.02 0 -0.02 0 0.02 80 100 140 160 180 200 220 2 0 0 120 0 -0.02 0 0.02 80 100 -0.02 120 140 160 180 200 220 2 0 0 -0.02 0 80 100 120 140 160 180 200 220 240 0 -0.04
170time, s 175
180
185
0.5
frequency, Hz
*
Initial regular waves are transformed in irregular. The beginning of formation of an irregularity corresponds to appearance of Benjamin-Feir nonlinear instability. During nonlinear interactions the main peak of spectrum is displaced toward the low frequencies. This displacement is discrete in both time and frequency. It is main reason of fluctuations of amplitudefrequency content of individual waves on deep water. The next development of an irregularity under influence of instability leads to formation of separate extreme high waves.
â&#x20AC;&#x201C;
Waves, cm
Waves, cm
Waves and its wavelet transform on distances 20 and 32 m (series 23 )
Time, s
Pseudofrequency, Hz
Pseudofrequency, Hz
Time, s
Time, s
Time, s
Wave group structure is complex. In waves at the same time exist several wave group structures with close frequency scales corresponding to nonlinear instability. Individual extreme waves have much wider band of frequencies in the crest, than neighboring waves. Obviously extreme waves are formed during the moment of superposition in time as maxima of waves of different frequency scales, and their maxima of envelope.
+
!
Frequency, Hz
Nonlinear instability of waves forms own wave group structure inside of existing waves.
Pseudofrequency, Hz
Waves of a frequency scale of the main spectral maximum have rather slowly fluctuating envelope. Waves of a frequency scales of nonlinear instability have envelopes with other frequency of fluctuations
2
Frequency, Hz
gauge 6 - 20 m 0.02 0.01 0
-0.02 -0.03
40
60
80
100
120
140
160
180
200
200
220
Pseudofrequency, Hz
gauge 10 - 32 m 0.02 0.01 Frequency, Hz
waves, cm
-0.01
0 -0.01 -0.02 -0.03
60
80
100
120
140 time, s
160
180
Pseudofrequency, Hz
Spectra of modulus of wavelet coefficients (spavelets) on distances 20 and 32 m , experimental series 23.
0
!
-
* "
Waves, cm
'
Time, s
Extreme wave is at the moment of superposition of maximums of waves of different frequency scales: scales of main maximum of spectrum and scales corresponding of nonlinear instability. Series 23, distance 32 m. a â&#x20AC;&#x201C; waves, h- high frequency part of waves, l â&#x20AC;&#x201C; low frequency part of waves corresponding to frequency scales of nonlinear instability.
seria-NewYearWave-gauge-0
seria-NewYearWave-gauge-0
20
seria-23-gauge-11
0.06
seria-23-gauge-11
4
0
-5
0.03
0.02
Frequency, Hz , "
, 0.04
2
waves, *cm
*
5
0.6
0.05
, "
10
waves, m ,
Frequency, Hz
15
0
-2
0.01
-10
-4
0 0
200
400
600 ,
800
1000
1200
0.04
time, s
0.06
0.08
0.1
0.12
0.14 , "
0.16
0.18
0.2
0
Pseudofrequency, Hz
50
100
0.5 0.4 0.3 0.2 0.1 0
150
1
time, ,s
2
4
Pseudofrequency, Hz
seria-23-gauge-11 seria-NewYearWave-gauge-0
3 , "
seria-23-gauge-11
seria-NewYearWave-gauge-0
2.5
400 6 350
8 10
2
18 20 22
250 200 150 100
+ , 22sc Spectra. cm
,
16
+
$
,
14
scales $ ,
c
2 Spectra. m s 2
12
scales
0.4
300
0.6
0.8
1
1.5 1 0.5
24 50 26
0 0 0
200
400
600 ,
time, s
800
1000
0.04
0.06
0.08
0.1
0.12 %
0.14 , "
0.16
0.18
0.2
50
100 ,
time, s
0
0
1
2
3
4
% , " Frequency, Hz
Frequency, Hz
New Year Wave
Laboratory experimental waves
3
.+
–
2009
!
*
0.7 - 0.714 ", H/L=0.135, .
!
10.5 cm, $ 28.06-r2, Signal [cm]
28.06-r2, Amplitude spectra [cm] 2 A1
G1
50 0 -50
0
100
200
300
400
500
0
600
A5
G5
0 0
100
200
300
400
500
A10
G10
100
200
300
400
500
600 A14
G15
0
1
1.2
1.4
1.6
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
0.2
0.4
0.6
0.8
1
1.2
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.2
0.4
0.6 0.8 1 frequency, Hz
1.2
1.4
1.6
1.4
1.6
0.5 0
0
100
200
300
400
500
0 1
600
20 0 -20
A20
G20
0.8
1
100
200
300
400
500
600
1
1.2
1.4
1.6
0.5 0
0
0
0.5
20 0 -20
A26
G26
0.6
1 0
0
50
0
100
200
300
400
500
0
600
A28
0 -20
0
1
20 G28
0.4
2
0
-50
0.2
1 0
600
50
-50
0
2
50
-50
1
0
100
200
300 time, s
400
500
600
0.5 0
0
/
-
,"
.
-
!
* 4 $
0.7 - 0.714 ", H/L=0.05,
!
,
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29.06-r1, Signal [V]
29.06-r1, Amplitude spectra [V] 1 A1
G1
10 0 -10
0
100
200
300
400
500
0.5 0 0.4
600
A5
G5
0 0
100
200
300
400
500
G15
0 0.4
A15 0
100
200
300
400
500
0.9
1
0.5
0.6
0.7
0.8
0.9
1
0.5
0.6
0.7
0.8
0.9
1
0.5 0 0.4
600
1 A20
20 G20
0.8
1
0
0 -20
0.7
0.5
600
20
-20
0.6
1
10
-10
0.5
0
100
200
300
400
500
0.5 0 0.4
600
0.5
0.6
0.7
0.8
0.9
1
0.5
0.6
0.7
0.8
0.9
1
0.9
1
A25
1 G25
20 0 -20
0 0.4 0
100
200
300
400
500
600 1 A27
G27
20 0 -20
0.5
0
100
200
300 time, s
400
500
600
0.5 0 0.4
0.5
0.6
0.7 frequency, Hz
0.8
#
,"
.
-
/
'
,2 "
, 8-21
2009
#
$
waves, m
,
-
2Hsign
150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 -10 -20 -30 -40 -50 -60 -70 400
450
500
550
600
650
700
750
800
850
time, s
H/Hsig=2.45
14.10.2009
"
'
4 row waves
150 G3 G4 G6 G17 100
50
0
-50
-100
4225
4230
4235
4240
4245
4250
4255
4260
4265
4270
7000
6000
spectrum, cm2 s
5000
4000
3000
2000
1000
0
0
0.05
0.1
0.15
0.2
0.25
frequency, Hz
0.3
0.35
0.4
0.45
0.5
waves, cm
120 110 100 90 80 70 60 50 40 30 20 10 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 0
100
200
300
time, s
H/Hsig=2.1
400
500
600
9000
8000
7000
spectrum, cm2 s
6000
5000
4000
3000
2000
1000
0
0
0.05
0.1
0.15
0.2
0.25
frequency, Hz
0.3
0.35
0.4
0.45
0.5
# .
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