JCOMM Workshop – June 2003 CanadianHurricaneCentre Waves-Storm Resonance Lab Why Do Waves Get So Big ? Peter Bowyer Allan MacAfee

JCOMM Workshop – June 2003

CanadianCanadianHurricaneHurricaneCentreCentre

Waves-StormWaves-StormResonance LabResonance Lab

Why Do WavesWhy Do Waves

Get Get So So BigBig??

Peter BowyerPeter BowyerAllan MacAfeeAllan MacAfee


Between Oct. 91 and Sept. 95, EC’s East CoastNOMAD buoys reported some extraordinary waves events, with the 100-year waves being greatly exceeded 3 times in those 4 years


““The Perfect Storm” - October 1991The Perfect Storm” - October 1991““Storm of the Century” - March 1993Storm of the Century” - March 1993

Hurricane Luis - September 1995Hurricane Luis - September 1995

. . . each reported significant wave. . . each reported significant waveheights of 17+ metres, and maximumheights of 17+ metres, and maximum

wave heights 30+ metreswave heights 30+ metres


Our work that has followedOur work that has followedhas focussed on the problemhas focussed on the problemof “what makes big waves?”of “what makes big waves?”


Basics of WavesBasics of Waves

= cT= cT


SPEED OF WAVES IN WATERSPEED OF WAVES IN WATER

c = g tanh 2d 2 ( )[ ]

g = gravitational constant

= wavelength

d = water depth

In deep water, d /gets very large, sotanh (big #) , therefore,

( )

12

12


SPEED OF WAVES IN DEEP WATERSPEED OF WAVES IN DEEP WATER

Since= cT= cT c = gTc = gT 22

= gT= gT 22

22

Therefore, speed (c) and wavelength () are only a function of period (T).

Since the speed is a function of the period,deep water is a “dispersive” medium.


BASIC DEEP WATER WAVE FORMULAEBASIC DEEP WATER WAVE FORMULAE

c = gT 2

c (m/s) = 1.56 T (sec)c (kts) = 3.03 T (sec)

(m) = 1.56 T (sec)(ft) = 5.12 T (sec)

S = H = H (m) 1.56 T (sec)

2

2

2


COMPOSITION OF COMPOSITION OF WAVESWAVES

Any observed wave pattern on the ocean can be shown to be comprised of a number of simple waves, which can differ from each other in height, wavelength and direction. The above profile is the result of two waves differing in only.


COMPOSITION OF COMPOSITION OF WAVESWAVES

In reality, In reality, the sea is a the sea is a superpositiosuperposition of many n of many wave sets.wave sets.


WAVE GENERATION & DECAYWAVE GENERATION & DECAY

W ind

Energy Input

Angular Spreading Dispersion

Friction & air resistance W hitecapping

W ave-bottom interaction ** Surf Breaking **

* Dissipation *

Energy Loss

Non-linear w ave-w ave interactions

* Energy Shift *


WIND-WAVES...depend on:WIND-WAVES...depend on:

Wind speed - the speed of the wind

Fetch - the area of sea surface over which a wind of constant direction (within 30o) and steady speed is, or has been blowing

Duration - the length of time the wind persists from a certain fetch


SIGNIFICANT WAVE HEIGHTSSIGNIFICANT WAVE HEIGHTS

HHsigsig V V22 tanh [ tanh [ (F/V (F/V22))aa]]

V = wind speedV = wind speedF = fetch lengthF = fetch length

““Law of Diminishing Returns”Law of Diminishing Returns”is at workis at work


WIND

FETCH of the wind

SEA CHANGINGTO SWELL

FULLY DEVELOPEDSEARIPPLES CHOP

WIND WAVES


THE WAVE THE WAVE SPECTRUMSPECTRUM

For a simple sine wave, the energy is proportional to the square of the wave height. However, the real sea is a combination of many sinewaves of varying and T. The simplest way of

determining the “energy” of the sea is to examine the relative amounts of energy contained within different period ranges in the sea surface. The plot here of energy vs. frequency (1/T) is a typical energy (or wave) spectrum.

ENERGY

PERIOD


WAVE SPECTRA FOR WAVE SPECTRA FOR DIFFERENT WIND SPEEDSDIFFERENT WIND SPEEDS

As wind speed isincreased, not onlyis more energyavailable (higherwave heights), butlonger waves(longer period orlower frequency) arealso present. Also,the period ofmaximum energyshifts to longerperiod waves.

SP

EC

TR

AL

EN

ER

GY

60 20 10 5

PERIOD (sec)

40 knots

30 knots

20 knots


WAVE ENERGY vs. WIND WAVE ENERGY vs. WIND SPEEDSPEED

Wave energy is very sensitive to wind speed:

Wave Energy (Wave Height)

Wave Height (Wind Speed)

Wave Energy (Wind Speed)

2

2

4

Best Wave Model Uses “Good” WindsBest Wave Model Uses “Good” Winds


STATISTICAL DESCRIPTION STATISTICAL DESCRIPTION OF WAVE HEIGHTSOF WAVE HEIGHTS

H = significant wave height = average height of highest 1/3 waves in record (corresponds roughly to visually observed heights)

H = average of all height values .625 H

H = average height of (1/n)th highest waves

H = 1.3 H

H = 1.8 to 2.2 times the H

SIG

SIGAV

SIG

1/n

1/10

MAX SIG


WAVE GROUPSWAVE GROUPS

Although individual crests advance at a speed correspondingto their wavelength (as a coherent unit), the group advances at its own speed, called the GROUP SPEED....Cg.

The group speed is the speed at which the energy propagates(moves with the speed of the “middle” of the pack...slower thanleading waves and faster than trailing waves.)

The energy is equally split between KE and PE, however, theKE is associated with movement of particles in nearly closedorbits....therefore, the KE is not propagated. The PE isassociated with net displacements of particles and this movesalong with the wave at the wave speed.


WAVE GROUPSWAVE GROUPS

Therefore, only1/2 of the energy (PE) is propagated at the wave speed which is the same as the total energy moving at 1/2 of the wave speed.

C (kts) = C = C (kts) = C = 1.51 T 1.51 T (sec)(sec) 22

gg


Period (sec) Group Speed (kts)5 86 97 118 129 14

10 1511 1712 1813 2014 2115 2316 2417 2618 2719 2920 30

6m waves developedby a marginal gale

Long swell well aheadof a storm system

16m “fully-developed”seas in a big storm

TYPICALTYPICALWAVEWAVE

PERIODSPERIODS


Bretschneider Wave CalculatorBretschneider Wave Calculator


Bretschneider Wave Growth Equations

Given a wind speed, an initializing fetch length (Fi), and a time interval, wave height and period,growth duration, and equivalent fetch are computed using a set of coefficients, constants, andEquations 3.1 to 3.5 below:

Wave Height H = .304801 a1U2 tanh(b1g1)/g

Wave Period P = 2a2U tanh(b2g2)/gEquivalent Fetch Fe = U2 g1

(1/r1) / (6077.28g)Duration Tc = 2 S U / 3600ga2r2b2

(1/r2) Growth 6S = cj X

(p+2j) / (p+2j) j=0

where cj = 22k B(2k) / (2k)! X = b2 (gf/U2)r2

B(2k) = Bernoulli number for k = 1,2,3…

Coefficients and Constants a1 = .283 r1 = .42 a2 = 1.2 r2 = .25 b1 = .0125 g = 32.2 b2 = .077 p = 3.0

Input Data Wind speed - U ( kt) Fetch length - F (nmi) Duration - Td (hr)

An iterative solution requires convergence on the wave growth duration to within 0.1%. Note thatthe computed time Tc may be less than the initial estimated wind duration as it is dependent onthe wave growth and limited by the time to reach a fully-developed sea. The equivalent fetch Fe

is the distance the waves must travel to achieve wave height H when subjected to a constantwind U. To insure Fe is not under-estimated during the iterative calculations, Fi is set at anarbitrarily large value (e.g. 2000 nmi) which is unlikely to occur during the life cycle of atypical weather system.


STATIONARY FETCHES - STATIONARY FETCHES - Example 1Example 1

Coast-lines - The fetch at point B is the distance AB. The fetch at point D is the distance CD. Since AB > CD, a wind from the coast would generate greater waves at B than at D because of the proximity of the coastline.


Curvature - The fetch at point B is limited by the curvature of the flow upwind. The fetch is now the distance upwind from B to the point where the wind direction becomes more than 30o different from that at B.



Fanning out of flow The fetch at point B is limited by the fanning out of the isobars upstream, therefore giving decreasing wind speeds. In this case, the criterion that is recommended is for wind-speed reductions > 20%.



Moving FetchesMoving Fetches

Most interesting wind systems are not stationary. Determining fetches in a moving system can be complex and time consuming.

As it turns out, the determination of the fetch is as critical as the determination of the wind speed


XO

CycloneMotion

WIND

WINDW

IND

WIN

D

11

22

33 44


Time T0

PB

..

.

PA

PC . PD

.PE

Winds Perpendicularto Fetch Motion

XO

1


Time T1

PB

.

PA

PC...

..

. PD

.PE.

.

Waves from Waves from PPA A & P& PCC & P & PEE

grew for less thangrew for less than1 time-step1 time-step

before movingbefore movingoutside the fetchoutside the fetch

Waves fromWaves fromPPB B & P& PDD

have grown forhave grown for1 time-step1 time-step


XO

1


Time T2

PB

.

PA

PC.....

...

. PD

.PE.

.

.

.

Waves fromWaves fromPPBB moved outside moved outside

the fetch afterthe fetch after1 time-step1 time-step

Waves from PWaves from PDD

grew for almost grew for almost 2 time-steps2 time-steps


XO

1



Time T0

PB

..

.

PA

PC .PD

.PE

XO

2


Time T1

PB

..

.

PA

PC .PD

.PE

..

...

Waves from Waves from PPA A & P& PDD & P & PEE



Waves fromWaves fromPPC C & P& PBB

have grown forhave grown for1 time-step1 time-step


XO

2


Time T2

PB

..

.

PA

PC .PD

.PE

...

.....

.

.

Waves fromWaves fromPPBB moved outside moved outside

the fetch afterthe fetch after1 time-step1 time-step

Waves from PWaves from PCC

have grown for have grown for 2 time-steps2 time-steps


XO

2


Time T3

PB

..

.

PA

PC .PD

.PE

....

....

.....

..

Waves from PWaves from PCC

grew for moregrew for morethan 2 time-stepsthan 2 time-steps



XO

2


Time T0

PB..PC . PD

.PE

PA.

XO3

Winds OpposingFetch Motion


Time T1

PB..PC . PD. .

.

Waves from PWaves from PC C & P& PDD

grew for 1 time-stepgrew for 1 time-step

Waves fromWaves fromPPE E & P& PB B & P& PAA



. .. PE

PA..

.

XO3



Time T2

PB

..

.

PA

PC . PD

.PE. .

.. .

. .

..

.

Waves from PWaves from PC C & P& PDD

moved outside themoved outside thefetch before growingfetch before growing

for evenfor even2 time-steps2 time-steps

XO3



Winds WithFetch Motion

Time T0

PB..PC . PD

. PA

.PE

XO 4


Time T1

PB

..

.

PA

PC . PD

.PE

. .

.. .

Waves from PWaves from PAA

fell behind thefell behind thefetch beforefetch before

even 1 time-stepeven 1 time-step


XO 4


Time T2

PB

..

.

PA

PC . PD

.PE

.. .

....

. ..

Waves from PWaves from PEE

grew for more thangrew for more than1 time-step but1 time-step but

were then outrunwere then outrunby the fetchby the fetch


XO 4


Time T3

PB

..

.

PA

PC . PD

.PE

..

.

..

.

..

...

..

..

Waves fromWaves fromPPC C & P& PBB & P & PDD

are still growingare still growingafter 3 time-stepsafter 3 time-steps. . . although those. . . although those

from Pfrom PBB will soon be will soon be

outrun by theoutrun by thefetchfetch


XO 4


Time T4

PB

..

.

PA

PC . PD

.PE

..

..

..

..

..

..

..

..

..

..

Waves fromWaves fromPPC C & P& PDD

are still growingare still growingafter 4 time-stepsafter 4 time-steps


XO 4


Time T5

PB

..

.

PA

PC . PD

.PE

..

..

.

..

..

.

..

..

..

..

..

..

..

.

Waves fromWaves fromPPDD were finally were finally

outrun by the fetchoutrun by the fetchafter more thanafter more than

4 time-steps4 time-steps

Waves fromWaves fromPPCC are still growing are still growing

after 5 time-stepsafter 5 time-steps


XO 4


XO

CycloneMotion

WIND

WINDW

IND

WIN

D

11

22

33 44

“Fetch Reduction”always occurs inQuadrants 1-2-3. . . as long as thecyclone is moving


XO

CycloneMotion

WIND

WINDW

IND

WIN

D

11

22

33 44

“Fetch Enhancement”may occur inQuadrant 4

. . . depending on thespeed of the cyclone


Waves Moving in Waves Moving in Same DirectionSame Directionas Their Stormas Their Storm

Potential for Potential for ResonanceResonance


Fetch movingmuch fasterthan waves

Mid-latitudesystems

A



Mid-latitudesystems

AWaves moving

much fasterthan fetch

Tropical stormsin the tropics

B



Mid-latitudesystems

AWaves moving



BSome wavesin harmonywith fetch

Strong windsystems in

mid-latitudes

C



Mid-latitudesystems

AWaves moving



BPerfect

Waves-StormResonance

The REALREAL“Perfect Storms”

DSome wavesin harmonywith fetch

Strong windsystems in

mid-latitudes

C


NASANASAScanning Radar Altimetry dataScanning Radar Altimetry datafor Hurricane Bonnie (98) asfor Hurricane Bonnie (98) asit tracked northward off theit tracked northward off the

US east coast.US east coast.


Courtesy of Ed Walsh, NASA(runs automatically in SlideShow mode)


The dominant waves are in the frontThe dominant waves are in the frontright quadrant where a degree of right quadrant where a degree of

resonance exists in a single spectralresonance exists in a single spectralmode.mode.

This allows for ease ofThis allows for ease ofmodelling and parametrization.modelling and parametrization.


Fetches moving withFetches moving withconstant speedconstant speed


All of theAll of thewaves quicklywaves quicklyoutrun the slow-outrun the slow-moving stormmoving stormsystemsystem

The steady-stateThe steady-statesolution issolution isreached inreached in7+ hours.7+ hours.


Most of theMost of thewaves stillwaves stilloutrun theoutrun theslower movingslower movingstorm systemstorm system



Waves leavingWaves leavingthe trailing edgethe trailing edgeof the fetch areof the fetch areoutrun by theoutrun by thewind system . . .wind system . . .however, allhowever, allothers move outothers move outahead.ahead.



Most waves areMost waves aresoon outrun by thesoon outrun by theinitially quicker initially quicker moving wind moving wind system . . .system . . .however, waveshowever, wavesstarting at thestarting at theleading edge “hold leading edge “hold on long enough” on long enough” until their speeduntil their speedcatches up to thecatches up to thesystem speed . . .system speed . . .and eventuallyand eventuallyoutruns the system.outruns the system.

Steady state isSteady state isreached in 30 hrs.reached in 30 hrs.


All waves areAll waves arequickly outrunquickly outrunby the muchby the muchquicker windquicker windsystem . . . andsystem . . . andgrowth is verygrowth is verylimited.limited.

The steady-stateThe steady-statesolution issolution isreached in reached in under 5 hours.under 5 hours.


Maximum waveMaximum wavegrowth occursgrowth occursfor a constantfor a constantsystem speed of system speed of 20.7 knots. All20.7 knots. Allspeeds greaterspeeds greateror less than thisor less than thiswill result inwill result inlower wavelower waveheights.heights.

The steady-stateThe steady-statesolution is notsolution is notreached untilreached until34 hours.34 hours.


Even for speedsEven for speedsonly slightlyonly slightlygreater, theregreater, thereis a significantis a significantdifference indifference inthe resonancethe resonanceof the storm-of the storm-waves system.waves system.


Consider . . .Consider . . .- a fixed fetch length (eg. 50 nmi)- a fixed fetch length (eg. 50 nmi)- fixed wind speed throughout fetch - fixed wind speed throughout fetch (eg. 50 kts)(eg. 50 kts)

What is the relationship between What is the relationship between fetch-enhancement and storm speed?fetch-enhancement and storm speed?


Storm-Wave Resonance CalculatorStorm-Wave Resonance Calculator





Fetch Enhancement

Fetch Reduction


Fetch Reduction

Enhancement

Significant Enhancement

Extreme Enhancement


Maximum Significant Wave Height for Storm Speed vs Wind Speed50 nm Fetch Area

0

5

10

15

20

25

30

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Storm Speed (kt)

Max

imu

m S

igW

ave

Hei

gh

t (m

)

Wind 20

Wind 30

Wind 40

Wind 50

Wind 60

Wind 70

Wind 80

Wind 90

Wind 100


Maximum Significant Wave Height vs Wind Speed at Optimum Storm Speed for 50 nm Fetch Area

y = 0.3216x - 3.65

R2 = 0.9984

0

5

10

15

20

25

3020 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 10 0

Wind Speed (kt)

Max

imu

m S

igW

ave

Hei

gh

t


Maximum Normalized Wave Height for Storm Speed vs Wind Speed50 nm Fetch Area

0

0.5

1

1.5

2

2.5

3

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Storm Speed (kt)

Max

imu

m N

orm

aliz

ed W

ave

Hei

gh

t

Wind 20

Wind 30

Wind 40

Wind 50

Wind 60

Wind 70

Wind 80

Wind 90

Wind 100

EnhancementEnhancement

ReductionReduction


Maximum Normalized Wave Height vs Wind Speedat Optimum Storm Speed for 50 nm Fetch Area

y = - 9/x + 1.7841x0.0873

R2 = 0.9576

0

0.5

1

1.5

2

2.5

3

20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 10 0

Wind Speed (kt)

No

rmal

ized

Wav

e H

eig

ht


Observation:Observation:

1. The greater the wind speed,1. The greater the wind speed, the greater the enhancementthe greater the enhancement


Maximum Possible Significant Wave HeightsMaximum Possible Significant Wave Heights35-knot winds35-knot winds










Observations:Observations:

2. The smaller the fetch, the2. The smaller the fetch, the greater the enhancementgreater the enhancement

3. The greater the wind speed,3. The greater the wind speed, the greater the optimumthe greater the optimum storm speedstorm speed


Maximum Duration of Wave Growth for Storm Speed vs Wind Speed50 nm Fetch Area

0

10

20

30

40

50

60

70

80

90

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Storm Speed (kt)

Ho

urs

of

Wav

e G

row

th

Wind 20

Wind 30

Wind 40

Wind 50

Wind 60

Wind 70

Wind 80

Wind 90

Wind 100


Maximum Duration of Wave Growth vs Wind Speedat Optimum Storm Speed for 50 nm Fetch Area

0

10

20

30

40

50

60

70

80

90

20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 10 0

Wind Speed (kt)

Wav

e G

row

th (

Ho

urs

)

Unlikely durationsUnlikely durations


Maximum Possible Hours of Wave Growth

0

50

100

150

200

25020

28

36

44

52

60

68

76

84

92

10 0

Wind Speed (kt)

Maxim

um

Du

rati

on

of

Wave

Gro

wth

50-SSDur

100-SSDur



4. Optimum fetch-enhancement is 4. Optimum fetch-enhancement is more probable for high wind / smallmore probable for high wind / small fetch events than low wind / highfetch events than low wind / high fetch events . . . because thefetch events . . . because the required durations are on the orderrequired durations are on the order of 1-day of 1-day (ie: these events can(ie: these events can actually occur)actually occur)


Conclusion 1Conclusion 1Observations 1-4 select sub-synoptic Observations 1-4 select sub-synoptic scale storm systems for the greatest scale storm systems for the greatest potential for optimum resonancepotential for optimum resonance(tropical cyclones and polar lows)(tropical cyclones and polar lows)


Wind Speed vs Storm Speed for Maximum Fetch Enhancement50 nm Fetch Area

y = -0.001x2 + 0.3131x + 3.65

R2 = 0.9986

0

5

10

15

20

25

20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 10 0

Wind Speed (kt)

Op

tim

um

Sto

rm S

pee

d (

kt)


Fetch EnhancementsWind Speed vs. System Speed for 50 nmi Fetch Length

0

5

10

15

20

25

30

35

40

45

20

26

32

38

44

50

56

62

68

74

80

86

92

98

104

110

116

122

128

134

140

146

Wind Speed (kt)

Syste

m S

peed

(kt)

Optimum Enhancement

Optimum Enhancement



0

5

10

15

20

25

30

35

40

45

50

20

27

34

41

48

55

62

69

76

83

90

97

104

111

118

125

132

139

146

Wind Speed (kt)

Syste

m S

peed

(kt)

Optimum Enhancement

Optimum Enhancement



0

5

10

15

20

25

30

35

40

45

50

20

27

34

41

48

55

62

69

76

83

90

97

104

111

118

125

132

139

146

Wind Speed (kt)

Syste

m S

peed

(kt)


0

5

10

15

20

25

30

35

40

4520

26

32

38

44

50

56

62

68

74

80

86

92

98

104

110

116

122

128

134

140

146

Wind Speed (kt)

Syste

m S

peed

(kt)


Optimum Storm Speeds (kt) for Maximum Wave Enhancement

0

5

10

15

20

25

30

20

29

38

47

56

65

74

83

92

Wind Speed (kt)

Sto

rm S

peed

(kt)

50-StormSpeed

100-StormSpeed

Average speed of TCs Average speed of TCs south of 30south of 30ooNN

Average speed of TCs Average speed of TCs north of 40north of 40ooNN

50 nm Fetch

100 nm Fetch



5. Fetch enhancement for tropical 5. Fetch enhancement for tropical cyclones of TS or Hurricane strength cyclones of TS or Hurricane strength is greater in mid latitudes than in the is greater in mid latitudes than in the tropics.tropics.


Conclusion 2Conclusion 2

The highest waves with tropical The highest waves with tropical storms or hurricanes could be storms or hurricanes could be expected in mid latitudes . . .expected in mid latitudes . . .

. . . a unique problem with ETs. . . a unique problem with ETs


As tropical cyclones become ET,As tropical cyclones become ET,they are typically increasing in speedthey are typically increasing in speed

under the influence of aunder the influence of amid-latitude stream.mid-latitude stream.

The seas associated with theseThe seas associated with thesesystems (and even minimal hurricanessystems (and even minimal hurricanesthat move “quickly”) can be greaterthat move “quickly”) can be greater

than those associated withthan those associated withmajor hurricanes.major hurricanes.


For example:For example:

A Hurricane in the TropicsA Hurricane in the Tropics Moving 5 kts . . . area of 65-kt windsMoving 5 kts . . . area of 65-kt windsover a fetch length of 100 nm . . . canover a fetch length of 100 nm . . . cangenerate Hgenerate Hsigsig of almost 11 m. of almost 11 m.

A Tropical Storm in Mid-LatitudesA Tropical Storm in Mid-LatitudesMoving 19Moving 1911//22 kts . . . area of 50-kt winds kts . . . area of 50-kt winds

over a fetch length of 100 nm . . . canover a fetch length of 100 nm . . . cangenerate Hgenerate Hsigsig of almost 15 m. of almost 15 m.

-27


Accelerating FetchesAccelerating Fetches

If the storm system accelerates with a speedIf the storm system accelerates with a speedmatching that of the waves it generates, thematching that of the waves it generates, theconditions for conditions for perfectperfect resonance exists and resonance exists andwave growth is more easily maximized.wave growth is more easily maximized.


Wave Speed vs Hours of Growth for Different Wind Speeds

0

10

20

30

40

50

60

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

113

120

Hours of Wave Growth

Wav

e G

rou

p S

pee

d (

kts)

20-Kt

40-Kt

60-Kt

80-Kt

100-Kt

Log. (100-Kt)

Log. (80-Kt)

Log. (60-Kt)

Log. (40-Kt)

Log. (20-Kt)


Storms moving in a straight line, atStorms moving in a straight line, atthe optimum speed,the optimum speed,

can result in the potential forcan result in the potential forphenomenally large waves tophenomenally large waves to

developdevelop


Luis (95)Luis (95) Felix (95)Felix (95)

Bonnie (98)Bonnie (98)Danielle (98)Danielle (98)

Luis (95)Luis (95) Felix (95)Felix (95)

Bonnie (98)Bonnie (98)Danielle (98)Danielle (98)


HURRICANELUIS

Sept. 10-11, 1995

85 knots

10 / 06Z

2585 knots

10 / 12Z

10 / 18Z

85 knots

95 knots

11 / 00Z

11 / 06Z

105 knots

32

38

39


Max ReportedMax ReportedSig. WavesSig. Waves17+ metres17+ metres

66

55

44

33

22

77 88

99

1010

HURRICANELUIS

Sept. 10-11, 1995

85 knots

10 / 06Z

2585 knots

10 / 12Z

10 / 18Z

85 knots

95 knots

11 / 00Z

11 / 06Z

105 knots

32

38

39

Wave Field atWave Field atSept.11 - 01ZSept.11 - 01Z

**

For 17 metres,For 17 metres,85 kts is required85 kts is requiredthroughout thisthroughout thisbox for aboutbox for about

14 hours14 hours

QEIIQEII


Significant & Maximum Wave Heights at Buoy 44141During Hurricane LuisSeptember 10-11, 1995

0

5

10

15

20

25

30

35

14

16

18

20

22 0 2 4 6 8 10

12

14

Time (UTC)

Wave H

eig

hts

(m

etr

es)

Sig.Wave

Max.Wave

Nearest pointNearest pointto storm to storm

Storm speedStorm speed40+ knots40+ knots

andandincreasing increasing


Since Luis was quickly outstripping Since Luis was quickly outstripping the waves generated by its wind-field,the waves generated by its wind-field,

the waves were not as large as theythe waves were not as large as theymight of been, had Luis movedmight of been, had Luis moved

considerably slower.considerably slower.

Since Luis was quickly outstripping Since Luis was quickly outstripping the waves generated by its wind-field,the waves generated by its wind-field,

the waves were not as large as theythe waves were not as large as theymight of been, had Luis movedmight of been, had Luis moved

considerably slower.considerably slower.


60 knots

55 knots

50 knots

50 knots

50 knots

50 knots

50 knots

21 / 00Z

21 / 06Z

21 / 12Z

21 / 18Z

22 / 00Z

22 / 06Z

22 / 12Z

43

35

31

28

TS FELIXAug. 21-22, 1995


60 knots

55 knots

50 knots

50 knots

50 knots

50 knots

50 knots

21 / 00Z

21 / 06Z

21 / 12Z

21 / 18Z

22 / 00Z

22 / 06Z

22 / 12Z

43

35

31

28

TS FELIXAug. 21-22, 1995

2

3

4

5

6

Max ReportedMax ReportedSig. WavesSig. Waves13+ metres13+ metres

**

Wave Field atWave Field atAug.22 - 00ZAug.22 - 00Z


36 hours36 hours

7


Significant & Maximum Wave Heights at 44137During Tropical Storm Felix

August 21-22, 1995

0

5

10

15

20

25

30

14

15

16

17

18

19

20

21

22

23 0 1 2 11 12

13

14

Time (UTC)

Wave H

eig

hts

(m

etr

es)

Sig.Wave

Max.Wave



andandincreasingincreasing


The waves in Felix were quiteThe waves in Felix were quitelarge, considering the wind field.large, considering the wind field.However, like Luis, Felix beganHowever, like Luis, Felix began

outstripping the waves . . . whichoutstripping the waves . . . whichmight have eventually grown larger,might have eventually grown larger,

had Felix’s translation remainedhad Felix’s translation remainedbelow 30 knots.below 30 knots.

The waves in Felix were quiteThe waves in Felix were quitelarge, considering the wind field.large, considering the wind field.However, like Luis, Felix beganHowever, like Luis, Felix began

outstripping the waves . . . whichoutstripping the waves . . . whichmight have eventually grown larger,might have eventually grown larger,

had Felix’s translation remainedhad Felix’s translation remainedbelow 30 knots.below 30 knots.


TS BONNIEAug. 29-30, 1998

45 knots

29 / 00Z 45 knots

29 / 06Z 45 knots

29 / 12Z45 knots

29 / 18Z

45 knots

30 / 00Z

45 knots

30 / 06Z

45 knots

30 / 12Z

45 knots

30 / 18Z

18

18

26

28

34

25 26


TS BONNIEAug. 29-30, 1998

45 knots

29 / 00Z 45 knots

29 / 06Z 45 knots

29 / 12Z45 knots

29 / 18Z

45 knots

30 / 00Z

45 knots

30 / 06Z

45 knots

30 / 12Z

45 knots

30 / 18Z

18

18

26

28

34

25 26

Max ReportedMax ReportedSig. WavesSig. Waves11 metres11 metres

**

2


42 hours42 hours

Wave Field atWave Field atAug.30 - 00ZAug.30 - 00Z

34

5

67


Significant & Maximum Wave Heights at Buoy 44137During Tropical Storm Bonnie

August 29-30, 1998

0

2

4

6

8

10

12

14

16

12

14

16

18

20

22 0 2 4 6 8 10

12

Time (UTC)

Wave H

eig

hts

(m

etr

es)

Sig.Wave

Max.Wave



andandincreasing increasing


The waves with Bonnie were closeThe waves with Bonnie were closeto being fully-developed for the windto being fully-developed for the wind

field associated with the storm.field associated with the storm.The proximity of the wave max withThe proximity of the wave max with

the storm centre shows that thethe storm centre shows that thetwo moved in reasonable harmony.two moved in reasonable harmony.A slightly slower translation speedA slightly slower translation speedfor the storm might have resultedfor the storm might have resulted

in slighly larger waves.in slighly larger waves.

The waves with Bonnie were closeThe waves with Bonnie were closeto being fully-developed for the windto being fully-developed for the wind

field associated with the storm.field associated with the storm.The proximity of the wave max withThe proximity of the wave max with

the storm centre shows that thethe storm centre shows that thetwo moved in reasonable harmony.two moved in reasonable harmony.A slightly slower translation speedA slightly slower translation speedfor the storm might have resultedfor the storm might have resulted

in slighly larger waves.in slighly larger waves.


HURRICANEDANIELLE

Sept. 2-3, 1998

32

30

24

23

23

70 knots

02 / 18Z

70 knots

03 / 00Z

70 knots

03 / 06Z

70 knots

03 / 12Z

65 knots

03 / 18Z 65 knots

04 / 00Z

**


HURRICANEDANIELLE

Sept. 2-3, 1998

32

30

24

23

23

70 knots

02 / 18Z

70 knots

03 / 00Z

70 knots

03 / 06Z

70 knots

03 / 12Z

65 knots

03 / 18Z 65 knots

04 / 00Z

2

Max ReportedMax ReportedSig. WavesSig. Waves16 metres16 metres

**

Wave Field atWave Field atSept.3 - 08ZSept.3 - 08Z

34 5

67

89


16 hours16 hours


Significant & Maximum Wave Heights at Buoy 44141During Hurricane Danielle

September 2-3, 1998

0

5

10

15

20

25

3021

23 1 3 5 7 9 11 13

15

17

19

Time (UTC)

Wave H

eig

hts

(m

etr

es)

Sig.Wave

Max.Wave


Storm speedStorm speed25 knots25 knots

andandslowing slowing


Like Bonnie, the max in the wave-field Like Bonnie, the max in the wave-field with Danielle was very close to the with Danielle was very close to the storm centre . . . showing that thestorm centre . . . showing that the

two were moving in reasonabletwo were moving in reasonableharmony. harmony.

Danielle actually began slowing,Danielle actually began slowing,allowing the wave-field to catch upallowing the wave-field to catch up

and grow larger what might beand grow larger what might beexpected.expected.

Like Bonnie, the max in the wave-field Like Bonnie, the max in the wave-field with Danielle was very close to the with Danielle was very close to the storm centre . . . showing that thestorm centre . . . showing that the

two were moving in reasonabletwo were moving in reasonableharmony. harmony.

Danielle actually began slowing,Danielle actually began slowing,allowing the wave-field to catch upallowing the wave-field to catch up

and grow larger what might beand grow larger what might beexpected.expected.


The Worst-Case Scenario is, therefore,The Worst-Case Scenario is, therefore,a storm centre . . . a storm centre . . .

- moving in a straight line, - moving in a straight line, - covering a large distance over open - covering a large distance over open ocean, ocean, - increasing in speed, continually - increasing in speed, continually matching the speed of the waves that matching the speed of the waves that corresponds closely with the peak in the corresponds closely with the peak in the energy spectrum energy spectrum

The Worst-Case Scenario is, therefore,The Worst-Case Scenario is, therefore,a storm centre . . . a storm centre . . .

- moving in a straight line, - moving in a straight line, - covering a large distance over open - covering a large distance over open ocean, ocean, - increasing in speed, continually - increasing in speed, continually matching the speed of the waves that matching the speed of the waves that corresponds closely with the peak in the corresponds closely with the peak in the energy spectrum energy spectrum


The Pattern . . . The Pattern . . .

- area of maximum waves to the right of- area of maximum waves to the right of track track- very tight gradient in the wave field at- very tight gradient in the wave field at the leading edge . . . as the trapped-fetch the leading edge . . . as the trapped-fetch arrives, it brings with it a “wall of water” arrives, it brings with it a “wall of water” (no forerunners to warn of storm) (no forerunners to warn of storm)- waves - waves cancan subside rather quickly in the subside rather quickly in the wake of these storms, however, the wake of these storms, however, the trailing gradient is usually much weaker trailing gradient is usually much weaker

The Pattern . . . The Pattern . . .

- area of maximum waves to the right of- area of maximum waves to the right of track track- very tight gradient in the wave field at- very tight gradient in the wave field at the leading edge . . . as the trapped-fetch the leading edge . . . as the trapped-fetch arrives, it brings with it a “wall of water” arrives, it brings with it a “wall of water” (no forerunners to warn of storm) (no forerunners to warn of storm)- waves - waves cancan subside rather quickly in the subside rather quickly in the wake of these storms, however, the wake of these storms, however, the trailing gradient is usually much weaker trailing gradient is usually much weaker


ExerciseExercise

Using the Wave Resonance Calculator on theUsing the Wave Resonance Calculator on theWorkstation, what significant wave heights Workstation, what significant wave heights would you expect along the coastline of Atlanticwould you expect along the coastline of AtlanticCanada with different fetch scenarios A-N?Canada with different fetch scenarios A-N?


Modelling the ProblemModelling the ProblemSpecifically for TCsSpecifically for TCs

• Resonance is, uniquely, a unidirectional problem, so Resonance is, uniquely, a unidirectional problem, so the spectral issues simplify considerablythe spectral issues simplify considerably

• Since wind is, by far, the most critical issue, even a Since wind is, by far, the most critical issue, even a simple first generation parametric approach will give simple first generation parametric approach will give superior results, if the wind field is treated accurately.superior results, if the wind field is treated accurately.


Currently, we are tacklingCurrently, we are tacklingthis problem by coupling the this problem by coupling the CHC’s hurricane wind modelCHC’s hurricane wind model

with a single-purpose wavewith a single-purpose wavemodel . . .model . . .

. . . that looks only at the . . . that looks only at the maximum possible Hmaximum possible Hsigsig

with a given storm with a given storm

Currently, we are tacklingCurrently, we are tacklingthis problem by coupling the this problem by coupling the CHC’s hurricane wind modelCHC’s hurricane wind model

with a single-purpose wavewith a single-purpose wavemodel . . .model . . .

. . . that looks only at the . . . that looks only at the maximum possible Hmaximum possible Hsigsig

with a given storm with a given storm




The output of theThe output of the“trapped-fetch” model shows“trapped-fetch” model shows

trajectories, maximum Htrajectories, maximum Hsigsig, and, and

duration of wave growth fromduration of wave growth fromindependent fetch areas withinindependent fetch areas within

the tropical cyclonethe tropical cyclone

The output of theThe output of the“trapped-fetch” model shows“trapped-fetch” model shows

trajectories, maximum Htrajectories, maximum Hsigsig, and, and

duration of wave growth fromduration of wave growth fromindependent fetch areas withinindependent fetch areas within

the tropical cyclonethe tropical cyclone


..

.

Point of initialwave development

Waves stopgrowing

Waves nolonger

sustained

9.237

54

Max.Sig. Wave

9.2 m

37 hoursof growth

54 hoursto end of

9.2 mmaintenance


For Bonnie, theFor Bonnie, theCHC model predictsCHC model predictsa maximum Ha maximum Hsigsig

passing throughpassing throughsouthern Maritimesouthern Maritimewaters of 10.3m.waters of 10.3m.

Compare this to theCompare this to themaximum Hmaximum Hsig sig of of

10.8m reported by a10.8m reported by aweather buoy.weather buoy.


For Luis, theFor Luis, theCHC model predictsCHC model predictsa maximum Ha maximum Hsigsig

of 18.9 m to theof 18.9 m to theright-of-track.right-of-track.

A weather buoyA weather buoyreported a maximumreported a maximumHHsigsig of 17.1 m. of 17.1 m.


For Danielle, theFor Danielle, theCHC model predictsCHC model predictsa maximum Ha maximum Hsigsig

of 15.5 m passingof 15.5 m passingthrough southern through southern Maritime waters.Maritime waters.

A weather buoyA weather buoyreported 15.8 m.reported 15.8 m.


Documents

JCOMM Workshop – June 2003 CanadianHurricaneCentre Waves-Storm Resonance Lab Why Do Waves Get So Big ? Peter Bowyer Allan MacAfee