ocean wave model andit a li tid its applications ... - unicamp · snl: wave : wave –– wave...

XI Brazil/Japan International WorkshopXI Brazil/Japan International WorkshopEnergy, Biofuels and Sustainable DevelopmentEnergy, Biofuels and Sustainable Development

Ocean Wave ModelOcean Wave Modeld it A li tid it A li tiand its Applicationsand its Applications

to Waves under Typhoonto Waves under Typhoonto Waves under Typhoonto Waves under Typhoon

Environment and Renewable Energy SystemsEnvironment and Renewable Energy SystemsGifu UniversityGifu University

T K b hiT K b hiTomonao KobayashiTomonao Kobayashi

Ocean Wave ForecastingOcean Wave ForecastingApplications:Applications:

••Environment AssessmentEnvironment Assessment••BioBio--enviromentenviroment in Ocean and Coastsin Ocean and Coasts

••NavigationNavigation••Scheduling of NavigationsScheduling of Navigations••Searching Safety PassesSearching Safety Passes

••Structures (Offshore and Nearshore)Structures (Offshore and Nearshore)••Construction Planning and DesignConstruction Planning and Design••MaintenanceMaintenance

Observations and Simulations

Onsite Wave Model Observations Simulations

Period Past Past andPeriod Past Past andFuture

Target Points (Observed) Points andTarget Pointsand Domain

(Observed)Points

Points and Domains

C fid Ob d E ti t dConfidence(Accuracy)

Observed Estimated

Today’s TopicsToday’s Topics

1.1. Characteristics of Ocean WavesCharacteristics of Ocean Waves1.1. Characteristics of Ocean WavesCharacteristics of Ocean Waves2.2. Ocean Wave ModelOcean Wave Model33 Waves under TyphoonWaves under Typhoon3.3. Waves under TyphoonWaves under Typhoon

•• Typhoons are …Typhoons are …T t T hT t T h•• Target TyphoonTarget Typhoon

•• Wave SimulationWave Simulation

Ocean WavesOcean Waves

Irregular wavesIrregular waves••Wave HeightWave Height

In Space…In Space…••Multi directionMulti directionWave Height Wave Height

••Wave LengthWave Length••Multi directionMulti directionRandomRandom

Irregular Wave AnalysisIrregular Wave Analysis

Wave HeightWave HeightWave PeriodWave Period RandomRandom

http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/Images/Fig16‐2.htm

Wave PeriodWave Period


i A l ii A l i

Real SpaceReal Space

Fourier AnalysisFourier Analysis

Spectrum SpaceSpectrum Space

http://www.wikiwaves.org/files/9/99/Fig16‐7s.jpg


Regular Waves

FourierAnalysis

Ocean Waves

Ocean Wave VelocityOcean Wave VelocityWave LengthWave Length

⎞⎛ hgL

Wave LengthWave Length

⎟⎠⎞

⎜⎝⎛=

L

hgLC π

π2tanh

2Wave VelocityWave Velocity ⎠⎝Wave VelocityWave Velocity

Wave Velocity Wave Velocity CC is depend on the Wave Length is depend on the Wave Length LL( also depend on the Wave Period ( also depend on the Wave Period TT

Shorter Shorter ← ← LL → → LongerLongerSlower Slower ← ← CC → → fasterfaster

Ocean Wave EnergyOcean Wave Energy

Wave Energy E

HgE21 ρ=

gy

Hg2ρ

Wave Height

Ocean Wave EnergyOcean Wave Energy

Wave Energy E

HgE21 ρ=

gy

Hg2ρ

f S d C

⎞⎛⎫⎧ hgLLhπ /41

Energy Transfer Speed Cg

( ) ⎟⎠⎞

⎜⎝⎛

⎭⎬⎫

⎩⎨⎧+=

L

hgL

Lh

LhCg

πππ

π2tanh

2/4sinh

/41

2

1





Ocean Wave ModelOcean Wave Model

B h DB h DBathymetry DataBathymetry Data Wind Data over OceanWind Data over Ocean

Wave ModelWave Model

Hori ontal Distrib tionsHori ontal Distrib tions Time Series at arbitrar pointsTime Series at arbitrar pointsHorizontal DistributionsHorizontal Distributions

Wave Height, Period, Direction, etcWave Height, Period, Direction, etc

Time Series at arbitrary pointsTime Series at arbitrary points

Variables in Wave ModelVariables in Wave Model

Target Area is TOO LARGE for the individual wavesTarget Area is TOO LARGE for the individual waves

Wave EnergyWave Energyin Spectrum Spacein Spectrum Space

Wave ProfileWave Profilein Real Spacein Real Space in Spectrum Spacein Spectrum Spacein Real Spacein Real Space

Conserved quantityConserved quantity

Ocean Wave ModelOcean Wave Model

Fundamental EquationsFundamental Equations

( )N∂

Wave EnergyWave Energy

( ) SSSt

Ndsnlin

TermAdvection ++=+∂∂

Energy Inflow from WindEnergy Inflow from Wind

ii

Energy DissipationEnergy Dissipation

Wave Wave –– Wave InteractionWave Interaction

Energy DissipationEnergy Dissipationdue to breakingdue to breaking

Ocean Wave Model :Ocean Wave Model :Ocean Wave Model : Ocean Wave Model : Fundamental EquationsFundamental Equations

Advection terms in XAdvection terms in X--Y planeY plane Source TermsSource Terms

Wave EnergyWave Energy Advection TermsAdvection Terms

Advection Terms on the Earth surfaceAdvection Terms on the Earth surface

LongitudeLongitudeLatitudeLatitude

SSinin :Energy inflow from Wind:Energy inflow from Wind

Phillips’s Resonant theoryPhillips’s Resonant theoryPhillips s Resonant theoryPhillips s Resonant theory

Miles’s Interactive theoryMiles’s Interactive theory

SSdsds :Energy Dissipation due to Breaking:Energy Dissipation due to Breaking

Hasselmann’s(1974) whitecap model (Offshore breaking model)Hasselmann’s(1974) whitecap model (Offshore breaking model)→→ Assuming the similarity of breaking wave profilesAssuming the similarity of breaking wave profiles→ → Assuming the similarity of breaking wave profilesAssuming the similarity of breaking wave profiles

••Unstable phenomenaUnstable phenomena →→ Modeling is difficultModeling is difficult →→ Rough modelRough modelUnstable phenomena Unstable phenomena → → Modeling is difficult Modeling is difficult →→ Rough modelRough model••Working well in the wave modelWorking well in the wave model

SSnlnl :Wave :Wave –– Wave InteractionWave Interaction

C W

Comp. WaveTotal Wave FieldTotal Wave Field

Comp. Wave

Comp. Wave

Comp. Wave

Total Wave Energy : ConstantTotal Wave Energy : Constanto W ve e gy : Co so W ve e gy : Co sSpectrum ProfileSpectrum Profile → → ChangeChange

SSnlnl : Wave : Wave –– Wave InteractionWave Interaction

(In High Frequency Zone)(In Low Frequency Zone)(In Low Frequency Zone) Energy TransferEnergy Transfer ( g eque cy o e)Energy is Inflow from Wind(Sin)

( ow eque cy o e)( ow eque cy o e)Energy is dissipated due toEnergy is dissipated due toBreaking (SBreaking (Sdsds))

With SWith Snlnl

SSnlnl : Wave : Wave –– Wave InteractionWave Interaction

Computation Computation ←←××→ Key Term of Wave Model→ Key Term of Wave Modelis complicateis complicateis complicateis complicate

i ii i i li di li dApproximate Computation Approximate Computation is appliedis applied

Source TermsSource Terms

Source TermsSource Terms

SSinin ：：Energy Inflow from WindEnergy Inflow from WindSS ：：Energy Dissipation due to Breaking (Whitecap offshore)Energy Dissipation due to Breaking (Whitecap offshore)SSdsds ：：Energy Dissipation due to Breaking (Whitecap, offshore)Energy Dissipation due to Breaking (Whitecap, offshore)SSbrbr ：：Energy Dissipation due to Breaking (Shallow breaking, nearshore)Energy Dissipation due to Breaking (Shallow breaking, nearshore)SSbfbf ：：Energy Dissipation due to Friction on the sea bedEnergy Dissipation due to Friction on the sea bedbfbf gy pgy pSSnlnl ：：Wave Wave –– Wave Interaction in Deep WaterWave Interaction in Deep WaterSStritri ：：Wave Wave –– Wave Interaction in Shallow WaterWave Interaction in Shallow Water





TyphoonsTyphoons

StructureStructureStructureStructurehttp://ja.wikipedia.org/wiki/http://ja.wikipedia.org/wiki/

Hurricanes KatrinaHurricanes Katrina（（20052005））http://ja.wikipedia.org/wiki/http://ja.wikipedia.org/wiki/

TyphoonsTyphoonsPaths of Typhoons, Hurricanes and CyclonesPaths of Typhoons, Hurricanes and Cyclones（（19851985～～20052005））

http://ja.wikipedia.org/wiki/http://ja.wikipedia.org/wiki/

http://en.wikipedia.org/wiki/File:Global_tropical_cyclone_tracks-edit2.jpg

TyphoonsTyphoons

Rotation DirectionRotation DirectionN h H iN h H i S hS h••Northern HemiNorthern Hemi--Sphere : Sphere :

Counter Clock WiseCounter Clock Wise••Southern HemiSouthern Hemi --Sphere :Sphere :Southern Hemi Southern Hemi --Sphere : Sphere :

Clock WiseClock Wise

Target TyphoonTarget Typhoon

Typhoon No.16, 2012yp ,

Minimum pressure :935 hPa,at the center of the Typhoon

Maximum Wind Speed :55 m/s ( 200 km/h )( )

Significant Wave Height : HSignificant Wave Height : HssSignificant Wave Height : HSignificant Wave Height : Hss



Origen :Origen :Typhoon’s CenterTyphoon’s Center

Plotted data :Plotted data :Relative peak locationRelative peak locationRelative peak locationRelative peak locationof Wave Height Hs of Wave Height Hs

ConclusionsConclusions




ocean wave model andit a li tid its applications ... - unicamp · snl: wave : wave –– wave...

Documents