wave dynamics

8/20/2019 Wave Dynamics

1/27

AN INTRODUCTION

WAVE DYNAMICS


2/27

Scope

• Wave generation• Regular Linear waves• Wave Charecteristics


3/27

Introduction

• Ocean surface waves cause periodic loads on allman-made structures in the sea

• Responses: accelerations, displacements, internal

loads• ffects of waves ! resulting motions on ships: " #dded resistance " Impaired safet$

" #ffect operations of weapons ! e%uipment " #ffect aircraft& helo operations " #ffect humans


4/27

Wave generation

• Waves generated '$ a ship or an$ other floating structure which ismoving, either at a constant forward speed or '$ carr$ing out anoscillator$ motion(

• Waves generated '$ the interaction 'etween wind and the sea

surface(• Waves generated '$ astronomical forces: )ides(• Waves generated '$ earth%ua*es or su'marine landslides: )sunamis(• Interaction of ocean currents can create ver$ large wave s$stem

• +ree surface waves generated in fluids in partiall$ filled tan*s suchas fuel or cargo tan*s on a ship(

• o single mathematical solution• #ppro.imations re%uired: 'e aware of simplifications


5/27


6/27

)sunami


7/27


8/27

Wind generated wave s$stems• )he si/e of the wave s$stem is dependent on the following

factors• Wind Strength :

" )he faster the wind speed, the larger the energ$ transfer to the sea( " Larger waves are generated '$ strong winds(

• Wind 0uration : " )he longer wind 'lows, the greater the time the sea has to 'ecomefull$ developed at that wind speed(

• Water 0epth : " Wave heights are affected '$ water depth(

" Waves traveling to 'each will turn into 'rea*ing wave '$ a deptheffect(

• +etch " +etch is the area of water that is 'eing influenced '$ the wind( " )he larger the fetch, the more efficient the energ$ transfer 'etween

wind and sea(


9/27

W i n d E n e r g y

Energy Dissipationdue to viscous friction

Fully Developed Wave(Wind energy =Dissipation Energy)

Swell (low frequency long wave)

Small Wave or dying out(Wind energy Dissipation Energy

Wave creation se%uence


10/27


11/27

Wind-generated waves

• Sea " )rain of waves driven '$ the prevailing local

wind field

" Short-crested with the lengths of the crests onl$a few 12-34 times the apparent wavelength " 5er$ irregular " 6ulti-directional " Crests are fairl$ sharp " #pparent wave period ! apparent wave length

var$ continuousl$


12/27

Wind-generated waves

• Swell " Waves which have propagated out of the area

and local wind in which the$ were generated

" o longer dependent upon the wind " Individual waves are more regular and the

crests are more rounded " Lengths of the crests are longer: several 17-84

times the virtual wave length " Wave height is more predicta'le


13/27

Superposition principle• Wind waves are ver$ irregular• Can 'e seen as a superposition of

man$ simple, regular harmonic wavecomponents, each with its ownamplitude, length, period or fre%uenc$

and direction of propagation• )o anal$/e complicated wave s$stems,it is necessar$ to *now the propertiesof the simple harmonic components " time and location-dependent pressure in

the fluid " relation 'etween wave length and wave period

" energ$ transport, etc(


14/27

Regular Waves: 0efinitions

• Origin ! conventions• Crest, )rough, #mplitude 1 ζ a 4, 9eight 19 2 ζ a 4• Wave length 1 λ4, Wave ;eriod 1)4• Wave steepness 9& λ•


15/27


16/27

=asic Categories

• 0eep water waves 1short waves4 " )he water is considered to 'e deep if the water depth, h,

is more than half the wavelength, λ " )hus, h& λ > ?&2 or λ &h @ 2

" )hese 1relativel$4 short waves do not AfeelA the seafloor(• Shallow water waves 1long waves4

" )he water is considered to 'e shallow if the waterdepth, h, is less than ?&2B of the wave length, λ

" )hus, h& λ @ ?&2B orλ &h > 2B( " )he sea floor has a ver$ large influence on the

characteristics of these 1relativel$4 long waves(


17/27


18/27

Linear Wave theor$

• ;rogressive harmonic wave:ζ ζ a cos1*.- ωt4

• Linear wave theor$: watersurface slope is ver$ small

• Wave steepness is small• 9armonic displacements,velocities, accelerations !

pressures have linear relationwith wave surface elevation

• ;rofile of such a wave loo*sli*e sine& cosine

• 6otion of water particle inwave depends on depth 'elow

SWL


19/27

Relations for Linear Waves• Continuit$ 1Laplace e%uation4• =oundar$ Conditions

" Sea 'ed " +ree surface d$namic " +ree surface *inematic

• 0ispersion relation: ω 2 = g.k. tanh(kh)- 0eep water: ω 2 = g.k or λ ≈ 1.56 T 2- Shallow water: ω =k.√ghor λ = T.√gh

• ;hase velocit$:- 0eep water: c = √(g/k) or c ≈1.25√λ ≈ 1.56 T- Shallow water: c= √gh 1 critical velocit$A4


20/27

5elocit$ field of water particles

In shallow water wave In deep water wave


21/27

)raDectories of water particles


22/27

+ig


23/27


24/27


25/27

;ressure and nerg$

• )otal pressure in short waves 1deep water4

• Einetic energ$ ;otential energ$ per unit width 1crest length4 per unit hori/ontal sea surface area

• )otal Wave nerg$ per unit hori/ontal sea surface area


26/27

Wave group


27/27

Froup 5elocit$

• In deep water,cg c&2

• In shallow water,cg c

wave dynamics

Documents