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Pipeng Free Online Software : Airy Wave Calculators
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Pipeng : Airy Linear Gravity Waves Calculation Module

Airy Wave Calculators

Description : Airy linear gravity water wave calculators.

Discussion : The Airy linear gravity wave theory is a first order model of freshwater and seawater gravity waves. The wavelength L is calculated by solving

L = Ldw tanh( 2 π d / L )

where

L = Ocean Wave Length
Ldw = Deep Water Wave Length = ( 9.80665 T 2 ) / ( 2 π )
T = Ocean Wave Period
d = Water Depth

The Airy wave is assumed to have a simple sinusoidal (first order harmonic) profile which is a reasonable approximation for small amplitude deep water waves. As the wave amplitude increases and or the water depth decreases the waves tend to become more peaky and are no longer a simple sinusoidal shape. The Airy wave model is then less accurate for analysing water particle motions. For large amplitude waves, or shallow water waves other wave theories such as Stokes wave theory, Cnoidal wave theory and solitary wave theory are often used. The water wave theory selection figure shows the range of validity of the wave models based on the dimensionless water depth and the dimensionless wave height.

Figures :

Calculator Tools In This Module:

CALC : Ocean : Wave 021 : Airy Linear Wave Theory : Calculator
CALC : Ocean : Wave 022 : Airy Wave Surface Profile And Wavelength Only : Calculator
CALC : Ocean : Wave 023 : Airy Wave Horizontal Velocity And Acceleration Only : Calculator
CALC : Ocean : Wave 024 : Airy Wave Vertical Velocity And Acceleration Only : Calculator
CALC : Ocean : Wave 025 : Airy Wave Horizontal And Vertical Velocity And Acceleration Only : Calculator
CALC : Ocean : Wave 026 : Airy Wave Check Calculations : Calculator


Link

Module List

CALC : Ocean : Wave 021 : Airy Linear Wave Theory : Calculator

Description : Calculate Airy linear gravity wave parameters.

Discussion : Calculates all Airy wave parameters : the wave length, surface profile, water particle velocity and acceleration, wave number, wave celerity, wave frequency, wave length over water depth ratio (lod), wave height over water depth ratio (hod), dimensionless wave height and dimensionless water depth. Check that the convergence check is close to or equal to one. For brevity the function working is not shown in the check calculations. Use the Airy wave check tool to check the function working.

Input Variables :

  • Θ = Wave Phase Angle
  • H = Ocean Wave Height
  • T = Ocean Wave Period
  • d = Water Depth
  • z = Height Above Seabed

Output Variables :

  • H* = Dimensionless Wave Height
  • L = Ocean Wave Length
  • Ua = Horizontal Velocity Amplitude
  • Up = Horizontal Velocity Phase
  • Va = Vertical Velocity Amplitude
  • Vp = Vertical Velocity Phase
  • c = Ocean Wave Celerity
  • cvg = Convergence Check
  • d* = Dimensionless Water Depth
  • dUa = Horizontal Acceleration Amplitude
  • dUp = Horizontal Acceleration Phase
  • dVa = Vertical Acceleration Amplitude
  • dVp = Vertical Acceleration Phase
  • f = Ocean Wave Frequency
  • hod = Wave Height Over Water Depth Ratio
  • lod = Wave Length Over Water Depth Ratio
  • n = Ocean Wave Number
  • w = Wave Trough Depth
  • y = Ocean Wave Surface Profile

Calculation :

list( L , cvg ) = AiryL( d , T )
y = AiryP( H , Θ )
list( Ua , dUa , Up , dUp ) = AiryAU( H , d , T , L , z , Θ )
list( Va , dVa , Vp , dVp ) = AiryAV( H , d , T , L , z , Θ )
c = L / T
w = d - H / 2
n = ( 2 π ) / L
f = 1 / T
hod = H / d
lod = L / d
H* = H / ( 9.80665 T 2 )
d* = d / ( 9.80665 T 2 )

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CALC : Ocean : Wave 022 : Airy Wave Surface Profile And Wavelength Only : Calculator

Description : Calculate Airy linear gravity wave surface profile and wavelength.

Discussion : Calculates only the wave length and surface profile. The surface profile is the height of the wave above sea level. Check that the convergence check is close to or equal to one. The function working is not shown in the check calculations. Use the Airy wave check tool to check the function working.

Input Variables :

  • Θ = Wave Phase Angle
  • H = Ocean Wave Height
  • T = Ocean Wave Period
  • d = Water Depth

Output Variables :

  • L = Ocean Wave Length
  • cvg = Convergence Check
  • y = Ocean Wave Surface Profile

Calculation :

list( L , y , cvg ) = AiryTP( H , d , T , Θ )

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CALC : Ocean : Wave 023 : Airy Wave Horizontal Velocity And Acceleration Only : Calculator

Description : Calculate Airy linear gravity wave horizontal water particle motion versus phase angle.

Discussion : Calculates only the horizontal water particle velocity and acceleration. Check that the convergence check is close to or equal to one. For brevity the function working is not shown in the check calculations. Use the Airy wave check tool to check the function working.

Input Variables :

  • Θ = Wave Phase Angle
  • H = Ocean Wave Height
  • T = Ocean Wave Period
  • d = Water Depth
  • z = Height Above Seabed

Output Variables :

  • Up = Horizontal Velocity Phase
  • cvg = Convergence Check
  • dUp = Horizontal Acceleration Phase

Calculation :

list( Up , dUp , cvg ) = AiryTU( H , d , T , z , Θ )

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CALC : Ocean : Wave 024 : Airy Wave Vertical Velocity And Acceleration Only : Calculator

Description : Calculate Airy linear gravity wave vertical water particle motion versus phase angle.

Discussion : Calculates only the vertical water particle velocity and acceleration. Check that the convergence check is close to or equal to one. For brevity the function working is not shown in the check calculations. Use the Airy wave check tool to check the function working.

Input Variables :

  • Θ = Wave Phase Angle
  • H = Ocean Wave Height
  • T = Ocean Wave Period
  • d = Water Depth
  • z = Height Above Seabed

Output Variables :

  • Vp = Vertical Velocity Phase
  • cvg = Convergence Check
  • dVp = Vertical Acceleration Phase

Calculation :

list( Vp , dVp , cvg ) = AiryTV( H , d , T , z , Θ )

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CALC : Ocean : Wave 025 : Airy Wave Horizontal And Vertical Velocity And Acceleration Only : Calculator

Description : Calculate Airy linear gravity wave horizontal and vertical water particle motion versus phase angle.

Discussion : Calculates only the horizontal and vertical water particle velocity and acceleration. Check that the convergence check is close to or equal to one. For brevity the function working is not shown in the check calculations. Use the Airy wave check tool to check the function working.

Input Variables :

  • Θ = Wave Phase Angle
  • H = Ocean Wave Height
  • T = Ocean Wave Period
  • d = Water Depth
  • z = Height Above Seabed

Output Variables :

  • Up = Horizontal Velocity Phase
  • Vp = Vertical Velocity Phase
  • cvg = Convergence Check
  • dUp = Horizontal Acceleration Phase
  • dVp = Vertical Acceleration Phase

Calculation :

list( [up, dUp , Vp , dVp ) = AiryTUV( H , d , T , z , Θ )

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CALC : Ocean : Wave 026 : Airy Wave Check Calculations : Calculator

Description : Calculate Airy linear gravity wave check values.

Discussion : Use this tool to check the Airy wave calculations. Check that the convergence check is close to or equal to one, and that the check wavelength is equal to the Airy wave length.

Input Variables :

  • Θ = Wave Phase Angle
  • H = Ocean Wave Height
  • T = Ocean Wave Period
  • d = Water Depth
  • z = Height Above Seabed

Output Variables :

  • H* = Dimensionless Wave Height
  • L = Ocean Wave Length
  • Lchk = Ocean Wave Length Check
  • Ldw = Deep Water Wave Length
  • Ua = Horizontal Velocity Amplitude
  • Up = Horizontal Velocity Phase
  • Va = Vertical Velocity Amplitude
  • Vp = Vertical Velocity Phase
  • c = Ocean Wave Celerity
  • cvg = Convergence Check
  • d* = Dimensionless Water Depth
  • dUa = Horizontal Acceleration Amplitude
  • dUp = Horizontal Acceleration Phase
  • dVa = Vertical Acceleration Amplitude
  • dVp = Vertical Acceleration Phase
  • f = Ocean Wave Frequency
  • hod = Wave Height Over Water Depth Ratio
  • lod = Wave Length Over Water Depth Ratio
  • n = Ocean Wave Number
  • w = Wave Trough Depth
  • y = Ocean Wave Surface Profile

Calculation :

list( L , cvg ) = AiryL( d , T )
Ldw = ( 9.80665 T 2 ) / ( 2 π )
Lchk = Ldw tanh( 2 π d / L )
y = H / 2 cos( Θ )
Ua = ( ( π H ) / T )( cosh( 2 π z / L ) / sinh( 2 π d / L ) )
dUa = ( 2 π 2 H / T 2 )( cosh( 2 π z / L ) / sinh( 2 π d / L ) )
Va = ( ( π H ) / T )( sinh( 2 π z / L ) / sinh( 2 π d / L ) )
dVa = ( 2 π 2 H / T 2 )( sinh( 2 π z / L ) / sinh( 2 π d / L ) )
Up = ( ( π H ) / T )( cosh( 2 π z / L ) / sinh( 2 π d / L ) )cos( Θ )
dUp = ( 2 π 2 H / T 2 )( cosh( 2 π z / L ) / sinh( 2 π d / L ) )sin( Θ )
Vp = ( ( π H ) / T )( sinh( 2 π z / L ) / sinh( 2 π d / L ) )sin( Θ )
dVp = - ( 2 π 2 H / T 2 )( sinh( 2 π z / L ) / sinh( 2 π d / L ) )cos( Θ )
c = L / T
w = d - H / 2
n = ( 2 π ) / L
f = 1 / T
hod = H / d
lod = L / d
H* = H / ( 9.80665 T 2 )
d* = d / ( 9.80665 T 2 )

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