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Ocean Wave Modules

Keyword(s) Ocean Wave. For a new search enter search key word(s) then click GO GO

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CALCULATOR MODULE : Dimensionless Number   ±

Calculate dimensionless numbers for fluid flow and other physical systems.

Dimensionless numbers are calculated from groups of variables so that the result is dimensionless. Dimensionless numbers can be calculated from any consistent set of units, and will have the same value. Dimensionless numbers can be a very powerful tool for analysing physical systems.

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CALCULATOR MODULE : Dimensionless Keulegan Carpenter Number   ±

Calculate the dimensionless Keulegen Carpenter number or period number.

The Keulegen Carpenter number approximates the ratio of drag forces to inertia forces acting on a structure in oscillating flow (typically wave flow).

`Kc = V T / (OOD) = V^2 / (A* OOD) `
`A* = V / T `

where :

Kc = Keulegan Carpenter number
V = velocity amplitude
T = oscillation period
OOD = structure outer diameter or characteristic length
A* = approximate acceleration amplitude

For small Keulegen Carpenter numbers inertia forces dominate. At large Keulegen Carpenter numbers drag forces dominate. The Keulegen Carpenter number can also be applied to structures oscillating in a stationary fluid.

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CALCULATOR MODULE : Dimensionless Wave Number   ±

Calculate common dimensionless and dimensional ocean wave numbers.

Ocean wave numbers include :

`kw = (2 pi) / L = 2 pi(fw) / c `
`fw = 1 / T `
`Ur = h l^2 / d^3 = (h/d)^3 / (l/d)^2 `
`H* = H / (g t^2) `
`d* = d / (g t^2) `

where :

kw = wave number (dimesion 1/length)
fw = wave frequency (dimension 1/time)
Ur = dimensionless Ursell number
H* = dimensionless wave height
d* = dimensionless water depth
L = wave length
f = wave frequency
c = wave celerity or propagation speed

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CALCULATOR MODULE : Dimensionless Ursell Number   ±

Calculate the dimensionless Ursell number.

The Ursell number is a measure of the non linearity of ocean waves.

`Ur = h L^2 / d^3 = (h/d)^3 / (L/d)^2 `

where :

Ur = Ursell number
h = wave height
L = wave length
d = water depth

The Airy wave is suitable for Ur < 1. Stokes wave should be used for Ur < 40. Cnoidal wave should be used for Ur > 40.

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CALCULATOR MODULE : Airy Linear Gravity Wave   ±

Calculate Airy wave velocity, acceleration and surface profile. The Airy linear gravity wave theory is a first order model of freshwater and seawater gravity waves. 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 models such as Stokes wave or Cnoidal wave should be used. The recommended wave type is displayed below the calc bar.

Check that the convergence is close to or equal to one. The wave period should be measured at zero current velocity to avoid Doppler effects.

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    CALCULATOR MODULE : Stokes Fifth Order Wave   ±

    Calculate Stokes wave velocity, acceleration and surface profile using Skjelbria and Hendrickson's fifth order wave method.

    Stokes wave model is suitable for waves with short wavelength or small amplitude. The calculators include the correction to the sign of the c 8 term in the C2 coefficient (changed from + to -2592 c 8 ). Check that the convergence is close to or equal to one. The wave period should be measured at zero current velocity to avoid Doppler effects.

    Note : The Stokes wave theory uses a truncated infinite series. The truncated series is only valid for certain conditions. For shallow water waves the cnoidal wave is recommended. The recommended wave type is displayed below the calc bar.

    Reference : Lars Skjelbria and James Hendrickson, Fifth Order Gravity Wave Theory

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      CALCULATOR MODULE : Cnoidal Fifth Order Wave   ±

      Calculate Cnoidal wave velocity, acceleration and surface profile using Fentons 1999 fifth order wave method.

      The Cnoidal wave is defined by the elliptic modulus m, the wave trough depth w, and the wave alpha parameter α. The Cnoidal wave model is a truncated series and is only valid within certain ranges. The Cnoidal wave theory is not recommended where the wavelength over water depth ratio (Lod) is less than 8. The recommended wave type is displayed below the calc bar.

      Note : The cnoidal wave theory uses a truncated infinite series. The truncated series is only valid for conditions where the series converges (m > 0.8). For deep water waves with small m, the series does not converge (use the Stokes wave instead).

      Check that the convergence is close to or equal to one. The wave period should be measured at zero current velocity to avoid Doppler effects.

      Reference : J D Fenton, The Cnoidal Theory Of Water Waves, Developments in Offshore Engineering, Gulf, Houston, chapter 2, 1999

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        CALCULATOR MODULE : Morison's Equation Wave And Current Load   ±

        Calculate wave and current loads on submerged structures using Morison's equation (Airy Stokes and Cnoidal waves).

        For vertical structures the load forces are due to the horizontal velocity and acceleration only. For horizontal structures the load forces also include vertical velocity and acceleration. Lateral (lift) forces are due to non symmetric flow around the structure, either because of proximity to the seabed or another structure, or by non symmetric cross section. The Keulegan Carpenter number is a measure of the ratio of wave inertial forces and drag forces.

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        CALCULATOR MODULE : Morison's Equation Wave Slam   ±

        Calculate wave slamming loads on submerged structures using Morison's equation (Airy Stokes and Cnoidal waves).

        Wave slamming loads are due to the impact of the wave surface against the structure. The combined wave loading includes wave drag load, inertia load, and lateral load. For horizontal structures buoyancy load is also included. Wave slamming loads occur on the front of the wave only (phase angle ≤ 180 degrees). Wave loads are calulated at the wave surface (wave surface height is calculated from wave phase angle).

        theoretical wave slamming load coefficient varies between π and 2 π. The calculated wave slamming load is force per length (unit force). To calculate the total load (force) on a vertical structure the wave curl coefficient can be used

        `Lt = λ Hw Fs `

        where :

        Lt = the total load (force)
        λ = the wave curl coefficient
        Hw = the wave height
        Fs = the slamming load (force per length)

        The wave curl coefficient accounts for the variation in time for the wave to contact the whole vertical structure. Typical values of the wave coefficient λ vary from 0.4 to 0.9.

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        CALCULATOR MODULE : Morison's Equation Drag Lift And Inertia Coefficient   ±

        Calculate drag coefficient, lift coefficient and inertia coefficient for Morison's equation.

        Drag, lift, and inertia coefficients are affected by proximity to the seabed or another structure. In open water the lateral coefficient tends to zero. The Keulegan Carpenter number is a measure of the ratio of inertial forces and drag forces.

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        CALCULATOR MODULE : Morison's Equation Subsea Pipeline Stability   ±

        Calculate stability of on bottom structures using Morison's equation (Airy Stokes and Cnoidal waves).

        For horizontal stability the horizontal wave and current loads must be less than the restraining friction force. For vertical stability the specific gravity should be greater than or equal to 1.1. Wave vertical velocity and acceleration are ignored. For some structures, depending on geometry, tipping should also be considered. Tipping does not generally occur on pipelines.

        Refer also to : DNV-RP-F109 On-Bottom Stability Design Of Submarine Pipelines.

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        CALCULATOR MODULE : Morison's Equation Wave And Current Amplitude   ±

        Calculate wave and current amplitude for Morison's equation from return period data.

        Wave and current amplitude is calculated from return period data using linear regression with either the Weibull, Gumbel or Frechet probability distributions. Use the Result Plot option to display plots for the selected wave type etc. Details of the linear regression are displayed in the output at the bottom of the page.

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        CALCULATOR MODULE : Ocean Wave And Current Velocity And Acceleration   ±

        Calculate ocean wave and current velocity and acceleration for Airy, Stokes, cnoidal and JONSWAP waves.

        Wave velocity and acceleration can be calculated for Airy, Stokes, and Cnoidal waves. The recommended wave type is displayed below the calc bar. Use the Result Plot option to compare the Airy, Stokes, and cnoidal wave profiles. The seabed significant wave velocity and zero upcrossing period can be calculated from the JONSWAP surface spectrum.

        Current velocity can be calculated near the seabed using either the logarithmic profile, or the 1/7th power law profile. The logarithmic and power law profiles are not valid For large elevations above the seabed.

        Note : The Stokes and cnoidal waves use trucated infinite series. Under certain conditions the truncated series do not converge properly. The Stokes wave is not suitable for shallow water waves. The cnoidal wave is not suitable for deep water waves. The recommended wave type is displayed below the calc bar. The JONSWAP wave uses an Airy wave transfer function to calculate seabed velocity. The JONSWAP wave is not suitable for very shallow waves (near breaking).

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        CALCULATOR MODULE : Ocean Wave Velocity And Acceleration   ±

        Calculate ocean wave velocity and acceleration for Airy, Stokes, cnoidal and JONSWAP waves.

        Wave velocity and acceleration can be calculated for Airy, Stokes, and Cnoidal waves. The recommended wave type is displayed below the calc bar. Use the Result Plot option to compare the Airy, Stokes, and cnoidal wave profiles. The seabed significant wave velocity and zero upcrossing period can be calculated from the JONSWAP surface spectrum.

        Note : The Stokes and cnoidal waves use trucated infinite series. Under certain conditions the truncated series do not converge properly. The Stokes wave is not suitable for shallow water waves. The cnoidal wave is not suitable for deep water waves. The recommended wave type is displayed below the calc bar. The JONSWAP wave uses an Airy wave transfer function to calculate seabed velocity. The JONSWAP wave is not suitable for very shallow waves (near breaking).

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        CALCULATOR MODULE : Ocean Wave Maximum Wave Height   ±

        Calculate ocean wave maximum wave height and significant wave height.

        The maximum wave height can be calculated from the significant wave height (and vice versas) by approximate relationships. In most cases the maximum wave height is approximately 1.86 times the significant wave height. For a narrow banded wave spectrum the maximum wave height is approximately 1.93 times the significant wave height.

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        CALCULATOR MODULE : Ocean Wave Shoaling And Wave Height   ±

        Calculate ocean wave shoaling wave height from water depth.

        Shoaling occurs as the water depth decreases or becomes more shallow. the wave length and celerity decrease (the wave becomes slower), and the wave height increases. The wave energy flux is assumed to be constant. For Airy waves the wave energy flux is proportional to c H^2 (the wave celerity times the wave height squared). The same relationship is assumed to also apply to Stokes and cnoidal waves. Use the Result Plot option to compare the initial wave and shoaling wave profiles, or the wave height versus water depth for Airy, Stokes and cnoidal waves. The recommended wave type is displayed below the calc bar.

        Note : The Stokes wave is the most suitable for a transtion from deep water to shallow water waves. The cnoidal wave is not suitable for deep water waves. The Airy wave is not suitable for shallow water waves.

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        CALCULATOR MODULE : Ocean Wave And Current Seabed Stability   ±

        Calculate subsea critical seabed velocity for seabed stability and sediment movement from the critical shields number.

        The Shields parameter is used to calculate the onset of seabed instability due to sediment movement. For subsea waves and currents the critical Shields parameter is approximately 0.04. For laminar flow the critical Shields parameter is approximately 0.03.

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        CALCULATOR MODULE : Ocean Wave And Current Self Burial   ±
        CALCULATOR MODULE : Ocean Wave Dimensionless Number   ±

        Calculate ocean wave dimensionless Keulegen Carpenter number, Ursell number and other wave numbers for Airy, Stokes and cnoidal waves.

        The Keulegan Carpenter number approximates the ratio of drag force to inertia force on a circular structure.

        `Kc = (V T) / (OOD) = V^2 / (A.OOD) `
        `A = V / T `

        where :

        Kc = Keulegan Carpenter number
        V = velocity amplitude
        T = oscillation period
        OOD = structure outer diameter or characteristic length
        A = approximate acceleration amplitude

        For small Keulegen-Carpenter numbers inertia forces dominate. At large Keulegen-Carpenter numbers drag forces dominate. The maximum horizontal wave velocity is calculated at zero degrees phase angle. Use the wave velocity reduction factor for structures which are not perpendicular to the wave velocity. The drag force over inertia force ratio varies with heading.

        The Ursell number is a measure of the non linearity of ocean waves.

        `Ur = (h l^2) / d^3 = (h/d)^3 / (l/d)^2 `

        where :

        Ur = Ursell number
        h = wave height
        l = wave length
        d = water depth

        The Airy wave is suitable for Ur < 1. Stokes wave should be used for Ur < 40. Cnoidal wave should be used for Ur > 40.

        Other ocean wave numbers include:

        `kw = (2 pi) / l = (2 pi fw) / c `
        `fw = 1 / T `
        `H^* = H / (g t^2) `
        `d^* = d / (g t^2) `

        where :

        kw = wave number (dimesion 1/length)
        fw = wave frequency (dimension 1/time)
        H* = dimensionless wave height
        d* = dimensionless water depth
        l = wave length
        f = wave frequency
        c = wave celerity or propagation speed

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        CALCULATOR MODULE : Ocean Wave Directionality And Spreading   ±

        Calculate ocean wave velocity reduction factor from relative heading and spreading factor.

        The spreading factor accounts for wave "choppiness" or superimposed multi directional waves. Locally generated waves are generally short crested and more "choppy", and are characterised by small spreading factors. Long range swells are generally long crested uni directional waves, and are characterised by large spreading factors.

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        CALCULATOR MODULE : Ocean Wave Theory Selection Airy Stokes And Cnoidal Waves   ±
        CALCULATOR MODULE : Breaking Wave Height   ±
        CALCULATOR MODULE : Ocean Wave Probability And Return Period   ±

        Calculate ocean wave height and period from return period data using the Weibull, Gumbel or Frechet probability distributions.

        The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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        CALCULATOR MODULE : Ocean Wave And Current Probability And Return Period   ±

        Calculate ocean wave height, wave period and current velocity from return period data using the Weibull, Gumbel or Frechet probability distributions.

        The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). Use the Data Plot option on the plot bar to display the data points and the calculated best fit. The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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        CALCULATOR MODULE : JONSWAP Wave Spectrum   ±

        Calculate JONSWAP wave surface spectral density, and seabed velocity spectrum.

        The seabed velocity spectrum is calculated using a first order Airy wave transformation.

        Reference : Hasselmann K et al : Measurements of Wind-Wave Growth And Swell Decay During The Joint North Sea Wave Project (JONSWAP)

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        CALCULATOR MODULE : JONSWAP Wave Velocity And Period   ±

        Calculate JONSWAP wave seabed velocity and zero upcrossing period from spectral moments.

        The seabed velocity and upcrossing period is calculated using a first order Airy wave transformation. The Airy wave transformation may not be valid in shallow water. The calculation has been optimised for elevations on or near the seabed, and is not recommended for elevations greater than half the water depth. Return period data can be analysed using either the Weibull, Gumbel or Frechet distribution.

        Reference : Hasselmann K et al : Measurements of Wind-Wave Growth And Swell Decay During The Joint North Sea Wave Project (JONSWAP)

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        CALCULATOR MODULE : JONSWAP Wave Directionality And Spreading   ±

        Calculate JONSWAP wave spreading and velocity reduction factor from relative heading and spreading factor.

        Wave spreading accounts for the effect of short crested "choppy" waves with non uniform velocity and heading. By comparison, long ocean swells tend to have uniform velocity and direction, expecially in mid ocean. Use small spreading factors for "choppy" waves, and large spreading factors for ocena swells.

        Reference : Hasselmann K et al : Measurements of Wind-Wave Growth And Swell Decay During The Joint North Sea Wave Project (JONSWAP)

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        CALCULATOR MODULE : JONSWAP Combined Wave And Current Velocity   ±

        Calculate JONSWAP seabed wave and current amplitude from return period data.

        Return period data can be analysed using either the Weibull, Gumbel or Frechet distribution. Current velocity can be calculated using either the logarithmic profile, or the 1/7th power law profile. The logarithmic and power law profiles are only valid in the boundary layer on or near the seabed. The seabed velocity and upcrossing period is calculated from the JONSWAP surface spectrum using a first order Airy wave transformation. The calculation may not be valid in shallow water, and is not recommended for elevations greater than half the water depth.

        Reference : Hasselmann K et al : Measurements of Wind-Wave Growth And Swell Decay During The Joint North Sea Wave Project (JONSWAP)

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        CALCULATOR MODULE : DNVGL RP F109 Submarine Pipeline Stability   ±

        Calculate DNVGL-RP-F109 pipeline lateral and vertical stability.

        Static or absolute stability can be calculated for clay seabed, sandy seabed (D50 ≤ 50 mm), or rocky seabed (D50 > 50 mm). The single oscillation velocity corresponds to the maximum wave velocity in the return period. Maximum current velocity data should be used.

        Dynamic stability can be calculated on clay and sandy seabeds for Lstable (pipe displacement ≤ 0.5 OOD), L10 (pipe displacement ≤ 0.5 OOD), or user defined pipe displacement. Significant current velocity data should be used.

        Seabed wave velocity is calculated from the JONSWAP surface spectrum with an Airy wave transfer function. The calculation should only be used for elevations at or near the seabed. The Airy wave transform may not be valid in shallow water.

        Reference : DNVGL-RP-F109 : On-Bottom Stability Design Of Submarine Pipelines (Download from the DNVGL website)

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        CALCULATOR MODULE : DNVGL RP F109 Wave Spreading And Directionality   ±

        Calculate DNVGL RP-F109 wave spreading and directionality from relative heading and spreading factor.

        The wave spreading factor accounts for the "choppiness" or multi directional properties of wave groups. Locally generated waves are generally more multi directional and should have small spreading factors. Long range swells tend to be more uni directional, and can be used with large spreading factors.

        Reference : DNVGL-RP-F109 : On-Bottom Stability Design Of Submarine Pipelines (Download from the DNVGL website)

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        CALCULATOR MODULE : DNVGL RP F109 Wave Seabed Velocity   ±

        Calculate DNVGL RP-F109 wave seabed velocity from the JONSWAP surface spectrum.

        An Airy wave transform is used to calculate the significant seabed velocity, and zero upcrossing wave period. The calculation is not valid in shallow water, or at elevations greater than half the water depth.

        Reference : DNVGL-RP-F109 : On-Bottom Stability Design Of Submarine Pipelines (Download from the DNVGL website)

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        CALCULATOR MODULE : DNVGL RP F109 Wave Probability And Return Period   ±

        Calculate DNVGL RP-F109 wave and current amplitude from return period data.

        Current velocity, wave height, and wave period can be calculated from return period data using either the Weibull, Gumbel or Frechet probability distributions. Enter data as comma or tab separated sets (eg R, Vc), with each set on a new row. Data can also be copied and pasted from a spreadsheet, or from a text document.

        Reference : DNVGL-RP-F109 : On-Bottom Stability Design Of Submarine Pipelines (Download from the DNVGL website)

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