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Wave Heading Modules

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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.

    Related Modules :

    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

      Related Modules :

      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

        Related Modules :

        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.

        Change Module :

        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 : 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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