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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 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 : 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. Change Module : |
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. Change Module : Related Modules : |
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). Change Module : |
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). Change Module : |
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. Change Module : |
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 Change Module : |
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. Change Module : |
| CALCULATOR MODULE : Ocean Wave Theory Selection Airy Stokes And Cnoidal Waves ±
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| CALCULATOR MODULE : Breaking Wave Height ±
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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. Change Module : Related Modules : |
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. Change Module : Related Modules : |