Numerical simulations of wave–current flow in an ocean basin

Silva, Monica C.; Vitola, Marcelo A.; Esperança, Paulo T. T.; Sphaier, Sergio H.; Levi, Carlos

doi:10.1016/j.apor.2016.10.005

Cited by 22 publications

(15 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The description of the model for regular wave‐current interaction in Thomas and Silva et al is roughly followed. For small‐amplitude waves propagating on currents, the resulting velocity fields are represented by the sum of the flow due to the current and the wave as

u_{T} (x,z,t) = U(z) + u(z) \cos false(κ normalx - ω normalt false),

w_{T} (x,z,t) = w(z) \sin false(κ normalx - ω normalt false),

p_{T} (x,z,t) = - ρ gz + p(z) \cos false(κ normalx - ω normalt false),

where ρ is the density of water, g is the gravitational acceleration, and κ and ω are the wavenumber and the angular frequency of the wave, respectively.…”

Section: Wave‐current Interaction Modelsmentioning

confidence: 99%

“…The system defined by Equations , , and can be solved analytically if the second derivative of the current velocity profile is equal to zero, ie, d 2 U(z)/dz 2 = 0. The solutions are given (see Silva et al for details) as

u_{T} (x,z,t) = U(z) + normalA false(ω - κ U_{0} false) \frac{\cosh ([], κ false({z+h}_{w} false))}{\sinh false(κ h_{w} false)} \cos false(κ normalx - ω normalt false),

w_{T} (x,z,t) = normalA false(ω - κ U_{0} false) \frac{\sinh ([], κ {(z+h}_{w} false))}{\sinh false(κ h_{w} false)} \sin false(κ normalx - ω normalt false),

p_{T} (x,z,t) = - ρ normalg normalz + \frac{ρ normalA false(ω - κ U_{0} false)}{κ \sinh false(κ h_{w} false)} ({}, ([], ω - κ U(z)) \cosh false[κ {(z+h}_{w} false) false] + \frac{normald U(z)}{normald normalz} \sinh false[κ {(z+h}_{w} false) false]) \cos false(κ normalx - ω normalt false),

where U 0 is the current velocity at z = 0. The wavenumber is determined from the modified dispersion relation as

{false(ω - κ U_{0} false)}^{2} = ([], normalg κ - false(ω - κ U_{0} false) \frac{normald U(z)}{normald normalz}) \tanh false(κ h_{}

…”

Section: Wave‐current Interaction Modelsmentioning

confidence: 99%

“…The system defined by Equations 5, 6, and 7 can be solved analytically if the second derivative of the current velocity profile is equal to zero, ie, d 2 U(z)∕dz 2 = 0. The solutions are given (see Silva et al 31 for details) as…”

Section: Regular Wave-current Interaction Modelmentioning

confidence: 99%

“…The model was subsequently improved to deal with the case when wave breaking may occur induced by opposite or adverse currents. 26,27 These analytical models have been validated by experiments [28][29][30] and verified by numerical simulations, 31 showing sufficient accuracy for small amplitude waves. They have then been applied to marine structures.…”

mentioning

confidence: 90%

See 3 more Smart Citations

Wave‐current interaction effects on structural responses of floating offshore wind turbines

Chen

Basu

2018

Wind Energy

View full text Add to dashboard Cite

This paper proposes a model considering the wave‐current interactions in dynamic analyses of floating offshore wind turbines (FOWTs) and investigates the interaction effects on the FOWT responses. Waves when traveling on current are affected by the current, leading to frequency shift and shape modification. To include such interactions in FOWT analysis, which has not been considered by the researchers till date, a nonlinear hydrodynamic model for multicable mooring systems is presented that is able to consider the cable geometric nonlinearity, seabed contact, and the current effect. The mooring model is then coupled with a spar‐type FOWT model that handles the structural dynamics of turbine blades and tower, aerodynamics of the wind‐blade interaction, and wave‐current effects on the spar. The analytical wave‐current interaction model based on Airy theory considering the current effect is used in the computation of flow velocity and acceleration. Numerical studies are then carried out based on the NREL offshore 5‐MW baseline wind turbine supported on top of the OC3‐Hywind spar buoy. Two cases, (1) when the currents are favorable and (2) when the currents are adverse, are examined. Differences of up to 15% have been observed by comparing the cable fairlead tension obtained excluding and including the wave‐current interactions. In particular, when irregular waves interact with adverse current, a simple superposition treatment of the wave and the current effects seems to underestimate the spar motion and the cable fairlead tension. This indicates that the wave‐current interaction is an important aspect and is needed to be considered in FOWT analysis.

show abstract

u_{T} (x,z,t) = U(z) + u(z) \cos false(κ normalx - ω normalt false),

w_{T} (x,z,t) = w(z) \sin false(κ normalx - ω normalt false),

p_{T} (x,z,t) = - ρ gz + p(z) \cos false(κ normalx - ω normalt false),

where ρ is the density of water, g is the gravitational acceleration, and κ and ω are the wavenumber and the angular frequency of the wave, respectively.…”

Section: Wave‐current Interaction Modelsmentioning

confidence: 99%

u_{T} (x,z,t) = U(z) + normalA false(ω - κ U_{0} false) \frac{\cosh ([], κ false({z+h}_{w} false))}{\sinh false(κ h_{w} false)} \cos false(κ normalx - ω normalt false),

w_{T} (x,z,t) = normalA false(ω - κ U_{0} false) \frac{\sinh ([], κ {(z+h}_{w} false))}{\sinh false(κ h_{w} false)} \sin false(κ normalx - ω normalt false),

p_{T} (x,z,t) = - ρ normalg normalz + \frac{ρ normalA false(ω - κ U_{0} false)}{κ \sinh false(κ h_{w} false)} ({}, ([], ω - κ U(z)) \cosh false[κ {(z+h}_{w} false) false] + \frac{normald U(z)}{normald normalz} \sinh false[κ {(z+h}_{w} false) false]) \cos false(κ normalx - ω normalt false),

where U 0 is the current velocity at z = 0. The wavenumber is determined from the modified dispersion relation as

{false(ω - κ U_{0} false)}^{2} = ([], normalg κ - false(ω - κ U_{0} false) \frac{normald U(z)}{normald normalz}) \tanh false(κ h_{}

…”

Section: Wave‐current Interaction Modelsmentioning

confidence: 99%

Section: Regular Wave-current Interaction Modelmentioning

confidence: 99%

mentioning

confidence: 90%

See 2 more Smart Citations

Wave‐current interaction effects on structural responses of floating offshore wind turbines

Chen

Basu

2018

Wind Energy

View full text Add to dashboard Cite

show abstract

“…Many studies also examine wave only flow characteristics and do not consider combined wave and current conditions. This study aims to build upon the findings of previous studies, for optimisation of the numerical model [11], [13], [20], while investigating combined wave and current interactions [18], [21], [22], specifically studying the sub surface particle velocities through the water depth. The main focus of this work is to establish a NWT which can accurately simulate the sub surface motions between a uniform current and regular S2OT waves.…”

Section: Introductionmentioning

confidence: 99%

Development of a wave-current numerical model using Stokes 2nd Order Theory

2019

View full text Add to dashboard Cite

The optimisation of a Numerical Wave Tank is proposed to accurately model the sub surface conditions generated by regular waves superimposed on a uniform current velocity. ANSYS CFX 18.0 was used to develop a homogenous multiphase model with volume fractions to define the different phase regions. By applying CFX Expression Language at the inlet of the model, Stokes 2nd Order Theory was used to define the upstream wave and current characteristics. Horizontal and vertical velocity components, as well as surface elevation of the numerical model were compared against theoretical and experimental wave data for 3 different wave characteristics in 2 different water depths. The comparison highlighted the numerical homogeneity between the theoretical and experimental data. Therefore, this study has shown that the modelling procedure used can accurately replicate experimental testing facility flow conditions, providing a potential substitute to experimental flume or tank testing.

show abstract