Abstract
A computational analysis is performed on the diffraction of water waves induced by large-diameter, surface-piercing, vertical circular cylinder. With reference to linear-wave cases, the phenomenon is preliminarly considered in terms of velocity potential, a simplified theoretical framework in which both hypotheses of inviscid fluid and irrotational flow are incorporated. Then, and as a first-approximation analysis, the Euler equations in primitive variables are considered (a framework in which the fluid is still handled as inviscid, but the field can be rotational). Finally, the real-fluid behavior is analyzed, by numerically integrating the full Navier-Stokes equations (viscous fluid and rotational field) in their velocity-pressure formulation, by following the approach of the Direct Numerical Simulation (DNS, no models are used for the fluctuating portion of the velocity field). For further investigation of the flow fields, the swirling-strength criterion for flow-structure extraction, and the Karhunen-Loève (KL) decomposition technique for the extraction of the most energetic flow modes respectively, are applied to the computed fields. It is found that remarkable differences exist between the wave-induced fields, as derived within the different computing frameworks tested.
Highlights
The phenomenon of diffraction of small-amplitude water waves impinging on large bodies has been studied in the recent past by several authors both numerically and experimentally, where the results related to the case of large-diameter surface-piercing vertical circular cylinder are often compared against the theoretical close-form potential solution devised by MacCamy and Fuchs [1]
The phenomenon of diffraction of linear waves impinging on large-diameter, surface-piercing, vertical circular cylinder has been investigated numerically, within three different theoretical frameworks of hypotheses, namely the velocity potential, the numerical integration of the primitive-variable Euler equations, and the numerical integration of the primitive-variable
The results obtained in terms of both global wave parameters, and wave-flow fields have shown that remarkable differences exist, depending on the frame of hypotheses that one eventually choses to follow, being though the numerical integration of the full Navier-Stokes equations in primitive variables the physically-consistent approach to be adopted to obtain flow fields that correctly represent the numerical equivalent of the phenomena at hand
Summary
The phenomenon of diffraction of small-amplitude water waves impinging on large bodies has been studied in the recent past by several authors both numerically and experimentally, where the results related to the case of large-diameter surface-piercing vertical circular cylinder are often compared against the theoretical close-form potential solution devised by MacCamy and Fuchs [1]. The velocity-potential approach, the numerical integration of the primitive-variable Euler equations, and the numerical integration of the primitive-variable full Navier-Stokes equations are considered for the analysis of given wave cases, and—in the case of the Navier-Stokes equations—the approach is followed of the Direct Numerical Simulation (DNS, no models for the fluctuating portion of the velocity field are used in the calculations, see Alfonsi [22,23] for extensive DNS reviews).
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