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# Froude–Krylov force

About: Froude–Krylov force is a research topic. Over the lifetime, 116 publications have been published within this topic receiving 1092 citations.

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TL;DR: A mean force exerted on a small rigid sphere by a sound wave in a viscous fluid is calculated and the mean force reduces to the radiation pressure, which can be expressed through source strengths of the scattered sound field.

Abstract: A mean force exerted on a small rigid sphere by a sound wave in a viscous fluid is calculated. The force is expressed as a sum of drag force coming from the external steady flow existing in the absence of the sphere and contributions that are cross products of velocity and velocity derivatives of the incident field. Because of the drag force and an acoustic streaming generated near the sphere, the mean force does not coincide with the acoustic radiation pressure, i.e., the mean momentum flux carried by the sound field through any surface enclosing the sphere. If the sphere radius R is considerably smaller than the viscous wave penetration depth delta, the drag force can give the leading-order contribution (in powers of delta/R) to the mean force and the latter can then be directed against the radiation pressure. In another limit, delta< or =R, the drag force and acoustic streaming play a minor role, and the mean force reduces to the radiation pressure, which can be expressed through source strengths of the scattered sound field. The effect of viscosity can then be significant only if the incident wave is locally plane traveling.

130 citations

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TL;DR: In this article, it was shown that a negative mean force arises from an asymmetry in the breaking waves, associated with a time-delay in the response to the change in depth.

Abstract: Water waves transport both energy and momentum, and any solid body which absorbs or reflects wave energy must absorb or reflect horizontal momentum also. Hence the body is subject to a mean horizontal force. In low waves, the force may be calculated immediately when the incident, reflected and transmitted wave amplitudes are known. For wave power devices the mean force can be large, so that anchoring presents practical problems. Experiments with models of the Cockerell wave-raft and the Salter ‘duck’ accurately confirm the predicted magnitude of the force at low wave amplitudes. For steeper waves, however, the magnitude of the force can be less than that given by linear theory. By experiments with submerged cylinders, it is shown that this is due partly to the presence of a free second harmonic on the down-wave side. In breaking waves, it is confirmed that the mean force on submerged bodies is sometimes reduced, and even reversed. An explanation is suggested in terms of the ‘wave set-up’ produced by breaking waves. Submerged cylinders act as a kind of double beach. A negative mean force arises from an asymmetry in the breaking waves, associated with a time-delay in the response to the change in depth. Similar arguments apply to submerged reefs and sand bars. Experiments with a model bar show that long low waves propel the bar towards the shore, whereas steep, breaking waves propel it seawards. This is similar to the observed behaviour of off-shore sand bars. The existence of a horizontal momentum flux (or radiation stress) in water waves is demonstrated by using it to propel a small craft.

106 citations

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TL;DR: In this paper, the authors used the Reynolds stress model (RSM) to simulate the turbulent flow of gas, and the outcome is used in the simulation of particle motion by adopting the stochastic Lagrangian particle tracking model (LPT).

81 citations

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TL;DR: In this paper, the wave force was evaluated based on the diffraction theory by Boundary Element Method first, and the effects of the size and the shape of SFT on the wave forces were discussed.

60 citations

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01 Feb 2017TL;DR: In this article, the authors proposed a computationally efficient representation of nonlinear static and dynamic Froude-Krylov forces, valid for any heaving axisymmetric point absorber.

Abstract: Most wave energy converters (WECs) are described by linear mathematical models, based on the main assumption of small amplitudes of motion. Notwithstanding the computational convenience, linear models can become inaccurate when large motions occur. On the other hand, nonlinear models are often time consuming to simulate, while model-based controllers require system dynamic models which can execute in real time. Therefore, this paper proposes a computationally efficient representation of nonlinear static and dynamic Froude–Krylov forces, valid for any heaving axisymmetric point absorber. Nonlinearities are increased by nonuniform WEC cross sectional area and large displacements induced by energy maximising control strategies, which prevent the device from behaving as a wave follower. Results also show that the power production assessment realized through a linear model can be overly optimistic and control parameters calculations should also reflect the true nonlinear nature of the WEC model.

58 citations