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Wake destructive behavior and vortex shedding behind bluff bodies may be controlled by use of active and passive methods. Computational fluid dynamics, experimental and analytical techniques have been utilized to study this problem. In this survey, existing studies on different methods of controlling the wake destructive behavior and suppression of vortex shedding behind bluff bodies are discussed, including the very recent developments. These methods are classified into two groups. In the first group, these methods are discussed according to the type of external source or modification of the geometry of bluff body for controlling the flow. In the second group, the methods are classified according to the part of the flow, boundary layer or wake, that is modified by the method. Advantages, limitations, energy efficiency, and particular applications of each method are discussed and summarized, followed by some conclusions and recommendations. Moreover, the effectiveness of each technique on the drag reduction is discussed.

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The interaction of solitary waves with multiple, in-line vertical cylinders is investigated. The fixed cylinders are of constant circular crosssection and extend from the sea floor to the free surface. In general, there are N of them lined in a row parallel to the incoming wave direction. Both the nonlinear, generalized Boussinesq and the Green-Naghdi shallow-water wave equations are used. A boundary-fitted curvilinear coordinate system is employed to facilitate the use of the finite-difference method on curved boundaries. The governing equations and boundary conditions are transformed from the physical plane onto the computational plane. These equations are then solved in time on the computational plane that contains a uniform grid and by use of the successive over relaxation method and a second-order finite-difference method to determine the horizontal force and overturning moment on the cylinders. Resulting solitary wave forces from the nonlinear Green-Naghdi and the Boussinesq equations are presented, and the forces are compared with the experimental data when available.Keywords Solitary wave · multiple inline vertical circular cylinders · wave force and moment · Boussinesq equations · Green-Naghdi equations 1 Introduction 1 Many marine structures are built on vertical cylinders; consequently, the de-2 termination of the forces which are a result of the wave-cylinder interaction is 3 an important problem in ocean engineering. However, very few studies have 4 considered nonlinear shallow-water wave equations to investigate solitary-and 5 cnoidal-wave diffraction by vertical cylinders and calculated the forces and 6 moments acting on it. 7 We consider here the interaction of solitary waves with fixed, multiple in-8 line vertical cylinders of constant circular cross section. The cylinders extend 9 from the seafloor to the free surface, and the still-water depth is held constant. 10Different shallow-water wave equations can produce different solitary waves, 11 and may describe the flow field differently, and thereby can lead to different 12 wave loads. Both the generalized Boussinesq (gB) (Wu (1981)) and the Green-13 Naghdi (GN) (Green and Naghdi (1977)) Level I equations are used to solve 14 numerically the initial-boundary-value problem to obtain the horizontal forces 15 and overturning moments on multiple cylinders in shallow water. 16The linearized potential problem of wave diffraction by a single vertical 17 cylinder was solved by MacCamy and Fuchs (1954) for an ideal fluid. The 18 infinite depth solution of the same problem was obtained earlier by Havelock 19 (1940). Scattering of waves for very long wave length (solitary wave) by a 20 cylindrical object (island) was first solved by Omer and Hall (1949). 21 Only few investigations of nonlinear effects in the time domain exist com-22 pared with the linear ones. Isaacson (1983) studied the interaction of a solitary 23 wave with an isolated cylinder by an approximate method by using the linear 24 boundary conditions although the solitary wave problem has to...

The Green-Naghdi (GN) wave models are categorized into different levels based on the assumptions made for the velocity field. The low-level GN model (Level I GN model or called the GN-1 model) is a weakly dispersive, strongly nonlinear wave model. As the level goes up, the high-level GN model becomes a strongly dispersive, strongly nonlinear wave model. This paper introduces the algorithm to solve the Green-Naghdi wave models of different levels in three dimensions. The high-level GN (GN-3 and GN-4) models are applied to three-dimensional wave problems for the first time. Three test cases are considered here. First one is on the wave evolution in a closed basin. The symmetry, in the x and y directions in this case, verifies that the algorithm introduced here works well. The GN-3 results are also compared with the linear analytical results for a small wave elevation in a closed basin, and the agreement is good. The last two cases involve wave diffraction problems caused by an uneven seabed. In both of the last two cases, the GN-3 model is proved to be the converged GN model. The agreement between the GN-3 model and the experimental data and numerical predictions of the fully nonlinear Boussinesq model of others is also very good.