Wave Forces on Inclined Smooth and Rough Circular Cylinders
Authors: Sarpkaya Turgut , Raines Thomas S. , Trytten Dean O. 
Published: October 2008

Abstract
The forces acting on yawed smooth and rough circular cylinders in a sinusoid ally oscillating planar flow have been investigated experimentally and the force transfer coefficients have been evaluated.
The results have shown that the so-called "independence principle" does not hold true over the range of Reynolds numbers and Keulegan-Carpenter numbers covered by the investigation. It has further been shown that the Morison equation predicts the measured force with the same degree of accuracy as that for the normal cylinder provided that the force coefficients appropriate to each yaw angle, Reynolds number, and Keulegan-Carpenter number are used.

Introduction
The effect of body orientation on resistance particularly for bodies of finite length has been the subject of extensive investigation in steady flow (for a critical review see e.g., Sarpkaya and Isaacson). It has not been possible to correlate the in-plane normal force and the out-of-plane transverse force with a single Reynolds number. Hoerner2 proposed the "independence principle", which stated that the normal pressure forces are independent of the tangential velocity for sub critical values of Ren, where Ren is the Reynolds number based upon the flow velocity normal to the cylinder. This principle allowed the decomposition of forces and velocities into normal and tangential components and the neglecting of the tangential components. Bushnell and Loftin3 found that the independence principle does not apply to the critical and Tran critical flow regimes. Norton, Heideman, and Mallard4 found that the independence principle does apply to post-critical as well as sub critical flow, but not to the critical and Trancritical" regions in between. Thus, recent research has shown that the independence principle applies to steady ambient flow about yawed cylinders when the boundary layer is wholly laminar or wholly turbulent, i.e., when the drag coefficient is nearly constant, but its use in the critical and Tran critical regions is uncertain, i.e., when Cd varies rapidly with the Reynolds number.
In oscillatory or wave flow the Reynolds number varies from zero to Remax during a half cycle. Thus it could be postulated the boundary layer would, at times, be fully laminar; at other times fully turbulent; and the rest of the time be in transition. In light of this, it is rather doubtful that the independence principle applies at all to oscillating or wave flow. Furthermore, Cd and Cm are really never constant.
The primary objective of this investigation was to study the forces exerted by a sinusoid ally oscillating planar flow on yawed circular cylinders to determine whether the independence principle is applicable or not. If so, the force-transfer coefficients calculated by Fourier analysis using the normal velocity component should reduce identically to the normal cylinder case at corresponding values of the Keulegan Carpenter number (K=UmnT/D), Reynolds number (Re = UmnD/v), and the relative roughness k/D. If the independence principle does not apply, it is desired to determine what the coefficients are as functions of yaw angle, roughness ratio k/D, Re, and K. It would also be necessary to determine how well Morison's equation works with the new coefficients.