On the Spanwise Correlation of Wave Forces on Slender Structures
Authors: Torum Alf , Reed Knut 
Published: October 2008

Abstract
This paper deals primarily with transversal forces at different elevations on a pile due to waves. Data are obtained from a model test setup with a 42 mm diameter pile in waves up to 0.70 m high. Some results of preliminary nature have been given.

Introduction
In-line wave forces on small diameter cylinders are usually calculated according to the Morison formulae. As is very well known much experimental work has been carried out to obtain values of the CD and me values. The experiments have been carried out on models of piles in laboratory way flume, laboratory experiments in oscillatory water tunnels and field measurement in almost full scale. The analysis has very often been concentrated on measurements of forces taken on small sections or on measurements of total forces on a structure.
In addition to the drag and inertia in-line forces as expressed by Morison equation there is also a lift force, caused by vortex shedding. This shedding mechanism is so complex that it has not been possible to do a theoretical analysis successfully yet.
The drag, added mass and lift coefficients obtained from section models are used in design for much larger sections or even the whole structures. By doing this one assumes that the forces are simultaneously acting over the whole length of a vertical pile. But how true is this? What do we know about the span wise correlation of the forces?
Toebes1 carried out extensive velocity measurements with an anemometer in the vicinity of a fixed and oscillating cylinder in steady current for Reynolds numbers up to approximately 70.000. Toebes' results showed that the correlation between velocities decreased along the cylinder. Dronkers and Massie2 carried out tests measuring forces on sectional element of a vertical, circular pile in a steady current
To the writers' knowledge there has been very little analysis done on the span wise correlation of forces along a vertical pile in waves. This paper gives some preliminary results from a laboratory study.

Wave Forces On Small Diameter Structures
The wave forces on a small diameter structure are calculated by the Morison formulae:In wave direction per unit pile length (Mathematical Equation Available In Full Paper)Transverse force per unit pile length (Mathematical Equation Available In Full Paper)
We will in the present paper concentrate on the nature of the lift or transverse forces on a pile. From previous work (see for example Sarpkaya3 we know that these forces are depending on the Keulegan-Carpenter (KC) number and the Reynolds(Mathematical Equation Available In Full Paper)

Test Setup
The model tests were carried out in the Ship Model Tank at the Norwegian Hydrodynamic Laboratories. The depth of the channel is 10 m. Fig. 1 shows the test setup. A fixed 42 mm diameter vertical cylinder was instrumented with three local force transducers spaced 0.35 m apart. Each force transducer was a ring 15 mm long, connected to the cylinder by two strain gauged leaf springs (Fig. 2). These springs were mounted at 900 to each other, thus yielding the two horizontal force components. The transducers had a natural frequency of 16 Hz in water and were located 0.60 m, 0.95 m and 1.35 m below the still water level.