Theoretical Analysis of Complex Center of Pressure (iCoP) on Immersed Circular Bodies

When a circular body is immersed in a fluid, its interaction with the surrounding water leads to the formation of waves and ripples. This fascinating phenomenon is primarily driven by the fluid encountering a crucial point on the body, known as the complex centre of pressure (iCoP). This point acts as a threshold that instigates disturbances in the fluid, illustrating why the body affects the fluid dynamics even before it is fully submerged. The concept of the iCoP introduces a new dimension to our understanding of fluid dynamics defined by the equation as . The iCoP is symmetric and dependent solely on the diameter of the body, which enables it to pinpoint where fluid disturbances originate in the water. The immersion depth and oscillatory behaviour of the circular body are described by . Here, signifies that the body should be half-immersed, with its centre positioned halfway below the waterline, while the term indicates that the body’s oscillatory movement, with an amplitude of , causes the body to move up and down from this equilibrium position which makes the body not to be totally half immersed as indicated by . Consequently, the immersion depth varies and reflecting both partial immersion and dynamic oscillation. The real part of the iCoP reveals critical locations for fluid displacement, which leads to wave formation, while the imaginary part uncovers the phase shifts that describe the body’s dynamic interaction with fluid motion.