TY - JOUR

T1 - Impulsive acceleration of a circular cylinder under free surface

AU - Tyvand, Peder A.

AU - Kostikov, Vasily K.

N1 - Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press.

PY - 2023/8/14

Y1 - 2023/8/14

N2 - A present paper generalizes the work of Tyvand & Miloh (J. Fluid Mech., vol. 286, 1995, pp. 67-101) on the problem of the free surface flow generated by a submerged circular cylinder moving impulsively with constant velocity to the case of a cylinder moving with both initial velocity and acceleration. The nonlinear small-time asymptotic solution for the velocity potential, free surface elevation and hydrodynamic pressure force is calculated analytically in bipolar coordinates for a cylinder of arbitrary radius. The analytical solution is obtained to the leading order of nonlinear interaction between initial impulsive velocity and initial impulsive acceleration directed at arbitrary angles. In the special case of the motion with constant acceleration, the complete fourth-order free-surface flow problem is solved and the associated second-order hydrodynamic force is computed. The leading-order contributions to the free surface elevation due to the constant velocity and constant acceleration are compared for finite rectilinear cylinder displacements. The role of constant acceleration consists of two contributions to the leading nonlinear terms, where the amplitude of the first one is 25 % below the case of constant velocity while the amplitude of the other exceeds it by 50 %.

AB - A present paper generalizes the work of Tyvand & Miloh (J. Fluid Mech., vol. 286, 1995, pp. 67-101) on the problem of the free surface flow generated by a submerged circular cylinder moving impulsively with constant velocity to the case of a cylinder moving with both initial velocity and acceleration. The nonlinear small-time asymptotic solution for the velocity potential, free surface elevation and hydrodynamic pressure force is calculated analytically in bipolar coordinates for a cylinder of arbitrary radius. The analytical solution is obtained to the leading order of nonlinear interaction between initial impulsive velocity and initial impulsive acceleration directed at arbitrary angles. In the special case of the motion with constant acceleration, the complete fourth-order free-surface flow problem is solved and the associated second-order hydrodynamic force is computed. The leading-order contributions to the free surface elevation due to the constant velocity and constant acceleration are compared for finite rectilinear cylinder displacements. The role of constant acceleration consists of two contributions to the leading nonlinear terms, where the amplitude of the first one is 25 % below the case of constant velocity while the amplitude of the other exceeds it by 50 %.

KW - general fluid mechanics

KW - surface gravity waves

KW - wave-structure interactions

UR - http://www.scopus.com/inward/record.url?scp=85168800898&partnerID=8YFLogxK

U2 - 10.1017/jfm.2023.557

DO - 10.1017/jfm.2023.557

M3 - Article

AN - SCOPUS:85168800898

SN - 0022-1120

VL - 969

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

M1 - A12

ER -