Heave added mass coefficient of a spherical buoy

Abstract We present a theoretical framework for estimating the added mass of a partially submerged spherical buoy undergoing heave oscillations. Asymptotic analyses are conducted in the limiting cases of low and high oscillation frequencies, where the classical potential flow theory applies. For each frequency regime, we consider two canonical geometries that approximate the wetted surface of the buoy: (i) a small perturbation about a reference flat disk, relevant when the immersion depth is small compared to the buoy radius (immersion ratio $$\varepsilon _d\ll 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ε</mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:mo>≪</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ), and (ii) a small perturbation about a reference hemisphere, appropriate when the immersion depth is comparable to the radius. Perturbation expansions for the added mass are derived in each case. By smoothly bridging the results from these asymptotic limits, we construct a composite approximation for the added mass across a wide range of immersion ratios. This theoretical prediction is validated against direct numerical simulations, showing excellent agreement: the error remains below 1.1% for $$\varepsilon _d\le 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ε</mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , below 6% for $$1 &lt; \varepsilon _d\le 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>ε</mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , and below 25% for $$2 &lt; \varepsilon _d\le 3.75$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>ε</mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>3.75</mml:mn> </mml:mrow> </mml:math> . Our results offer a tractable and yet physically grounded model for added mass evaluation, applicable to the analysis and optimization of systems involving floating oscillating bodies, such as two-body wave energy converters.