Corrigendum. Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel (Journal of Fluid Mechanics (2021) 928 (A4) DOI: 10.1017/jfm.2021.792)

Yang, Y.F., Wu, G.X. and Ren, K. (2025) Corrigendum. Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel (Journal of Fluid Mechanics (2021) 928 (A4) DOI: 10.1017/jfm.2021.792). Journal of Fluid Mechanics, 1020, [E3]. (doi:10.1017/jfm.2025.10746).

Abstract

In the Appendix B of Yang, Wu & Ren (2021), we made the statement that the Green function G has the symmetry property with respect to the field point P(x ₁, y ₁, z ₁) and field point P ₀(x ₀, y ₀, z ₀), or G(x ₁, y ₁, z ₁; x ₀, y ₀, z ₀) = G(x ₀, y ₀, z ₀; x ₁, y ₁, z ₁). This is not always correct. The mistake arose from the statement below (B2) that 'Although G and ξ involve only the real part, we may use the whole complex function here'. In the derivations followed, the full complex functions of G _i and ξ _i (i = 0, 1) in (B1) and (B2) were directly used without taking their real parts, which led to an incorrect conclusion. However, it should be noted that when 0 < Fn < Fn ⁽¹⁾ _c , G _i and ξ _i contain only the k ₀ component. G ⁽⁰⁾ _i is fully real and ξ ⁽⁰⁾ _i is fully imaginary, and they can be taken out of the operator Re{}. Therefore, the symmetry property is satisfied within this range. In summary, the symmetry property G(x ₁, y ₁, z ₁; x ₀, y ₀, z ₀) = G(x ₀, y ₀, z ₀; x ₁, y ₁, z ₁) holds only when 0 < Fn < Fn ⁽¹⁾ _c, and it is incorrect when Fn > Fn ⁽¹⁾ _c. This mistake is confined solely to the Appendix B, and it does not affect any other formulas or results presented in the paper.

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Contributors

Author: K. Ren

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