A model for the two dimensional interaction between non-linear waves and uniform currents

Song, Shaowen (1988) A model for the two dimensional interaction between non-linear waves and uniform currents. Masters thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (15MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

The interaction of water wave trains with a uniform current normal to the wave crests is considered. The combined wave-current motion resulting from the interaction is assumed stable and irrotational. The velocity potential, dispersion relation, the particle kinematics and pressure distribution upto the third order are developed. The conservation of mean mass, momentum and energy of the current-free wave, wave-free current and combined wave-current fields before and after the interaction are used, together with the dispersion relation on the free surface to derive a set of four nonlinear equations, through which the relationship between H, L, d, U and H₀, L₀, d₀, U₀ is established, where H₀, L₀, d₀ are respectively the current-free wave height, wave length, mean water depth, and U₀ the wave-free current speed, H, L, d, U are respectively the wave height, wave length, water depth, current speed of the combined wave-current field after the interaction. This is a new approach to an old problem. A numerical method is used to solve the system of nonlinear equations to calculate H, L, d, and U when given the values of H₀, L₀, d₀ and U₀. Numerical results for the changes of wave height, length, water depth, and current speed in the form of H/H₀, L/L₀, Δd/d₀, and ΔU/U₀ are presented, where Δd = d - d₀, ΔU = U - U₀. the prediction of the combined wave-current properties through H₀, L₀, d₀ and U₀ is established by using the velocity potential of the combined wave-current field and the numerical results of H, L, d, and U. A comparison between the experimental results of Thomas (1981) and the results of the present theory is presented, and surprising agreement is observed. -- Discussions on the radiation stress and energy transfer in the combined wave-current field, and on the numerical method and precision control are given in the appendices.

Actions (login required)

View Item