Breaker depth index of a wave breaking at a coastal structure – the modified Weggel’s nomogram revisited

A modified version of Weggel’s nomogram for the breaker depth index is limited along the abscissa, ending up below values required by some practical applications. The nomogram indicates that the progression of the breaker depth function, obtained for the case of horizontal sea bottom, is represented by a horizontal line. This could falsely indicate that the modified Weggel’s nomogram does not consider the limiting wave steepness condition. Assuming a pure case of sloped sea bottom without any coastal structure, the breaker depth index, incorporating Miche’s limiting wave steepness condition, has been derived analytically and compared with the envelope to Weggel’s lines, proving the correctness of the envelope analytical technique used in the paper. Considering a practical case of a wave breaking in front of a coastal structure, a correct form of Weggel’s equation for the breaker depth index (without the limiting wave steepness condition) has been derived, and a correction procedure for implementing the limiting wave steepness condition to the breaker depth index has been presented. A set of high-quality practical nomograms for the breaker depth index has been prepared for the extended range of the nomogram abscissa. A programme code has been also elaborated, enabling coastal engineers a precise calculation of the breaker depth index.