Very-low-frequency WKB turning mode model in deep ocean

A WKB method is presented to compute very-low-frequency turning modes in the deep ocean. Utilizing the comparison equation method, the WKB approximate solution based on parabolic cylinder function for the depth-separated wave equation is obtained by comparing with the exact solution for mapping equation. The approximate conditions are further discussed. The global approximate error of the mode function is numerically analyzed for an Epstein layer, while the normal mode sound field is assessed for a Munk environment. The proposed method demonstrates a smaller global approximation error compared to the classical WKB approximation method and the Langer transform method. The results indicate that the normal modes in seawater do not necessitate a piecewise representation, making it suitable for investigating very-low-frequency sound propagation in the deep ocean.