Singular Points Location Pattern Analysis based on Modes Interference

Given the lack of research on the regularity of distribution of singular points, the singular points under different influence factors are analyzed. The location of singular points for adjacent modes group (AMG) generated by the interference modes is derived using normal modes theory in the far field of the ideal shallow waveguide. The singular points are verified by simulation, which compares the distribution of the acoustic field and singular points. Moreover, it is concluded that the number and distribution of singular points in the period of the interference structure of the field (PISF) has a relationship with order (lower order of AMG) and adjacent order (difference between two orders of AMG). The arrangement of upper-lower-two-points increases by 2 with each increase of order and is distributed at both ends of PISF. The arrangement of rhombic-four-points increases by 1 with each increase of adjacent order and increases alternately at both ends of PISF. Meanwhile, there is a periodic relationship between the depth of the source and the location of singular points.