Abstract
Numerical simulations have been carried out on ocean acoustic scales for a simple array of three nonlinear sources. The nonlinear progressive wave equation (NPE) model [B. E. McDonald and W. A. Kuperman, J. Acoust. Soc. Am. 81, 1406–1417 (1987)] has been used to calculate the evolution of initially nonintersecting underwater shocks of Mach number 0.05. Three impulsive sources equally spaced on a vertical line are fired with top and bottom elements together, and the middle one phase delayed. The resulting wave produces a weak “focus” at the intersection of the three expanding spherical waves. Linear and nonlinear calculations are compared. In the linear calculation, the individual waves retain their identity past the focal range. In the nonlinear calculation, however, Mach stems form as individual shocks merge. A directed beam is formed, with the three shocks joined irreversibly into a single shock. Nonlinear processes are seen to increase peak pressures in the farfield as compared to a linear solution.
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