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WISpec_readme, May. 7, 2022, Houwang Tu

Ph.D candidate of National University of Defense Technology

[email protected]

The program WISpec.m computes the acoustic field in arbitrary horizontally stratified media (as shown in Figure 1) using the wavenumber integration model discretized by the Chebyshev--Tau spectral method. The spectral algorithm is described in the article (H. Tu, Y. Wang, W. Liu et al., A spectral method for the depth-separated solution of a wavenumber integration model for horizontally stratified fluid acoustic waveguides [J], Physics of Fluids, 2023(35), 057127, https://doi.org/10.1063/5.0150221).

The 'ReadEnvParameter' function is used to read "input.txt" file. User can make changes to "input.txt" for the desired simulation. The "input.txt" file contains the parameters defining the modal calculation. See the following example:

Example1                          ! casename
P                                 ! Src, type of sound source
1                                 ! Layers of media
20                                ! Nl (truncation order of layers, Layers rows)
2                                 ! kmax (maximum integral interval)
20.0                              ! freq (frequency of source)
36.0                              ! zs (depth of source)
0.25                              ! dz (discrete length in depth direction)
3000.0                            ! rmax (receiver ranges(m))
1                                 ! dr (discrete length in horizontal direction)
40                                ! tlmin (minimum value of TL in colorbar)
70                                ! tlmax (maximum value of TL in colorbar)
100.0                             ! h (bathmetries of ocean)
2                                 ! n (profiles' points in water column)
    0.0 1500.0  1.0   0.0         ! dep c rho alpha
  100.0 1500.0  1.0   0.0
A                                 ! Lowerboundary (rigid/free/halfspace lower boundary condition)
  100.0 2000.0  2.0   2.0         ! sound speed, density and attenuation of semi-infinite space

The "input.txt" file include:

• casename is the name of current example;

• Src is the type of sound source, P denotes point source, L denotes line source;

• Layers is the number of the layers of media;

• Nls are the numbers to truncated order of media. Generally speaking, the more complicated the shape of the sound speed profile, the more Nls are needed to accurately fit.

• kmax, the integral interval is [0, kmax].

• freq (frequency of sound source, Hz),

• zs (the depth of source, m),

• dz (step size in depth direction, m),

• rmax (the maximum range of horizontal direction, m),

• dr (horizontal discrete step, m),

• tlmin and tlmax are the minmum and maximum value transmission loss, respectively, which used to determine the color range of the output transmission loss graph, tlmin must less than tlmax.

• hs are the bathmetries of ocean of ocean, unit: m.

• ns are the amount of environmental profile data in medium columns.

  There is a table of environmental parameter: the units are depth(m), speed(m/s), density(g/cm$^3$) and attenuation (dB/wavelength), with nw points in each layer. It is necessary that depw(n)=depb(1) where the density usually has a discontinuity. The first entry dep(1)=0 is the free surface. The last entry dep(n)=H determines the total thickness of the waveguide.

• Lowerboundary (User used to specify whether the seabottom boundary condition is perfectly free 'V', perfectly rigid 'R' or semi-infinite space 'A'), The last line is the parameters for the semi-infinite space.

Figure 1. Schematic of arbitrary horizontally stratified marine environment.

The plots resulting from the above dialog are as follows:

Figure 2. Wavenumber spectrum of the waveguide.

Figure 3. A colorful plot of transmission loss, range versus depth.