Numerical Modeling using the Nonlinear Progressive Wave
Equation (NPE)
Nonlinear
Acoustic Propagation in an Ocean Waveguide
| Here is a simple time reversal example that shows for linear (Fig. 4.a) and nonlinear (Fig. 4.b) cases, backpropagated signals at 10km-range when a 50Hz single cycle sine source is initially used. A good focusing in the linear case is obtained whereas in the nonlinear case the nonlinear steepening inducing shock attenuation forbids reciprocity and demodulation effects are clearly observed at the focus range. |
Fig. 4.a : Back propagation with the linear model (the nonlinear steepening term of the NPE is removed)
Fig. 4.b : Back propagation with the nonlinear model