Skip to contents

Overview

Validated Experimental

The viscous-elastic spherical model (VESM) calculates resonant scattering from a gas core, elastic shell, and outer viscous layer. The package interface uses model = "vesms" and stores output under VESMS.

Core idea

Solve the concentric layered sphere mode by mode, including acoustic waves in the exterior and gas, elastic waves in the shell, and complex compressional and shear response in the viscous layer (Khodabandeloo et al. 2021; Feuillade and Nero 1998).

Best for

  • Gas-bearing layered targets represented by a concentric spherical idealization
  • Resonance studies in which shell elasticity and viscous damping both matter
  • Comparison with simpler bubble, fluid-sphere, or elastic-shell models

Supports

  • Spherical ESS objects containing the elastic shell and inner gas-like fluid
  • Run-time viscous-layer density, sound speed, shear viscosity, bulk viscosity, and thickness or relaxation time
  • Configurable spherical modal truncation

Main assumptions

  • Concentric spherical interfaces and homogeneous properties in each layer
  • Linear acoustics, elasticity, and the documented viscous constitutive model
  • No nonspherical posture, eccentric core, or spatial material gradients
  • Validation is limited to the documented layered-sphere cases

Validation status

  • Validated against the reference Python VESM implementation on the documented layered-sphere case.
  • VESM is currently marked experimental because the documented public workflow is still limited to the current layered-sphere scope.

Family pages

  • Implementation: building the layered object, required arguments, and output
  • Theory: fields in all four regions and interface systems

References

Feuillade, C., and R. W. Nero. 1998. “A Viscous-Elastic Swimbladder Model for Describing Enhanced-Frequency Resonance Scattering from Fish.” The Journal of the Acoustical Society of America 103 (6): 3245–55. https://doi.org/10.1121/1.423076.
Khodabandeloo, Babak, Mette Dalgaard Agersted, Thor Klevjer, Gavin J. Macaulay, and Webjørn Melle. 2021. “Estimating Target Strength and Physical Characteristics of Gas-Bearing Mesopelagic Fish from Wideband in Situ Echoes Using a Viscous-Elastic Scattering Model.” The Journal of the Acoustical Society of America 149 (1): 673–91. https://doi.org/10.1121/10.0003341.