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Area of Science:

  • Acoustics
  • Fluid Dynamics
  • Wave Physics

Background:

  • Sound beams in fluids exhibit complex behaviors.
  • Understanding beam propagation is crucial for acoustics applications.
  • Previous studies have focused on specific beam types or properties.

Purpose of the Study:

  • To identify and prove the existence of conserved quantities for sound beams.
  • To introduce a framework for analyzing angular momentum conservation.
  • To demonstrate these invariants using known beam solutions.

Main Methods:

  • Derivation of invariants from fundamental conservation laws.
  • Introduction of an angular momentum flux density tensor.
  • Application of the theory to Gaussian and generalized Bessel beams.

Main Results:

  • Seven quantities remain constant along the length of transversely finite sound beams.
  • The cycle-averaged momentum per unit length is identified as the simplest invariant.
  • The conservation of angular momentum is formulated using a flux density tensor.

Conclusions:

  • The study establishes a comprehensive set of invariants for sound beams.
  • The findings provide a theoretical foundation for analyzing sound beam propagation.
  • The demonstrated examples validate the conservation principles for various beam types.