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Generalized fundamental solutions for unsteady viscous flows.

J J Shu1, A T Chwang

  • 1Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 21, 2001
PubMed
Summary

Researchers developed fundamental solutions for unsteady Oseen and Stokes flows, applicable to time-dependent motions. These solutions, decomposed into wave components, aid in calculating hydrodynamic forces on objects like spheres and cylinders in complex flow fields.

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Area of Science:

  • Fluid dynamics
  • Mathematical physics
  • Rheology

Background:

  • Unsteady Oseen and Stokes flows present challenges in fluid dynamics.
  • Analytical solutions for time-dependent motions are crucial for understanding complex fluid-structure interactions.
  • Existing models often lack generalized fundamental solutions for arbitrary translational and rotational movements.

Purpose of the Study:

  • To develop closed-form fundamental solutions for generalized unsteady Oseen and Stokes flows.
  • To analyze solutions based on their decomposition into longitudinal and transversal wave components.
  • To apply these solutions for calculating hydrodynamic forces on submerged bodies.

Main Methods:

  • Development of closed-form fundamental solutions for generalized unsteady Oseen and Stokes equations.

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  • Decomposition of solutions into wave components (longitudinal and transversal).
  • Application of derived solutions to calculate hydrodynamic forces on a sphere and a circular cylinder.

    • Main Results:

    • Successfully developed generalized fundamental solutions for unsteady flows.
    • Demonstrated the decomposition of solutions into distinct wave phenomena.
    • Calculated hydrodynamic forces on a sphere and a cylinder in unsteady rotating flow fields at low Reynolds numbers.

    Conclusions:

    • The developed fundamental solutions provide a powerful analytical tool for generalized unsteady flows.
    • The wave decomposition offers insights into the nature of fluid disturbances.
    • The methodology is effective for analyzing hydrodynamic interactions in complex, time-dependent flow scenarios.