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Understanding fluid flow behavior through pipes is critical in fluid mechanics, especially in applications like oil transportation through pipelines. Hagen-Poiseuille's law provides an exact solution derived from the Navier-Stokes equations for steady, incompressible, and laminar flow within a circular pipe. Hagen-Poiseuille's law helps determine the necessary pressure drop across a pipeline section by determining parameters like pipe length, radius, oil viscosity, and the desired volumetric...
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Parity-breaking flows in precessing spherical containers.

R Hollerbach1, C Nore, P Marti

  • 1Institute of Geophysics, ETH Zürich, Sonneggstrasse 5, 8092 Zürich, Switzerland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 18, 2013
PubMed
Summary
This summary is machine-generated.

Numerical simulations reveal how fluid flow in precessing spheres transitions from symmetric to asymmetric states. Different inner boundary conditions influence the sequence of bifurcations as the Reynolds number increases.

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Area of Science:

  • Fluid dynamics
  • Nonlinear dynamics
  • Computational physics

Background:

  • Understanding fluid flow in rotating geometries is crucial for various scientific and engineering fields.
  • Precessing spheres exhibit complex behaviors, including symmetry breaking, which are not fully understood.

Purpose of the Study:

  • To numerically investigate the flow dynamics in precessing spheres and spherical shells.
  • To analyze the sequence of bifurcations and symmetry-breaking transitions with varying inner boundary conditions.

Main Methods:

  • Numerical solutions were employed to model the fluid flow.
  • The study examined three cases: a solid sphere and spherical shells with stress-free or no-slip inner boundaries.
  • The Reynolds number (Re) was systematically increased to observe bifurcations.

Main Results:

  • All cases exhibited steady and time-periodic symmetric solutions at lower Reynolds numbers.
  • At higher Reynolds numbers, quasiperiodic asymmetric solutions were observed across all cases.
  • The specific pathways to asymmetry, including periodic asymmetric and quasiperiodic symmetric solutions, varied depending on the boundary conditions.

Conclusions:

  • The study elucidates the complex transition pathways in precessing spherical flows.
  • Inner boundary conditions significantly influence the onset and nature of symmetry-breaking bifurcations.
  • Numerical solutions provide critical insights into the nonlinear dynamics of rotating fluids.