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Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent...
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The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Phenomenology of transition to quantum turbulence in flows of superfluid helium.

Proceedings of the National Academy of Sciences of the United States of America·2024
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Phenomenology of quantum turbulence in superfluid helium.

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Related Experiment Video

Updated: Jan 13, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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On Grid-Generated Quantum Turbulence.

Ladislav Skrbek1

  • 1Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague, Czech Republic.

Entropy (Basel, Switzerland)
|October 28, 2025
PubMed
Summary

Grid experiments with classical fluids and superfluid helium provide insights into turbulence. Oscillating grids in superfluid helium reveal key physics of quantum turbulence.

Area of Science:

  • Fluid dynamics
  • Quantum physics
  • Condensed matter physics

Background:

  • Turbulence remains a fundamental unsolved problem in fluid dynamics.
  • Grid-generated turbulence in classical fluids is a well-established research area.
  • Superfluid helium phases (He II and He III-B) offer unique systems for studying quantum turbulence.

Purpose of the Study:

  • To review complementary grid experiments in classical and quantum fluids.
  • To deepen the understanding of the physics of turbulent quantum flows.
  • To highlight pioneering experiments on quantum turbulence using oscillating grids in He II.

Main Methods:

  • Generating turbulence using grids in classical viscous fluids (air, water).
  • Generating and probing quantum turbulence using oscillating grids in superfluid 4He (He II) and 3He-B.
Keywords:
grid turbulenceheliumquantized vorticesquantum turbulencetwo-fluid model

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  • Conducting experiments in the zero temperature limit for superfluid helium.
  • Main Results:

    • Grid experiments provide a basis for studying turbulence across different fluid types.
    • Oscillating grid experiments in He II have been crucial for understanding quantum turbulence.
    • These studies have advanced the understanding of the physics governing turbulent quantum flows.

    Conclusions:

    • Grid-based experiments are essential for studying both classical and quantum turbulence.
    • Research on superfluid helium turbulence, particularly using oscillating grids, is vital for resolving fundamental questions about turbulence.
    • Pioneering work in this field has significantly contributed to the understanding of quantum fluid dynamics.