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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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Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
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Updated: Feb 28, 2026

Chemotactic Response of Marine Micro-Organisms to Micro-Scale Nutrient Layers
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Intrinsic flow structure and multifractality in two-dimensional bacterial turbulence.

Lipo Wang1, Yongxiang Huang2

  • 1UM-SJTU Joint Institute, Shanghai JiaoTong University, Shanghai 200240, People's Republic of China.

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Bacteria-fluid interactions create turbulence even at zero Reynolds number. Analysis reveals scale similarity and a lognormal multifractal feature, aligning with 3D turbulence, with inverse energy and mixed enstrophy cascades observed.

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Area of Science:

  • Fluid dynamics
  • Microbiology
  • Complex systems

Background:

  • Active biological matter, like bacteria, can induce fluid motion and generate complex flow structures.
  • Understanding fluid dynamics at low Reynolds numbers is crucial for microscale phenomena.

Purpose of the Study:

  • To investigate the turbulent structures generated by bacteria-fluid interactions at zero Reynolds number.
  • To analyze the scaling properties and multifractal characteristics of these flows.
  • To determine the energy and enstrophy cascade directions.

Main Methods:

  • Experimental measurement of flow velocity using streamline segment analysis.
  • Scale similarity analysis to identify different flow regimes.
  • Multifractal analysis using a lognormal formula.
  • Filter-space technique to measure cascade direction.

Main Results:

  • A transition in flow regimes was observed around 16 times the organism's body length, attributed to viscous effects.
  • Scale similarity was found even at the zero Reynolds number limit.
  • A lognormal multifractal feature was quantified (H=0.76, μ=0.20), matching 3D turbulence.
  • An inverse energy cascade and a mixed enstrophy cascade (forward for r/R≤3, inverse for r/R>3) were confirmed.
  • Lognormal statistics were verified for energy dissipation and enstrophy.

Conclusions:

  • Bacteria-driven flows exhibit scale similarity and multifractal properties analogous to 3D hydrodynamic turbulence, despite the low Reynolds number.
  • The observed cascade dynamics provide insights into energy transfer mechanisms in active fluid systems.
  • The findings support the applicability of lognormal statistics to describe scaling exponents in such complex flows.