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Related Concept Videos

Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

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Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
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Typical Model Studies01:30

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Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
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Design Example: Creating a Hydraulic Model of a Dam Spillway01:21

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Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
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Newtonian Fluid: Problem Solving

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Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
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Navier–Stokes Equations01:28

Navier–Stokes Equations

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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
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Accelerating Fluids01:17

Accelerating Fluids

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When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
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The Diffusion of Passive Tracers in Laminar Shear Flow
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From Inverse-Cascade to Subdiffusive Dynamic Scaling in Driven Disordered Bose Fluids.

Elisabeth Gliott1, Adam Rançon2, Nicolas Cherroret1

  • 1<a href="https://ror.org/01h14ww21">Laboratoire Kastler Brossel</a>, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75005 Paris, France.

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We discovered universal dynamic scaling in a Bose gas near condensation, driven by external forces and disorder. The gas transitions through three regimes, all explained by self-similar scaling laws.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Bose-Einstein condensation describes a state of matter formed by cooling bosons to near absolute zero.
  • Understanding dynamic scaling is crucial for characterizing phase transitions in quantum systems.
  • Interacting Bose gases exhibit complex dynamics influenced by external forces and disorder.

Purpose of the Study:

  • To investigate the emergence of universal dynamic scaling in an interacting Bose gas.
  • To analyze the system's behavior around the condensation transition under combined drive and disorder.
  • To identify and describe the distinct dynamical regimes observed.

Main Methods:

  • Theoretical exploration of an interacting Bose gas model.
  • Analysis of the system's dynamics under external driving force and spatial disorder.
  • Identification of crossover between different dynamical regimes.

Main Results:

  • The Bose gas exhibits three distinct dynamical regimes: inverse turbulent cascade, stationary regime, and sub-diffusive cascade.
  • These regimes are characterized by the interplay of interactions, drive, and disorder.
  • All observed dynamical regimes are described by universal self-similar scaling laws.

Conclusions:

  • Universal dynamic scaling governs the behavior of an interacting Bose gas near condensation.
  • The interplay of drive and disorder leads to distinct, yet universally scalable, dynamical regimes.
  • Findings align with recent experimental observations of sub-diffusive cascades.