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Related Concept Videos

Entropy02:39

Entropy

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Entropy01:18

Entropy

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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
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Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
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Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
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Second Law of Thermodynamics02:49

Second Law of Thermodynamics

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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
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Second Law of Thermodynamics00:53

Second Law of Thermodynamics

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The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...
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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Enstrophy Cascade in Decaying Two-Dimensional Quantum Turbulence.

Matthew T Reeves1,2, Thomas P Billam3, Xiaoquan Yu1

  • 1Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin, New Zealand.

Physical Review Letters
|December 9, 2017
PubMed
Summary
This summary is machine-generated.

Large-scale simulations reveal an enstrophy cascade in decaying two-dimensional quantum turbulence. This cascade, characterized by a k^{-3} energy spectrum, emerges with over 500 vortices and scales with the superfluid Reynolds number.

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Area of Science:

  • Fluid Dynamics
  • Quantum Turbulence
  • Statistical Mechanics

Background:

  • Two-dimensional turbulence exhibits an inverse energy cascade.
  • Quantum turbulence, governed by vortex dynamics, presents unique characteristics.
  • Understanding energy and enstrophy transfer is crucial for characterizing turbulent flows.

Purpose of the Study:

  • To investigate the presence and characteristics of an enstrophy cascade in decaying two-dimensional quantum turbulence.
  • To establish a link between classical and quantum turbulence through vortex dynamics.
  • To determine the scaling laws and constants associated with this cascade.

Main Methods:

  • Large-scale point-vortex simulations of decaying two-dimensional quantum turbulence.
  • Generation of quantum vortex configurations with localized kinetic energy.
  • Analysis of kinetic energy spectra and enstrophy flux.

Main Results:

  • Evidence for an enstrophy cascade with a k^{-3} power-law kinetic energy spectrum.
  • Cascade signatures emerge for N≳500 vortices.
  • The Kraichnan-Batchelor constant converges to C^{'}≈1.6 at high Reynolds numbers.
  • The width of the k^{-3} range scales as Re_{s}^{1/2}.

Conclusions:

  • Decaying two-dimensional quantum turbulence exhibits a classical enstrophy cascade.
  • The superfluid Reynolds number (Re_{s}) characterizes the dynamics.
  • Simulations confirm theoretical predictions for classical turbulence at large scales.