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Related Concept Videos

Steady Flow of a Fluid Stream01:27

Steady Flow of a Fluid Stream

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Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
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Bernoulli's Equation for Flow Along a Streamline01:30

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Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
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Stream Function01:20

Stream Function

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In two-dimensional incompressible fluid flow, the continuity equation is essential for ensuring mass conservation, meaning that any change in fluid entering or exiting a region is balanced by a corresponding change elsewhere. For incompressible flow, where density remains constant, this requirement simplifies to the condition that the divergence of the velocity field must be zero. Mathematically, this is expressed as,
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Navier–Stokes Equations01:28

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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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Isochoric and Isobaric Processes01:21

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A thermodynamic process that occurs at constant volume is called an isochoric process. According to the first law of thermodynamics, heat supplied or removed from the system is partially utilized to perform work and change the internal energy of the system. However, in an isochoric process, the volume remains constant. Hence, the work done by the system is zero. Therefore, the exchange of heat changes the internal energy of the system only. 
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Streamlines, Streaklines, and Pathlines01:18

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A streamline represents the trajectory that is always tangent to the fluid's velocity vector at any given point. The velocity of a fluid particle is always directed along the streamline, ensuring the particle continuously follows the streamline's path. Streamlines are particularly useful for visualizing the overall direction of flow in a fluid system, and they provide an instantaneous representation of the flow's velocity field. In steady flow, where conditions do not change over...
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Simulating Impacts of Ice Storms on Forest Ecosystems
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Stochastic ice stream dynamics.

Elisa Mantelli1, Matteo Bernard Bertagni2, Luca Ridolfi2

  • 1Department of Environment, Land and Infrastructure Engineering, Politecnico di Torino, 10129 Turin, Italy elisa.mantelli@polito.it.

Proceedings of the National Academy of Sciences of the United States of America
|July 27, 2016
PubMed
Summary
This summary is machine-generated.

Stochastic climate variability can cause ice streams to exhibit multiple behaviors and deviate from steady-state predictions. Environmental noise is crucial for understanding past ice sheet dynamics and future evolution.

Keywords:
Hopf bifurcationclimate variabilityice streamsnoise-induced phenomena

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Area of Science:

  • Glaciology
  • Climate Science
  • Earth System Science

Background:

  • Ice streams are critical components of ice sheet drainage systems, influencing sea level and paleoclimate.
  • Ice stream dynamics are influenced by climate factors like temperature and snowfall, which exhibit natural variability.
  • Understanding these dynamics is vital for predicting ice sheet behavior during past and future climate changes.

Purpose of the Study:

  • To investigate the impact of stochastic climate forcing on the temporal dynamics of ice streams.
  • To determine if realistic climate fluctuations can alter expected ice stream behaviors.
  • To assess the role of environmental noise in ice sheet evolution.

Main Methods:

  • Modeling ice stream dynamics under fluctuating climate conditions.
  • Analyzing the interplay between stochastic climate forcing and ice stream flow.
  • Comparing model outputs with theoretical expectations for deterministic systems.

Main Results:

  • Realistic climate fluctuations can induce multiple, coexisting dynamic behaviors in ice streams.
  • Stochastic forcing drives ice stream flow away from steady-state regimes predicted by deterministic models.
  • Environmental noise significantly impacts the temporal evolution of ice stream activity.

Conclusions:

  • Environmental noise is a critical factor in ice stream dynamics, not merely a secondary effect.
  • Past ice sheet behavior, particularly during deglaciation, may be better understood by incorporating stochastic climate influences.
  • Accurate predictions of future ice sheet changes necessitate the inclusion of environmental noise in climate models.