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Related Concept Videos

Free Jet01:14

Free Jet

Free jets describe the flow of liquid exiting a reservoir through an opening into the atmosphere without resistance. The velocity (v) of the liquid jet is derived using Bernoulli's principle and expressed as:
Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

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:
Accelerating Fluids01:17

Accelerating Fluids

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.
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:
Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
Turbulent Flow01:24

Turbulent Flow

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 spots,...
Laminar and Turbulent Flow01:07

Laminar and Turbulent Flow

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 streamlines...

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Related Experiment Video

Updated: May 13, 2026

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

Direct statistical simulation of out-of-equilibrium jets.

S M Tobias1, J B Marston

  • 1Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom. smt@maths.leeds.ac.uk

Physical Review Letters
|March 26, 2013
PubMed
Summary
This summary is machine-generated.

We simulated fluid jet formation using a cumulant expansion method. While accurate near equilibrium, this method’s precision decreases for more complex, meandering jets.

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Last Updated: May 13, 2026

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
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Published on: February 27, 2016

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Area of Science:

  • Fluid dynamics
  • Statistical mechanics
  • Atmospheric science

Background:

  • Jet formation is crucial in fluid systems.
  • Statistical methods offer efficient simulation approaches.
  • Cumulant expansions approximate complex fluid statistics.

Purpose of the Study:

  • To assess the accuracy of a second-order cumulant expansion (CE2) for simulating fluid jet formation.
  • To compare CE2 results with direct numerical simulations (DNS).
  • To investigate CE2's performance under varying degrees of non-equilibrium conditions.

Main Methods:

  • Direct statistical simulation of jet formation on a β plane.
  • Utilizing a cumulant expansion truncated at second order (CE2).
  • Comparing CE2 statistics against data from direct numerical simulations (DNS).

Main Results:

  • CE2 accurately reproduces jet structure for systems near equilibrium.
  • Some discrepancies were observed in the second cumulant even near equilibrium.
  • CE2 accuracy diminishes as jets deviate further from equilibrium (increased zonostrophy), leading to more meandering.
  • Higher-order cumulants may be necessary for improved accuracy in non-equilibrium cases.

Conclusions:

  • The second-order cumulant expansion (CE2) is a viable method for simulating near-equilibrium fluid jets.
  • Jet meandering and departure from equilibrium significantly impact CE2's predictive accuracy.
  • Incorporating higher-order cumulants presents a potential avenue for enhancing simulation fidelity in complex, non-equilibrium fluid flows.