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Turbulent Flow

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 Flow

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...

Poiseuille's Law and Reynolds Number

Poiseuille's Law and Reynolds Number

Any fluid in a horizontal tube can flow due to pressure differences—fluid flows from high to low pressure. The flow rate (Q) is the ratio of pressure difference and resistance through a horizontal tube. The greater the pressure difference, the higher the flow rate. The flow resistance is expressed as:

Couette Flow

Couette Flow

Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...

Bernoulli's Equation for Flow Along a Streamline

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:

Bernoulli's Equation for Flow Normal to a Streamline

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...

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Related Experiment Video

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Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

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Preturbulent regimes in graphene flow.

M Mendoza¹, H J Herrmann, S Succi

¹ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Schafmattstrasse 6, HIF, CH-8093 Zürich, Switzerland. mmendoza@ethz.ch

Physical Review Letters

|May 17, 2011

Summary

Electronic preturbulent phenomena in graphene can be observed via current fluctuations. Relativistic corrections to fluid dynamics equations affect vortex generation and stability in graphene.

Area of Science:

Condensed matter physics
Fluid dynamics

Background:

Graphene exhibits complex electronic behaviors under specific conditions.
Understanding fluid dynamics in nanoscale materials is crucial for technological applications.

Purpose of the Study:

To provide numerical evidence for observing electronic preturbulent phenomena in graphene.
To investigate vortex generation and the impact of relativistic corrections on fluid stability in graphene.

Main Methods:

Numerical simulations of electronic phenomena in graphene.
Analysis of current fluctuations to detect preturbulence.
Application of relativistic corrections to Navier-Stokes equations for vortex dynamics.

Main Results:

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Electronic preturbulence in graphene can be detected through current fluctuations.

Vortex generation is influenced by micron-sized constrictions.

Relativistic corrections delay stability breakout and slightly alter vortex shedding frequency.

Conclusions:

Current fluctuations serve as a viable experimental signature for electronic preturbulence in graphene.
Relativistic effects play a role in the fluid dynamics of graphene, impacting vortex behavior.