Related Experiment Video
Updated: Jun 14, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Low Reynolds number turbulence in nonlinear Maxwell-model fluids
Chris Goddard1, Ortwin Hess, Siegfried Hess
1Department of Physics, Faculty of Engineering and Physical Sciences, University of Surrey, Advanced Technology Institute, Guildford GU2 7XH, United Kingdom. c.j.goddard@surrey.ac.uk
Summary
A generalized nonlinear Maxwell model simulates lid-driven cavity flow, revealing smooth laminar and low Reynolds number turbulent flows. These findings closely resemble experimentally observed elastic turbulence in polymer solutions.
Area of Science:
- Fluid Dynamics
- Polymer Physics
- Computational Science
Background:
- Nonlinear viscoelastic models are crucial for understanding complex fluid behaviors.
- Elastic turbulence, observed in polymer solutions, presents unique flow characteristics.
- Previous analysis of the Maxwell model was limited to plane Couette geometry.
Purpose of the Study:
- To apply a generalized nonlinear Maxwell model to a lid-driven cavity flow.
- To numerically investigate the three-dimensional hydrodynamical problem.
- To compare simulation results with experimental observations of elastic turbulence.
Main Methods:
- Numerical treatment of the full three-dimensional hydrodynamical problem.
- Application of a generalized nonlinear Maxwell model.
- Analysis of flow patterns and turbulence measures.
Main Results:
- The model successfully reproduces both smooth laminar and low Reynolds number turbulent flows.
- Simulated flow patterns exhibit striking similarities to experimentally observed elastic turbulence.
- Graphical representations of flow patterns and turbulence metrics are provided.
Conclusions:
- The generalized nonlinear Maxwell model is effective in simulating complex flows like lid-driven cavity flow.
- The model's predictions align well with experimental data on elastic turbulence.
- This study provides a computational framework for understanding viscoelastic turbulence.
Related Concept Videos
01:10Poiseuille'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:
01:15Dimensionless Groups in Fluid Mechanics
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...
01:18Newtonian Fluid: Problem Solving
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.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
01:28Navier–Stokes Equations
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...
01:07Laminar 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...
01:24Reynolds Transport Theorem
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit mass.