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Related Concept Videos

General State of Stress01:21

General State of Stress

The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...
Transformation of Plane Stress01:18

Transformation of Plane Stress

Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's faces...
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
Navier–Stokes Equations01:28

Navier–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...
Principal Stresses01:24

Principal Stresses

The graphical depiction of normal and shearing stress equations is represented by a circle, demonstrating the interplay between these stresses under different angular conditions. The center of this circle C, located on the vertical axis, represents the average normal stress, while its radius shows the range of stress variations. At points A and B, where the circle intersects the horizontal axis, the maximum and minimum normal stresses are observed, occurring without shearing stress. These...

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Related Experiment Video

Updated: Jun 25, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor.

Yi Li1, Laurent Chevillard, Gregory Eyink

  • 1Department of Mechanical Engineering and Center of Environmental and Applied Fluid Mechanics, The Johns Hopkins University, Baltimore, Maryland 21218, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2009
PubMed
Summary

This study introduces matrix exponential closures for turbulence modeling, offering a novel approach to the subgrid-scale stress tensor. The method shows feasibility in large eddy simulations, providing an alternative to traditional eddy-viscosity models.

Related Experiment Videos

Last Updated: Jun 25, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Area of Science:

  • Fluid Dynamics
  • Turbulence Modeling
  • Computational Science

Background:

  • Accurate modeling of the subgrid-scale stress tensor is crucial for large eddy simulations (LES) of turbulent flows.
  • Traditional eddy-viscosity models often struggle to capture the complex dynamics of subgrid-scale turbulence.

Purpose of the Study:

  • To introduce and compare two novel approaches for closing the turbulence subgrid-scale stress tensor using matrix exponentials.
  • To explore the theoretical underpinnings and practical feasibility of matrix-exponential closures.

Main Methods:

  • Developed two distinct approaches for matrix exponential closure of the subgrid-scale stress tensor.
  • Investigated formal solutions of the stress transport equation and Eulerian-Lagrangian transformations.
  • Implemented the proposed closure in large eddy simulations of forced isotropic turbulence.

Main Results:

  • Both approaches converge to a basic closure expressing the stress tensor as a matrix exponential of the resolved velocity gradient tensor and its transpose.
  • Short-time expansions reveal connections to eddy-viscosity and quadratic stress closures.
  • Successful implementation in LES of forced isotropic turbulence demonstrates the feasibility of the matrix-exponential closure.

Conclusions:

  • The matrix-exponential closure offers a simple, local, and theoretically grounded alternative to traditional subgrid-scale models.
  • This approach provides a new perspective on turbulence closure, derived directly from the stress transport equation.
  • While omitting pressure-strain correlations, it shows promise for LES applications.