Understanding the behaviour of scalar isosurfaces in a turbulent flow is of particular interest for many problems in turbulent mixing that contain sharp interfaces between regions of the flow. Common examples include combustion, where the chemical reactions occur in thin regions within the flow, and the turbulent/non-turbulent interface in shear flows, where a thin region separates the rotational, turbulent motions from the irrotational, non-turbulent background. Recent advances in computing technology allow for in-depth analysis of these interface problems that are difficult to quantify in a laboratory setting. In this paper, the results of a direct numerical simulation of a passive scalar
$\varPhi$
evolving on a turbulent, temporally developing mixing layer are described. A novel approach has been taken to calculate the surface area of individual scalar isosurfaces,
$A_{iso}$
, throughout the simulation, as well as the mean isosurface area density,
$\varSigma$
, as a function of the cross-stream direction and time. A notable finding is that the profiles of
$\varSigma$
develop in a self-similar manner when scaled by the Taylor scale of the scalar field,
$\lambda _\phi$
. Remarkably, the scaling appears to hold for a wide range of isovalues. A rough scaling argument based on the formal definition of
$\varSigma$
and properties of a temporal mixing layer is presented which also exposes a dependence on
$\lambda _\phi$
. Based on these results, a possible scaling for the isosurface area is presented as
$A_{iso}/A_0 \sim (Re \, Sc)^{1/2}$
, where
$Re$
and
$Sc$
are local Reynolds and Schmidt numbers, respectively.
The stress-magnetism effect can be used as a novel and convenient potential NDE method, called the magnetic memory method. However, whether and how this can be used as a quantitative measurement are still subjects that are as yet rarely studied by researchers. In this paper, circle tensile stress within the elastic region was applied to a ferromagnetic sample under geomagnetic field. The relationships between the surface leakage magnetic field and the tensile stress are presented. The stress-magnetic field equivalent model is derived and discussed and reconciled with the experimental results. A new model of stress-permeability that represents the relationship of the material permeability versus stress is proposed, which reconciles with the experimental results. It confirms that quantitative measurement and estimation of the integrity of ferromagnetic items by magnetic memory testing is feasible.
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