Statistical Fluid Mechanics, Vol. II

Monin, A. S.; Yaglom, A. M.; Lundgren, T. S.

doi:10.1115/1.3423915

Cited by 326 publications

(564 citation statements)

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“…One can ask a question what happened to the term proportional to f 3/2 ? This term results from interactions between eddy currents generated in different points (r i , t i ), whereas in our approach all interactions are taken into account by the very general assumption concerning the scale invariance of SMM which is expressed by (9). In effect we obtain formula (10) depending onf = f /B α m which we interpret as effective frequency dressed by all types of interactions present in the considered system.…”

Section: Discussionmentioning

confidence: 99%

“…The main aim of this work is to confirm that the total energy loss in soft magnetic materials P tot obeys the scaling law (9) and to discuss its relation to the Bertotti formula (1). All conclusions of this paper have been derived from measurements of total energy loss, carried out for the ten samples of soft magnetic materials, which exhibit diverse internal structure -from crystalline to amorphous and nanocrystalline.…”

Section: Introductionmentioning

confidence: 94%

“…Therefore, correlations between the currents [8,9] can be expressed with the postulate of the generalized homogeneity of correlation function current density-current density [10]. In a particular case we obtain the scaling relation for the average of j 2 :…”

Section: Soft Magnetic Materials As a Complex Systemmentioning

confidence: 99%

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Formula for Energy Loss in Soft Magnetic Materials and Scaling

Sokalski

Szczygłowski

2009

Acta Phys. Pol. A

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Basing on scale invariance of considered system an improvement of the Bertotti formula for energy loss in soft magnetic materials has been achieved. Assumptions of the Bertotti theory were discussed and criticized. As an alternative to this theory a new approach basing on the scale invariance of complex systems has been presented. The generalized description of energy loss has been recently postulated by us in the form of the homogeneous function in a general sense which leads to a series expansion for the energy loss. On the basis of measurement data it has been proved that only two first terms of the series are relevant. New measurements of the energy loss in soft magnetic materials have been performed which confirms the scaling theory. The obtained formula enables very simple description of the energy loss in soft magnetic materials, taking into considerations wide ranges of frequency and magnetic induction. The revealed data collapse of energy loss enables comparison of energy losses data taken by different methods. This phenomenon also supplies new criterion for correctness of empirical data.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

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Formula for Energy Loss in Soft Magnetic Materials and Scaling

Sokalski

Szczygłowski

2009

Acta Phys. Pol. A

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“…In the present study, we applied a simple approach to calculate the eddy diffusivity coefficient (K z ) based on the solution of the vertical component of the temperature equation; the modelling of the heat transport using K z is an assumption provided from a simplification for coarse grained boxes of the dynamics (Monin and Yaglom, 1971). We use observations taken for two years at regular depths in Lake Alchichica, Mexico.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the eddy diffusivity coefficient in a warm monomictic tropical Lake

et al. 2016

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We used a two-year dataset (1998-1999) of monthly temperature profiles from Lake Alchichica, Mexico to estimate values of the vertical coefficient of eddy diffusivity. This lake is located in a tropical region at high altitude and shows considerable seasonal variations (i.e., rainy and dry seasons). It has an area of 2.3 km2 and a mean depth of 40.9 m. Alchichica is a warm monomictic lake, which annually becomes isothermal near the end of December or early January at the onset of the dry season and remains stratified for the rest of the year (from late March or early April to early December) during the warm-rainy season. Mathematical models of the spatial and temporal variation of passive substances in lakes and oceans require a quantitative formulation of the vertical transport. Vertical mixing is generally a function of the density profile, which, in lakes, can be directly related to the temperature profile. A widely used method to estimate the vertical diffusion coefficients in lakes from temperature data is the flux-gradient method. In the present study, we applied a simple approach to calculate the eddy diffusivity coefficient (Kz) based on the solution of the vertical component of the modeled temperature equation. We characterized the eddy diffusivity coefficient (Kz) in Lake Alchichica as a dynamic coefficient that changes during the year, between years, and with depth, ranging from 10-10 to 10-6 m2 s-1, whereas typical values of Kz in thermally stratified lakes range from 10-9 to 10-2 m2 s-1. As expected, we found the lowest values in the deeper regions of the lake, and that the temporal variation of temperature with depth showed a quasi-bimodal shape from one year to the next. We also found a structure of alternating peaks and troughs in the vertical Kz, which indicates a response to oscillating vertical mixing. We concluded that the solution of the vertical component of the temperature equation could be a useful tool to estimate the eddy diffusivity in lakes. The major advantage of this method is its simplicity. We also conclude that the differences observed in the estimations of eddy diffusivity coefficients in other lakes are attributable to the differences in local characteristics of the thermal conditions in each lake.

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“…The connection between the Lagrangian and Eulerian coordinates of fluid particles is given by the equation, see [6],…”

Section: Notationmentioning

confidence: 99%

Ecological modeling and Lagrangian approach

et al. 2013

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A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a deformable Lagrangian grid is used. A special grid reconstruction procedure with the subsequent interpolation of the parameters computed is proposed, which ensures computational stability and preserves the values of the most important hydrophysical parameters. Numerical results are presented. MSC:92-08

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Statistical Fluid Mechanics, Vol. II

Cited by 326 publications

References 0 publications

Formula for Energy Loss in Soft Magnetic Materials and Scaling

Formula for Energy Loss in Soft Magnetic Materials and Scaling

Estimation of the eddy diffusivity coefficient in a warm monomictic tropical Lake

Ecological modeling and Lagrangian approach

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