Lognormality in Turbulence Energy Spectra
The maximum entropy principle states that the energy distribution will tend toward a state of maximum entropy under the physical constraints, such as the zero energy at the boundaries and a fixed total energy content. For the turbulence energy spectra, a distribution function that maximizes entropy...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-06-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/22/6/669 |
| _version_ | 1797565114092617728 |
|---|---|
| author | Taewoo Lee |
| author_facet | Taewoo Lee |
| author_sort | Taewoo Lee |
| collection | DOAJ |
| description | The maximum entropy principle states that the energy distribution will tend toward a state of maximum entropy under the physical constraints, such as the zero energy at the boundaries and a fixed total energy content. For the turbulence energy spectra, a distribution function that maximizes entropy with these physical constraints is a lognormal function due to its asymmetrical descent to zero energy at the boundary lengths scales. This distribution function agrees quite well with the experimental data over a wide range of energy and length scales. For turbulent flows, this approach is effective since the energy and length scales are determined primarily by the Reynolds number. The total turbulence kinetic energy will set the height of the distribution, while the ratio of length scales will determine the width. This makes it possible to reconstruct the power spectra using the Reynolds number as a parameter. |
| first_indexed | 2024-03-10T19:07:23Z |
| format | Article |
| id | doaj.art-b525208a8352450f9e6ef26cfe05bb9d |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T19:07:23Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-b525208a8352450f9e6ef26cfe05bb9d2023-11-20T04:03:55ZengMDPI AGEntropy1099-43002020-06-0122666910.3390/e22060669Lognormality in Turbulence Energy SpectraTaewoo Lee0Mechanical and Aerospace Engineering, SEMTE, Arizona State University, Tempe, AZ 85287, USAThe maximum entropy principle states that the energy distribution will tend toward a state of maximum entropy under the physical constraints, such as the zero energy at the boundaries and a fixed total energy content. For the turbulence energy spectra, a distribution function that maximizes entropy with these physical constraints is a lognormal function due to its asymmetrical descent to zero energy at the boundary lengths scales. This distribution function agrees quite well with the experimental data over a wide range of energy and length scales. For turbulent flows, this approach is effective since the energy and length scales are determined primarily by the Reynolds number. The total turbulence kinetic energy will set the height of the distribution, while the ratio of length scales will determine the width. This makes it possible to reconstruct the power spectra using the Reynolds number as a parameter.https://www.mdpi.com/1099-4300/22/6/669maximum entropy principleinformation theory |
| spellingShingle | Taewoo Lee Lognormality in Turbulence Energy Spectra Entropy maximum entropy principle information theory |
| title | Lognormality in Turbulence Energy Spectra |
| title_full | Lognormality in Turbulence Energy Spectra |
| title_fullStr | Lognormality in Turbulence Energy Spectra |
| title_full_unstemmed | Lognormality in Turbulence Energy Spectra |
| title_short | Lognormality in Turbulence Energy Spectra |
| title_sort | lognormality in turbulence energy spectra |
| topic | maximum entropy principle information theory |
| url | https://www.mdpi.com/1099-4300/22/6/669 |
| work_keys_str_mv | AT taewoolee lognormalityinturbulenceenergyspectra |