Ambit Field Modelling of Isotropic, Homogeneous, Divergence-Free and Skewed Vector Fields in Two Dimensions
We discuss the application of ambit fields to the construction of stochastic vector fields in two dimensions that are divergence-free and statistically homogeneous and isotropic but are not invariant under the parity operation. These vector fields are derived from a stochastic stream function define...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-08-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/8/1265 |
| _version_ | 1797560636780052480 |
|---|---|
| author | Jürgen Schmiegel |
| author_facet | Jürgen Schmiegel |
| author_sort | Jürgen Schmiegel |
| collection | DOAJ |
| description | We discuss the application of ambit fields to the construction of stochastic vector fields in two dimensions that are divergence-free and statistically homogeneous and isotropic but are not invariant under the parity operation. These vector fields are derived from a stochastic stream function defined as a weighted integral with respect to a Lévy basis. By construction, the stream function is homogeneous and isotropic and the corresponding vector field is, in addition, divergence-free. From a decomposition of the kernel in the Lévy-based integral, necessary conditions for the violation of parity symmetry are inferred. In particular, we focus on such fields that allow for skewness of projected increments, which is one of the cornerstones of the Kraichnan–Leith–Bachelor theory of two-dimensional turbulence. |
| first_indexed | 2024-03-10T18:03:25Z |
| format | Article |
| id | doaj.art-a354ac7ddcbd4d0b8e1714f59cedbea5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T18:03:25Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a354ac7ddcbd4d0b8e1714f59cedbea52023-11-20T08:44:49ZengMDPI AGSymmetry2073-89942020-08-01128126510.3390/sym12081265Ambit Field Modelling of Isotropic, Homogeneous, Divergence-Free and Skewed Vector Fields in Two DimensionsJürgen Schmiegel0Department of Engineering, Aarhus University, 8000 Aarhus, DenmarkWe discuss the application of ambit fields to the construction of stochastic vector fields in two dimensions that are divergence-free and statistically homogeneous and isotropic but are not invariant under the parity operation. These vector fields are derived from a stochastic stream function defined as a weighted integral with respect to a Lévy basis. By construction, the stream function is homogeneous and isotropic and the corresponding vector field is, in addition, divergence-free. From a decomposition of the kernel in the Lévy-based integral, necessary conditions for the violation of parity symmetry are inferred. In particular, we focus on such fields that allow for skewness of projected increments, which is one of the cornerstones of the Kraichnan–Leith–Bachelor theory of two-dimensional turbulence.https://www.mdpi.com/2073-8994/12/8/1265ambit fieldsturbulenceisotropyhomogeneityskewnessdivergence-free |
| spellingShingle | Jürgen Schmiegel Ambit Field Modelling of Isotropic, Homogeneous, Divergence-Free and Skewed Vector Fields in Two Dimensions Symmetry ambit fields turbulence isotropy homogeneity skewness divergence-free |
| title | Ambit Field Modelling of Isotropic, Homogeneous, Divergence-Free and Skewed Vector Fields in Two Dimensions |
| title_full | Ambit Field Modelling of Isotropic, Homogeneous, Divergence-Free and Skewed Vector Fields in Two Dimensions |
| title_fullStr | Ambit Field Modelling of Isotropic, Homogeneous, Divergence-Free and Skewed Vector Fields in Two Dimensions |
| title_full_unstemmed | Ambit Field Modelling of Isotropic, Homogeneous, Divergence-Free and Skewed Vector Fields in Two Dimensions |
| title_short | Ambit Field Modelling of Isotropic, Homogeneous, Divergence-Free and Skewed Vector Fields in Two Dimensions |
| title_sort | ambit field modelling of isotropic homogeneous divergence free and skewed vector fields in two dimensions |
| topic | ambit fields turbulence isotropy homogeneity skewness divergence-free |
| url | https://www.mdpi.com/2073-8994/12/8/1265 |
| work_keys_str_mv | AT jurgenschmiegel ambitfieldmodellingofisotropichomogeneousdivergencefreeandskewedvectorfieldsintwodimensions |