{"id":7898,"date":"2024-09-13T11:31:22","date_gmt":"2024-09-13T08:31:22","guid":{"rendered":"https:\/\/quantum-electronics.ru\/en\/?p=7898"},"modified":"2024-09-13T13:45:15","modified_gmt":"2024-09-13T10:45:15","slug":"hydrodynamic-approximation-for-two-dimensional-optical-turbulence-symmetries-of-statistical-distributions","status":"publish","type":"post","link":"https:\/\/quantum-electronics.ru\/en\/hydrodynamic-approximation-for-two-dimensional-optical-turbulence-symmetries-of-statistical-distributions\/","title":{"rendered":"Hydrodynamic approximation for two-dimensional optical turbulence: symmetries of statistical distributions"},"content":{"rendered":"<p>V. N. Grebenev, A. N. Grishkov, S. B. Medvedev, M. P. Fedoruk<\/p>\n<ul>\n<li>Federal Research Center for Information and Computational Technologies<\/li>\n<li>Universidade de S\u00e3o Paulo, Instituto de Matem\u00e1tica e Estat\u00edstica<\/li>\n<li>Novosibirsk State University<\/li>\n<\/ul>\n<div class=\"around-button\"><b>Abstract:<\/b> Optical turbulence is described in terms of multipoint probability density functions (PDFs) <i>f<sub>n<\/sub><\/i> using the Lundgren\u2013Monin\u2013Novikov (LMN) equation (statistical form of the Euler equations) for the vortex field <i><b>w<\/b><\/i> = <b>\u2207<\/b> \u00d7 <i><b>u<\/b><\/i> in a two-dimensional flow (<i><b>u<\/b><\/i> is the velocity weight field). Lagrangian particles are shown to evolve along the characteristics of the <i>f<sub>n<\/sub><\/i>-equation from the LMN hierarchy. The vorticity is preserved along the characteristics in the absence of an external random force. It is shown that the group <i>G<\/i> of conformal transformations invariantly transforms the characteristics of the equation with zero vorticity and the family of <i>f<sub>n<\/sub><\/i>-equations for PDFs along these lines, or the statistics of the line of zero vorticity. Along other lines of the level <i><b>w<\/b><\/i> = const \u2260 0, the statistics is not conformally invariant. Moreover, the action <i>G<\/i> preserves the PDF class.<\/div>\n<div><\/div>\n<div class=\"around-button\"><b>Keywords:<\/b> two-dimensional Schr\u00f6dinger equation, Lundgren\u2013Monin\u2013Novikov equations, conformal invariance, lines of zero vorticity.<\/div>\n<div><\/div>\n<div><b>Received:<\/b> 16.09.2022<\/div>\n","protected":false},"excerpt":{"rendered":"<p>V. N. Grebenev, A. N. Grishkov, S. B. Medvedev, M. P. Fedoruk Federal Research Center for Information and Computational Technologies Universidade de S\u00e3o Paulo, Instituto de Matem\u00e1tica e Estat\u00edstica Novosibirsk State University Abstract: Optical turbulence is described in terms of multipoint probability density functions (PDFs) fn using the Lundgren\u2013Monin\u2013Novikov (LMN) equation (statistical form of the\u2026 <span class=\"read-more\"><a href=\"https:\/\/quantum-electronics.ru\/en\/hydrodynamic-approximation-for-two-dimensional-optical-turbulence-symmetries-of-statistical-distributions\/\">Read More &raquo;<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[3083,1786,1167,1787],"class_list":["post-7898","post","type-post","status-publish","format-standard","hentry","category-stats","tag-v-n-grebenev","tag-a-n-grishkov","tag-m-p-fedoruk","tag-s-b-medvedev"],"_links":{"self":[{"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/posts\/7898","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/comments?post=7898"}],"version-history":[{"count":0,"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/posts\/7898\/revisions"}],"wp:attachment":[{"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/media?parent=7898"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/categories?post=7898"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/tags?post=7898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}