2017/07/31 by Yaron Oz · 16 citations
Engineering · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Conformal anomaly #Conformal field theory #Conformal map #Cosmology and Gravitation Theories #Dilaton #Fluid Dynamics and Turbulent Flows #Geometry #Intermittency #Inviscid flow #Mathematical analysis #Mathematical physics #Mathematics #Physics #Scaling #Thermodynamics #Turbulence #hep-th #nlin.CD
paper · pdf · doi:10.1007/jhep11(2017)040
published in Journal of High Energy Physics 2017(11) (Springer Nature) · 27 pages, revtex; added discussions, added formulas, added reference
openalex publication_date 2017/11/01 · arxiv created 2018/12/29 · arxiv updated 2019/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent z=(2)/(3) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>z</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mn>2</mml:mn> <mml:mn>3</mml:mn> </mml:mfrac> </mml:math> . The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength.