Riemann’s wave and an exact solution of the main turbulence problem

References

• Brown G, Charnotskii M, Churnside J, et al. Professor Valerian Il’ich Tatarskii an appreciation. Wave Random Complex. 2020;30(1):1–4. doi:10.1080/17455030.2019.1654149.
   Google Scholar
• Monin AS, Yaglom AM. Statistical Fluid Mechanics. MIT Press; 1971. Vol. 1 [2nd Russian ed. (Gidrometeoizdat, St. Petersburg, 1992)]; (MIT Press, 1975), Vol. 2 [2nd Russian ed. (Gidrometeoizdat, St. Petersburg, 1996)].
   Google Scholar
• Riemann B. Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite, Abh. Koniglichen Ges. Wiss. Gottingen. 1860;8:43–66.
   Google Scholar
• Landau LD, Lifshitz EM. Fluid Mechanics. 2nd ed. Theoretical Physics. Vol. 6. Oxford: Pergamon; 1987.
   Google Scholar
• Toro EF. Riemann solvers and numerical methods for fluid dynamics: A practical introduction. 3rd ed. Berlin: Springer-Verlag; 2009. doi:10.1007/978-3-540-49834-6
   Google Scholar
• Pelinovskii EN. Spectral analysis of simple waves. Radiophys Quantum Electron. 1976;19:262–270. doi:10.1007/BF01034583.
   Google Scholar
• Malakhov AN, Saichev AI. On the question of kinetic equations in the theory of random waves. Radiophys Quantum Electron. 1974;17:699–709.
   Google Scholar
• Saichev AI. On the spectra of some random waves propagating in a nonlinear medium. Radiophys Quantum Electron. 1974;17:1025–1034.
   Google Scholar
• Gurbatov SN, Saichev AI. One-dimensional turbulence in a viscous polytropic gas. Radiophys Quantum Electron. 1988;31:1043–1054. doi:10.1007/BF01044815.
   Google Scholar
• Gurbatov SN, Saichev AI, Malakhov AN. Nonlinear random waves and turbulence in nondispersive media: waves, rays, particles. Manchester University Press; 1991, and John Wiley and Sons Ltd; 1992,
   Google Scholar
• Polyakov AM. Turbulence without pressure. Phys Rev E. 1995;52:6183–6188.
   PubMed Web of Science ®Google Scholar
• Ee W, Eijnden EV. On the statistical solution of the Riemann equation and its implications for Burgers turbulence. Phys Fluids. 1999;11:2149–2153.
   Web of Science ®Google Scholar
• Gurbatov SN, Rudenko OV, Tyurin AV AV. Singularities and spectral asymptotics of a random nonlinear wave in a nondispersive system. Wave Motion. 2020;95:102519–102524. doi:10.1016/j.wavemoti.2020.102519.
   Web of Science ®Google Scholar
• Sreenivasan KR, Yakhot V V. Dynamics of three-dimensional turbulence from Navier-Stokes equations. Phys Rev Fluids. 2021;6:Article 104604. doi:10.1103/PhysRevFluids.6.104604.
   Web of Science ®Google Scholar
• Chefranov SG. On the theory of turbulent viscosity. Sov Phys.JETP. 1989;69:94–102.
   Google Scholar
• Chefranov SG. Exact statistically closure description of vortex turbulence and admixture in compressible medium. Sov Phys Dokl. 1991;36:286–289.
   Google Scholar
• Chefranov SG, Chefranov AS. Exact solution of the compressible Euler–Helmholtz equation and the millennium prize problem generalization. Phys. Scr. 2019;94:054001, doi:10.1088/1402-4896/aaf918.
   Web of Science ®Google Scholar
• Chefranov SG, Chefranov AS. The new exact solution of the compressible 3D Navier–Stokes equations. Commun. Nonlinear Sci Numer Simul. 2020;83:105118, doi:10.1016/j.cnsns.2019.105118.
   Web of Science ®Google Scholar
• Chefranov SG, Chefranov AS. Exact solution to the main turbulence problem for a compressible medium and the universal -8/3 law turbulence spectrum of breaking waves. Phys Fluids. 2021;33:076108, doi:10.1063/5.0056291.
   Web of Science ®Google Scholar
• YaG S. Statistics of shocks in solutions of inviscid Burgers equation. Commun Math Phys. 1992;148:601–621.
   Web of Science ®Google Scholar
• She Z-S, Aurell E, Frisch U. The inviscid Burgers equation with initial date of Brown type. Commun Math Phys. 1992;148:623–641.
   Web of Science ®Google Scholar
• YaG S. New results in mathematical and statistical hydrodynamics. Adv Math Sci. 2000;55:25–58. doi:10.4213/rm313.
   Google Scholar
• Sulem P-L, Frisch U. Bounds of energy flux for finite energy turbulence. J Fluid Mech. 1975;72:417–423.
   Web of Science ®Google Scholar
• Kadomtsev BB, Petviashvili VI. On acoustic turbulence. Sov Phys Dokl. 1973;18:115–119.
   Google Scholar
• L’vov VS, L’vov Y, Newell AS, et al. Statistical description of acoustic turbulence. Phys Rev E. 1997;56:390–405.
   Web of Science ®Google Scholar
• Kuznetsov EA, Krasnoselskikh V. Anisotropic spectra of acoustic type turbulence. Phys Plasmas. 2008;15:062305, doi:10.1063/1.2928160.
   Web of Science ®Google Scholar
• Chefranov SG, Chefranov AS. Universal turbulence scaling law-8/3 at fusion implosion, www.arxiv.org/2111.15360 [physics.flu-dyn] 24 Nov 2021.
   Google Scholar
• Chefranov AS, Chefranov SG, Golitsyn GS. Universal turbulence scaling law -8/3 for cosmic rays. Forthcoming.
   Google Scholar
• Sulem C, Sulem P-L, Frisch H. Tracing complex singularities with spectral methods. J Comput Phys. 1983;50:138.
   Web of Science ®Google Scholar
• Pelinovsky D, Pelinovsky E, Kartashova E, et al. Universal power law for the energy spectrum of breaking Riemann waves. JETP Lett. 2013;98:237.
   Web of Science ®Google Scholar
• Gurvich AS, Zubkovskii SL. On an experimental evolution of turbulent energy dissipation fluctuations. Izv Acad Sci. USSR. Geophys. Ser. 1963;12:1856.
   Google Scholar
• Pond S, Stewart RW. Measurements of statistical characteristics of small-scale turbulent motions. Izv Atmos Ocean Phys. Ser. 1965;1:914.
   Google Scholar
• Kholmyansky MZ. Measurements of turbulent micro-fluctuations of the wind velocity derivative in the atmospheric surface layer. Izv Acad Sci USSR Atmos Oceanic Phys. 1972;8:818.
   Google Scholar
• Novikov EA, Stewart RW. Intermittency of turbulence and the spectrum of energy dissipation fluctuations. Izv Acad Sci USSR Geophys Ser. 1964;3:408.
   Google Scholar
• Kadanoff LP. Scaling laws for Ising models near Tc. Physics. 1966;2:263.
   Google Scholar
• Mandelbrot B B. Self-similar error clusters in communication systems and the concept of conditional stationarity. IEEE Trans Commun Technol. 1965;13:71.
   Google Scholar
• Konopelchenko BG, Ortenzi G. On universality of homogeneous Euler equation. J Phys A Math. Theor. 2021;54:205701, doi:10.1088/1751-8121/abf586.
   Web of Science ®Google Scholar
• Glasner A, Livne E, Meerson B. Vorticity generation in slow cooling flows. Phys Rev Lett. 1997;78:2112.
   Web of Science ®Google Scholar
• Antonia RA, Chambers AJ, Satyaprakash BR. Reynolds number dependence of high-order moments of the streamwise turbulent velocity derivative. Boundary Layer Meteorol. 1981;21:159, doi:10.1007/BF02033934.
   Web of Science ®Google Scholar
• Antonia RA, Satyaprakash BR, Chambers AJ. Reynolds number dependence of velocity structure functions in turbulent shear flows. Phys Fluids. 1982;25:29, doi:10.1063/1.863624.
   Web of Science ®Google Scholar
• Anselmet F, Gagne Y, Hopfinger EJ, et al. High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 1984;140:63, doi:10.1017/S0022112084000513.
   Web of Science ®Google Scholar
• Antonia RA, Djenid L, Danaila L, et al. Small scale turbulence and the finite Reynolds number effect. Phys Fluids. 2017;29:020715, doi:10.1063/1.4974323.
   Web of Science ®Google Scholar
• Chefranov SG, Chefranov AS. Hydrodynamic method and exact solutions in application to the electromagnetic field theory in medium. In: Lembrikov B, editor. Nonlinear optics- novel results in theory and applications. IntechOpen; 2018. doi:10.5772/intechopen.80813
   Google Scholar
• Fairlie DB. Equations of hydrodynamic type. www.arxiv.org/hep-th/9305049v1 12 May 1993.
   Google Scholar
• Fairlie DB. Integrable systems in higher dimensions. Prog Theor Phys Suppl. 1995;118:309–327. doi:10.1143/PTPS.118.309.
   Google Scholar
• Takenchi KA. An appetizer to modern development on the Kardar-Parisi-Zhang universality class. Physics A. 2018;504:77–105. doi:10.1016/j.physa.2018.03.009.
   Web of Science ®Google Scholar
• Ezra GS. On the statistical mechanics of non-Hamiltonian systems: the generalized Liouville equation, entropy, and time-dependent metrics. J Math Chem. 2004;35:29.
   Web of Science ®Google Scholar