Oceanic Internal Wave Field Theory of Scale-invariant Spectra.pdf

Oceanic Internal Wave Field: Theory of Scale-invariant Spectra Yuri V. Lvov Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180 USA Kurt L. Polzin Woods Hole Oceanographic Institution, MS#21, Woods Hole, MA 02543 USA Esteban G. Tabak Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA Naoto Yokoyama Department of Mechanical Engineering, Doshisha University, Kyotanabe, Kyoto 610-0394 Japan∗ 8 (Dated: July 10, 2008) 0 Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal 0 gravity waves based on wave turbulence theory are investigated. It is shown that the scale-invariant 2 collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These l divergences come from resonant interactions with infra-red and/or ultra-violet wavenumbers with u J extreme scale-separations. We identify a small domain in which the scale-invariant collision integral converges and numer- 0 ically find a convergent power-law solution. This numerical solution is close to the Garrett–Munk 1 spectrum. Power-law exponents which potentially permit a balance between the infra