A treatment of three dimensional incompressible turbulence

• Published in: Astrophysics and space science Vol. 89; no. 1; pp. 229 - 232
• Main Authors: Vithal, K. L., Vats, R. P.
• Format: Journal Article
• Language: English
• Published: 1983
• ISSN: 0004-640X; 1572-946X
• DOI: 10.1007/BF01008399

Reference is made to the statistical study of the incompressible hydrodynamical turbulence without any mean motion that was carried out using the one-dimensional Burgers equation (Vithal and Vats, 1983). This resulted in an explicit proof of the existence of the 'cascade process' in turbulence, thus explaining the maintenance of atmospheric turbulence during a long period, even after the withdrawal of the external energy supply from solar radiations. In practice, however, it is necessary to deal with three-dimensional phenomena. The analysis is therefore extended here to a three-dimensional incompressible model, and it is shown that a cascade process also occurs in this system.