Quasi Two dimensional Compressible Turbulence

Quasi Two Dimensional Compressible TurbulenceApplication no. 2018118Michael Mond - Ben-Gurion UniversityAlexei Kritsuk - University of California San Diego - La JollaAbstractTurbulence is a ow regime that is characterised by chaotic motion of the uid as well as by chaotic changes inthe uid properties like the pressure. Turbulence is ubiquitous in nature and occurs on a wide range of scales,from smoke coming out of chimneys to the turbulent rotations of galaxies. Turbulent ow develops from alaminar one in which the ow is arranged in orderly layers that do not mix with one another. Turbulent owsare ubiquitous in Nature and play a major role in the dynamical development of a wide range of astrophysicalobjects. Two dimensional turbulence is particularly intriguing as it gives rise to the self organisation ofvortices to produce coherent large-scale structures and motions. Two dimensional ows and turbulence aregood approximations to a great variety of uid ows encountered in nature, from the terrestrial atmosphereas viewed on planetary scale to accretion disks around black holes. Most eorts has been devote over the lastdecades to understanding the complexities of incompressible turbulent. In such ows, the amplitude of theuctuating velocity is much smaller than the local sound speed. In many occasions though this assumption isnot valid and the velocity uctuations may be as high as 100 times the local sound speed. In such cases theturbulent ow is fundamentally dierent from its incompressible counterpart. In particular, as in the latterthe mass density distribution is essentially uniform, in the former case the mass density settles on complexstructures that have fractal an multifractal dimensions. Another example is the amplication of magnetic eldby two dimensional compressible turbulence, a process that is prohibited in its incompressible counterpart.

The proposed research is expected to have a signicant impact on the understanding of the subtleties andcomplexities of two dimensional compressible turbulence, and thus shedding light on various astrophysicalphenomena and processes. Its impact however is expected to reach beyond the original astrophysical goalsand contribute to such technological applications as supersonic combustion and mixing.