Fluid dynamics on logarithmic lattices

Open problems in fluid dynamics, such as the existence of finite-time singularities (blowup), explanation intermittency developed turbulence, etc., are related to multi-scale structure and symmetries underlying equations motion. Significantly simplified motion, called toy-models, traditionally employed analysis complex systems. In models, modified preserving just a part believed be important. Here we propose different approach for constructing which instead simplifying one introduces configuration space: velocity fields defined on multi-dimensional logarithmic lattices with proper algebraic operations calculus. Then, motion retain their exact original form and, therefore, naturally maintain most scaling properties, invariants Classification models reveals fascinating relation renowned mathematical constants golden mean plastic number. Using both rigorous numerical analysis, describe various properties solutions these from basic concepts uniqueness blowup development turbulent dynamics. particular, observe strong robustness chaotic scenario three-dimensional incompressible Euler equations, well Fourier mode statistics turbulence resembling full Navier-Stokes system.