Turbulence is everywhere around us. It arises whenever a fluid is stirred by some external mechanism (mechanical, thermal, magnetic,..) and there is a large separation of spatial scales between the typical scale of the forcing and the scale at which kinetic energy is transformed into heat, by molecular viscosity. The most ideal case is a statistically stationary, Homogeneous and Isotropic Turbulent (HIT) flow. Yet this is the central problem in turbulence, whose understanding would impact a large variety of applications, from geophysics to engineering. The main deadlock of HIT is unanimously recognized to be the strong non-Gaussian statistics (intermittent) developing at smaller and smaller scales. Still, we do not know what are the physical, kinematical and topological ingredients leading to intermittency in HIT. Moreover, we do not know what is the role played by the inviscid quadratic invariants, Energy and Helicity; we ignore what are the necessary -and sufficient-- degrees of freedom needed to develop (or to kill) intermittency; we do not understand if the entangled population of small-scales vortex filaments is important or not to determine turbulent statistical properties in the bulk volume. Turbulence is also considered one of the most challenging problems for extreme computations, a paradigmatic problem for peta-, exa- and even yotta-scale HPC. This project aims to implement numerically a novel theoretical tool to investigate the key questions raised above. In particular, we intend to apply a decimation of the Navier-Stokes equations dynamics on a Fractal-Fourier set, in order to understand the dependence of small-scales intermittency on the number of degrees of freedom involved in the energy cascade. Such question has never been asked before using this promising methodology. What is absolutely remarkable is that such questions can be asked only in-silico, by performing state-of-the-art direct numerical simulations at high Reynolds and at changing the embedding Fractal dimension in the Fourier space. We are going to use numerical simulations in a most innovative way, investigating nature with tools unavailable in the labs.
Eulerian and Lagrangian Turbulence over a Reduced Fractal Skeleton
A S Lanotte
2013
Abstract
Turbulence is everywhere around us. It arises whenever a fluid is stirred by some external mechanism (mechanical, thermal, magnetic,..) and there is a large separation of spatial scales between the typical scale of the forcing and the scale at which kinetic energy is transformed into heat, by molecular viscosity. The most ideal case is a statistically stationary, Homogeneous and Isotropic Turbulent (HIT) flow. Yet this is the central problem in turbulence, whose understanding would impact a large variety of applications, from geophysics to engineering. The main deadlock of HIT is unanimously recognized to be the strong non-Gaussian statistics (intermittent) developing at smaller and smaller scales. Still, we do not know what are the physical, kinematical and topological ingredients leading to intermittency in HIT. Moreover, we do not know what is the role played by the inviscid quadratic invariants, Energy and Helicity; we ignore what are the necessary -and sufficient-- degrees of freedom needed to develop (or to kill) intermittency; we do not understand if the entangled population of small-scales vortex filaments is important or not to determine turbulent statistical properties in the bulk volume. Turbulence is also considered one of the most challenging problems for extreme computations, a paradigmatic problem for peta-, exa- and even yotta-scale HPC. This project aims to implement numerically a novel theoretical tool to investigate the key questions raised above. In particular, we intend to apply a decimation of the Navier-Stokes equations dynamics on a Fractal-Fourier set, in order to understand the dependence of small-scales intermittency on the number of degrees of freedom involved in the energy cascade. Such question has never been asked before using this promising methodology. What is absolutely remarkable is that such questions can be asked only in-silico, by performing state-of-the-art direct numerical simulations at high Reynolds and at changing the embedding Fractal dimension in the Fourier space. We are going to use numerical simulations in a most innovative way, investigating nature with tools unavailable in the labs.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
