We study precessing turbulence, which appears in several geophysical and astrophysical systems, by direct numerical simulations of homogeneous turbulence where precessional instability is triggered due to the imposed background flow. We show that the time development of kinetic energy K occurs in two main phases associated with different flow topologies: (i) an exponential growth characterizing three-dimensional turbulence dynamics and (ii) nonlinear saturation during which K remains almost time independent, the flow becoming quasi-two-dimensional. The latter stage, wherein the development of K remains insensitive to the initial state, shares an important common feature with other quasi-two-dimensional rotating flows such as rotating Rayleigh-Bénard convection, or the large atmospheric scales: in the plane k_{∥}=0, i.e., the plane associated to an infinite wavelength in the direction parallel to the principal rotation axis, the kinetic energy spectrum scales as k_{⊥}^{-3}. We show that this power law is observed for wave numbers ranging between the Zeman "precessional" and "rotational" scales, k_{S}^{-1} and k_{Ω}^{-1}, respectively, at which the associated background shear or inertial timescales are equal to the eddy turnover time. In addition, an inverse cascade develops for (k_{⊥},k)

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Copyright

This paper presents a method for identifying a cluster of small blockages (i.e., blockages with length on the order of centimeters and radial extent on the order of millimeters and separated by a distance on the order of few centimeters) in pressurized fluid-filled pipes using sound waves. This focus on defects with small scale, and, thus, small scattering strength is exploited to develop a Neumann series solution for the scattered acoustic wave field. The probing waves are such that the Helmholtz number (ratio of blockage longitudinal length scale and probing acoustic wavelength) is of order 1 or larger. A high resolution inverse technique for identifying a cluster of small blockages based on the maximum likelihood estimation principle is developed. The proposed technique uses two-dimensional search space to resolve each blockage in the cluster and requires a single measurement point only. The method is successfully tested through both numerical and laboratory experiments. The proposed methodology allows an early identification of a cluster of small defects and leads to reliable condition assessment of pipelines, which is necessary to inform decisions as to when remedial actions are required.