The Second Monte Verita Colloquium Fundamental Problematic Issues in Turbu­ lence was held in Monte Verita, Switzerland, on March 23-27, 1998. The main goal of the Colloquium was to bring together in the relaxed atmo­ sphere of Monte Verita a group of leading scientists (consisting of representatives of different generations) and to discuss informally and free of the influence of funding agencies and/or other "politics" of nonscientific nature the basic issues of turbulence. The intention was to put major emphasis on the exposition of the problematic aspects and discussion(s) - not mere reporting of results, i. e. not hav­ ing just one more meeting. For this purpose it was originally thought to leave all the afternoons free of formal presentations at all. However, this intention became unrealistic due to a number of reasons, and, in the first place, due to strong pres­ sure from various parts of the scientific community and non-scientific constraints to broaden the scope and to increase the number of participants as compared to the First Colloquium held in 1991. This resulted in a considerable reduction of time for discussions. Nevertheless, the remaining time for discussions was much larger than usually allocated at scientific conferences. On the scientific side the main idea was to bring together scientists work­ ing in turbulence from different fields, such as mathematics, physics, engineering and others. In this respect the Colloquium was definitely very successful and re­ sulted in a number of interesting interactions and contacts.

1 Mathematical issues.- Does turbulence saturate global transport estimates?.- The closure problem for Friedman-Keller infinite chain of moment equations, corresponding to the Navier-Stokes system.- Vorticity alignment results for the 3D Euler and Navier-Stokes equations.- On the finite-time singularity problem in hydrodynamics.- The outer regions in singular Euler.- 2 Control and related.- On controllability of the Navier-Stokes equations.- Low dimensional models, the minimal flow unit and control.- Active control of turbulence in boundary layer flows.- Origin and growth of structures in boundary layer flows.- Vortex control in a spatially growing round jet.- 3 Observational aspects.- The lack of a simple paradigm in fully developed turbulence: characteristics of local concentrations of vorticity and Reynolds stress in turbulent shear flows.- Near-singular flow structure in small-scale turbulence.- Some thoughts on similarity, the POD, and finite boundaries.- Worms in a turbulence experiment, from hot wire time series.- Intermittency in the closed flow between coaxial disks.- 4 Two- and quasi-two-dimensional flows.- Turbulent statistical dynamics of a system of point vortices.- Combining deterministic and statistical approaches to compute two-dimensional turbulent flows with walls.- Evolution of decaying two-dimensional turbulence and self-similarity.- Linear and nonlinear models for turbulence in the presence of waves.- On the stationary energy spectra of the stratified fluid in a weak turbulence regime.- On a possible mechanism of anomalous diffusion in geophysical turbulence.- 5 Basic aspects of turbulence modelling.- Basic issues of turbulence modeling.- Physics and modeling of small scale turbulence for large eddy simulation.- On dynamical systems obtained via Galerkin projections onto low-dimensional bases of eigenfunctions.- Symmetries of the Navier-Stokes equations and their implications for subgrid-models in large-eddy simulation of turbulence.- Subgrid modeling for the filtered scalar transport equation.- 6 Statistical aspects.- Turbulent fluctuations, predictability, and action principles.- Instantons in the theory of turbulence.- A variational approach to turbulent boundary layers.- Scaling laws of a passive scalar energy flux in fully developed turbulence.- Intermittency in channel-flow turbulence.- Structure functions in homogeneous and non-homogeneous turbulent flows.- Pressure fluctuations in a turbulent channel.- Statistics of longitudinal and transverse velocity increments.- Turbulent transport in a liquid layer heated on its free surface.- On the statistics of small-scale turbulence and its universality.- A new method to characterize inhomogeneous turbulence.- Multiscale similarity of isotropic homogeneous turbulence.- 7 Passive objects.- The role of Lagrangian chaos in the creation of multifractal measures.- On the geometry of two-dimensional slices of irregular level sets in turbulent flows.- Universal and nonuniversal properties of the passive scalar statistics.- Multi-scalar mixing and Lagrangian approaches.- Turbulent transport of vector (magnetic) field: intermittency and anomalous scalings.- Intermittency and anomalous scalings of inertial particles distribution in turbulent flow.- Scalar fluctuation PDF's and kinetics of turbulent mixing.- Magnetohydrodynamics in turbulent swirling flow.- List oficipants and authors.