Stochastic Approaches to Turbulence in Hydrodynamical Equations (22w5015)

The Banff International Research Station will host the "Stochastic Approaches to Turbulence in Hydrodynamical Equations: New Challenges at the Mathematics-Physics Interface" workshop in Banff from February 27 to March 4, 2022.

The interest in turbulent flow goes back many centuries, but progress has been slow until recently, from the point of view of ab initio theory, which starts from the Euler or Navier–Stokes equations for a fluid. Since the 20th century, innumerable applications, e.g., in aeronautics or atmospheric and oceanic circulation, have been a major driving force for progress. In the last eighty years, thanks (a) to the scaling predictions of Kolmogorov in 1941, (b) to Onsager’s 1949 criterion for anomalous energy dissipation, and (c) to Kraichnan’s discovery of the inverse energy cascade for 2D turbulence, we have had the beginnings of a theoretical understanding.

The workshop brings together leading researchers from diverse branches of the theory of turbulence. We will discuss ways of developing a theoretical understanding of turbulence in stochastically forced hydrodynamical equations by using variants of the theories of spontaneous stochasticity and of rough paths, and regularity structures and state-of-the-art numerical simulations. We hope that cross-fertilization of ideas between these areas will foster new collaborations and lead to new developments, in mathematical, physical, and numerical aspects of problems in turbulence.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).