Polynomial sum of squares in fluid dynamics: a review with a look ahead.

The first part of this paper reviews the application of the sum-of-squares-of-polynomials technique to the problem of global stability of fluid flows. It describes the known approaches and the latest results, in particular, obtaining for a version of the rotating Couette flow a better stability range than the range given by the classic energy stability method. The second part of this paper describes new results and ideas, including a new method of obtaining bounds for time-averaged flow parameters illustrated with a model problem and a method of obtaining approximate bounds that are insensitive to unstable steady states and periodic orbits. It is proposed to use the bound on the energy dissipation rate as the cost functional in the design of flow control aimed at reducing turbulent drag.

Streaks and vortices in near-wall turbulence.

This paper presents evidence that organization of wall-normal motions plays almost no role in the creation of streaks. This evidence consists of the theory of streak generation not requiring the existence of organized vortices, extensive quantitative comparisons between the theory and direct numerical simulations, including examples of large variation in average spacing of the streaks of different scalars simultaneously present in the flow, and an example of the scalar streaks in an artificially created purely random flow.