Streamwise roll circulations commonly observed in frontal regions are primary agents of momentum and tracer transport in the planetary boundary layer (PBL) both in the atmosphere and ocean. Traditionally, the formation of the streamwise roll/streak structure (RSS) has been ascribed to symmetric instability (SI). In part 1, we studied RSS formation in the classical Eady front problem using statistical state dynamics (SSD), which allows incorporating the Reynolds stress (RS) torque instability mechanism together with SI in the dynamics underlying RSS formation. We found using SSD theory that the RS torque mechanism acts synergistically with the SI mechanism in forcing symmetric circulations in fronts when Richardson number Ri < 1, and also that the turbulence-mediated RS torque mechanism supports RSS formation in fronts with Ri > 1 for which the SI mechanism does not operate. Although SI theory provides an explanation for initial roll formation, it leaves open the question of RSS equilibration. An advantage of the SSD formulation of RSS dynamics is that it consistently incorporates the equilibration process. In this paper, we extend perturbation analysis of RSS dynamics in the SSD framework to a nonlinear analysis to understand roll formation, equilibration, and maintenance in the turbulent RSS regime.
Passive scalar cascade in the intermediate layer of turbulent channel flow for $Pr\leq 1$
Univ. Lille（里尔大学）；CNRS（法国国家科学研究中心）；ONERA（法国航空航天研究院）；Arts et Metiers Institute of Technology（巴黎高科国立高等工艺学院）；Centrale Lille（里尔中央理工学院）；Graduate School of Engineering Science, University of Osaka（大阪大学工学研究科）
Statistical equilibria of two-dimensional turbulent flows for generic initial vorticity fields on a sphere, calculated on the basis of the original Miller-Robert-Sommeria theory
Research Institute for Applied Mechanics, Kyushu University（九州大学应用力学研究所）；Graduate School of Science, Kyoto University（京都大学理学研究科）
Vertically Sheared Horizontal Flow-Forming Instability in Stratified Turbulence: Analytical Linear Stability Analysis of Statistical State Dynamics Equilibria
