Supervisor's Foreword; Parts of this thesis have been published in the following journal articles: ; Acknowledgments; Contents; Symbols and Abbreviations; Persons Mentioned in This Work; Part I Preliminaries; 1 Introduction; 1.1 Turbulence Regimes; 1.2 Global Intermittency; 1.3 Approaches to Studying the Stable Boundary Layer; 1.4 Research Proposition; References; 2 Problem Formulation and Tools; 2.1 The Governing Equations; 2.2 Non-dimensionalization and Parameter Space; 2.2.1 The Neutrally Stratified Regime; 2.2.2 Uniqueness of the Solution

2.2.3 Imposing Stratification: Initial and Boundary Conditions2.2.4 Parameter Space of the Non-dimensionalized Problem; 2.3 Analysis Tools; 2.3.1 Conditional Sampling; 2.3.2 Temporally Resolved Probes; 2.4 Summary; References; Part II Numerics; 3 Discretization; 3.1 The Pressure Problem; 3.2 Spatial Discretization; 3.3 Time Stepping Schemes; 3.3.1 Explicit Runge
Kutta Schemes; 3.3.2 Semi-implicit Runge
Kutta Schemes; 3.3.3 Multi-level Schemes and Other Methods; 3.3.4 Choice of a Method; 3.4 Stability of the SIRK3 Scheme; 3.5 Implementation of the SIRK3 Scheme

3.5.1 Rotation of the Grid: Equations Solved by the DNS3.5.2 Buffer Zone; 3.5.3 Discretization in the Interior of the Domain; 3.5.4 Dirichlet Boundary Conditions for the Semi-implicit Solver; 3.5.5 Integration of a Scalar Variable; 3.5.6 Description of the Implementation; References; 4 Overlapping Communication and Computation; 4.1 Motivation
A Rough Estimate of the Computational Demand; 4.1.1 Memory Demand; 4.1.2 Computational Demand; 4.1.3 The Link Between Spatial Discretization and Communication; 4.2 Approach and Implementation; 4.2.1 Why Overlap Communication and Computation?

4.2.2 Design of the NB3DFFT Library4.2.3 Re-Organization of the Algorithm; 4.3 Performance Measurements; 4.3.1 Performance Metrics: Strong and Weak Scaling; 4.3.2 Performance on the Supercomputer juqueen; References; 5 A Test Bed for the Numerical Tool; 5.1 Behavior of the Semi-implicit Scheme When Solving a Non-linear ODE; 5.2 Analytical Solution of Ekman Flow; 5.2.1 The Stationary Laminar Solution; 5.2.2 Temporally Evolving Solution; 5.2.3 Convergence of the Errors; 5.3 Two-Dimensional Taylor
Green Vortex; 5.4 Three-Dimensional Turbulent Ekman Layer; References; Part III Physics

6 The Neutrally Stratified Ekman Layer6.1 Conventional Statistics; 6.1.1 Global Measures; 6.1.2 Vertical Profiles; 6.2 Local Versus Ensemble Statistics; 6.2.1 Data Analysis Procedure; 6.2.2 Convergence of local estimates to the ensemble mean; 6.3 External Intermittency and Its Impact in the Surface Layer; 6.3.1 Definition of external intermittency; 6.3.2 A Vorticity Source in the Outer Layer; 6.3.3 A Modified Logarithmic Law for the Mean Velocity; 6.4 Flow Synopsis; 6.5 Summary; References; 7 Turbulence Regimes and Stability; 7.1 Initial Conditions and Time Scales Under Stable Stratification