Introducing GeoFLOW: Single point statistics in decaying multidimensional Burgers turbulence

We introduce the GeoFLuid Object Workbench (GeoFLOW) computational framework by considering high order numerical solutions to the multi-dimensional Burgers (generalized nonlinear advection-diffusion) equation. The Burgers equation is chosen to highlight the required computational elements and complexity of nearly all parallel continuum geophysics fluid solvers. We present important aspects of the framework's object-oriented design and numerical algorithms that will be leveraged in future solvers for atmospheric and oceanic applications. Results will be shown for single point statistical properties of decaying Burgers turbulence as a function of Reynolds number on the two-dimensional plane and sphere. Comparisons with well-known one-dimensional results will be made which will help establish this work as a basis for an investigation of atmospheric and oceanic turbulent boundary (Ekman) layers.