1. Wavelet estimation of coherent modes in turbulence; 2. Development of spectral-element and finite-volume methods; 3. Other research

Wavelet analysis is now a method of well recognized effectiveness in a range of disciplines, including atmospheric science e.g., 39 publications from NCAR from [10] to [11]. Our recent research includes applying a wavelet-based criterion to identify coherent structures in turbulence simulations, §2.1. Also, as detailed in recent reports [6 §1; 7; 8 & op. cit. therein], a need is well known and pursued at NCAR and elsewhere, to create high-resolution numerical simulation methods for atmospheric dynamics, that are accurate similarly to spectral methods and efficient similarly to finite-element type methods. A research code that demonstrates the strengths of the spectral-element method (SEM) with dynamic-nonconforming adaptive mesh refinement (AMR) is the geophysical-astrophysical spectral-element adaptive refinement (GASpAR) code (§§2.2, 2.3) [18, 19]. Especially for long-time, potentially parameter-sensitive simulations such as climate, spatial discretizations should accurately validate physical conservation laws such as mass and energy; this motivates another part of our research (§§2.3, 2.4). ∗[email protected], http://www.image.ucar.edu/ ̃fournier/ †Sponsored by the NSF cooperative agreement through UCAR