{'fraction_non_alphanumeric': 0.01898047722342733, 'fraction_numerical': 0.0021691973969631237, 'mean_word_length': 5.428571428571429, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Comparison of Lorenz and Charney–Phillips vertical discretisations for dynamics–boundary layer coupling. Part II: Transients

A numerical comparison of the Lorenz and Charney–Phillips vertical grids for capturing the steady state of a set of equations that models the large‐scale dynamics of the atmosphere and the planetary boundary layer (Part I of this article) has revealed important differences between the grids. Due to suppression of a negative feedback, Charney–Phillips grids that involve averaging of shear in the boundary‐layer terms are not able to capture the structure of the boundary layer accurately. The Lorenz grid performs well in terms of capturing the boundary layer on its own, but the Charney–Phillips grids that use averaging of potential temperature gradient are generally preferred once dynamics are included. Any finite‐difference approximation of the problem must be capable of accurately representing both the steady‐state and time‐dependent parts of the solution. In this Part II of the article, the ability of the Lorenz and Charney–Phillips configurations to capture the transient part of the system is considered. The configurations are compared in terms of their ability to capture the eigenmodes of the solution. Full comparison between Lorenz and Charney–Phillips grids is limited by non‐normality of the linearised system, associated with the boundary layer. The Lorenz grid computational mode is examined. The structure is modified by the boundary layer but it still exists. For the modes that could be accurately examined, it is found that both grids perform well in terms of capturing spatial and temporal mode structure. Some Lorenz grid modes are identified that have spurious computational mode‐like behaviour occurring near the top of the boundary layer. Copyright © 2012 Royal Meteorological Society