Large eddy simulation of turbulent boundary layers over rough bathymetry

Numerical modeling of turbulent boundary layers over regular roughness such as square ribs and monochromatic sinusoids has been an important focal area for some time. Extremely irregular roughness such as coral reefs in oceanic boundary layers and urban canopies in atmospheric boundary layers are only beginning to attract the attention of numerical and experimental researchers. The response of the boundary layer to roughness, summarized in terms of flow characteristics such as roughness length, zo, can be parameterized in terms of the physical length scales of the bed. The difficulty arises in the case of broadbanded and highly irregular roughness distributions where the length scales that determine the response of the boundary layer are not clear. Thus, a primary objective for this work is to identify physical scales of broad-banded roughness that determine the hydrodynamic response to the rough wall.;One method to characterize the irregular nature of roughness is through the use of a spectral distribution. In order to establish the relationship between the spectral slope and the hydrodynamic characteristics of the boundary layer, a variety of rough beds with different spectral slopes are generated using 2D square waves as basis functions. These waves can reproduce flow separation characteristics common to flow over rough beds. Large Eddy Simulation (LES) is then used to simulate the turbulent boundary layer over the rough beds. The LES solver is first validated with laboratory experiments on k type square ribs. A grid convergence study is undertaken to ascertain the accuracy of results from the irregular bed. The results indicate that there is only a weak relationship between the spectral slope and the response of the flow. However the study identifies the mean cavity aspect ratio of the rough walls as a robust parameter that determines the location of the hydrodynamic origin and roughness length, from which the drag of the wall can be predicted. The concept of a hydrodynamic bottom is introduced which enables classification of irregular walls into k- and d-type walls. The study further shows that the lower wavenumber region of the roughness spectrum has a greater influence on the hydrodynamic characteristics.