Multiscale Analysis and Modelling of the Roughness Sublayer over Obstacle Arrays
對於障礙物邊界層內層湍流的多尺度分析與模擬
Student thesis: Doctoral Thesis
Author(s)
Related Research Unit(s)
Detail(s)
Awarding Institution | |
---|---|
Supervisors/Advisors |
|
Award date | 2 Sept 2022 |
Link(s)
Permanent Link | https://scholars.cityu.edu.hk/en/theses/theses(01a7e430-114a-422e-a98c-74902f0732a3).html |
---|---|
Other link(s) | Links |
Abstract
The turbulent flow over obstacle array is prototypical rough-wall turbulence that has received considerable attention for its application in urban flows. However, despite the flow involving a wide range of interscale interactions, the fundamental turbulence properties, like energy production, transfer and interscale transfer, are rarely studied in the spectral space. In this thesis, we introduce the wavelet method, which has space-scale bases, for the spectral analysis of turbulence over various obstacle arrays. The results are used to discuss possible implications in mesoscale subgrid-scale (SGS) modelling.
First, we examine the application of the orthogonal wavelets to turbulence statistics within the square and staggered arrays. For flow motions larger than the canyon scale, the turbulent kinetic energy (TKE) spectra are obtained by expanding the definition of the scale to include both obstacles and fluid. While the inertial sub-range indicated by the –5/3 slope is observed within both arrays, the energy spectra peaks depend on the array type. For smaller scales, the spatial distribution and intermittency for the energy and transfer are compared for different flow regions formed by repeating units, revealing the strongest small-scale energy for the most refined units R1,7 and the maximum energy extraction for R1.
Second, we investigate the scale dependence of TKE budget terms for the square and staggered cases and contrast the results with smooth-wall turbulence. The staggered array introduces a stronger influence on the turbulence production and transfer, showing a greater increase in peak scale and magnitude from below the roof level to above. The decomposed production spectra show that energy production is maximized at the obstacle geometry scales. The spatial distribution of the decomposed production shows that energy production is exhibited at the interfaces of the most refined repeating units, where the local strain is maximized. Above the canopy, the flow motions larger than the canyon scale provide the majority of (~80%) production and transfer. Moreover, for cut-off scales smaller than the canyon scale, the subfilter-scale (SFS) transfer is the strongest at scales larger than the cut-off scale, suggesting a non-local energy cascade.
Third, the sensitivity of small-scale motions to flow configurations is examined. For rough boundary layers with different obstacle layouts, obstacle heights and wind directions, the small-scale motions are filtered by the space-scale filter. The energy contribution from subfilter motions is examined along the vertical direction, and the vertical profiles show maximum decays at the greatest obstacle height. The subfilter-scale transfer and TKE define the effective eddy viscosity for subfilter-scale motions in the wavelet space. The vertical distribution of effective eddy viscosity indicates the importance of modelling roughness sublayer, especially around the roof level. The probability density functions of effective eddy viscosity reveal a non-negligible amount of negative eddy viscosity commonly omitted in subgrid-scale modelling.
Last, we introduce the roughness eddy viscosity to account for unresolved dynamic effects for the roughness sublayer in the mesoscale meteorological simulation. Using the Weather Research and Forecasting (WRF) model, different SGS viscosity models, which are formulated by the vertical dependence and statistic distribution of the wavelet eddy viscosity, are applied to the urban area to account for the unsolved urban dynamic effects. The application of spatial-dependent eddy viscosity introduces vertical-dependent changes in the velocity field.
This study shows that the wavelet presentation can be a powerful tool for rough-wall turbulence and shows that the TKE budget is related to the obstacle geometries scales inside the canopy layer. The sensitivity analysis of subfilter-scale motions shows promising properties for the SGS turbulence modelling.
First, we examine the application of the orthogonal wavelets to turbulence statistics within the square and staggered arrays. For flow motions larger than the canyon scale, the turbulent kinetic energy (TKE) spectra are obtained by expanding the definition of the scale to include both obstacles and fluid. While the inertial sub-range indicated by the –5/3 slope is observed within both arrays, the energy spectra peaks depend on the array type. For smaller scales, the spatial distribution and intermittency for the energy and transfer are compared for different flow regions formed by repeating units, revealing the strongest small-scale energy for the most refined units R1,7 and the maximum energy extraction for R1.
Second, we investigate the scale dependence of TKE budget terms for the square and staggered cases and contrast the results with smooth-wall turbulence. The staggered array introduces a stronger influence on the turbulence production and transfer, showing a greater increase in peak scale and magnitude from below the roof level to above. The decomposed production spectra show that energy production is maximized at the obstacle geometry scales. The spatial distribution of the decomposed production shows that energy production is exhibited at the interfaces of the most refined repeating units, where the local strain is maximized. Above the canopy, the flow motions larger than the canyon scale provide the majority of (~80%) production and transfer. Moreover, for cut-off scales smaller than the canyon scale, the subfilter-scale (SFS) transfer is the strongest at scales larger than the cut-off scale, suggesting a non-local energy cascade.
Third, the sensitivity of small-scale motions to flow configurations is examined. For rough boundary layers with different obstacle layouts, obstacle heights and wind directions, the small-scale motions are filtered by the space-scale filter. The energy contribution from subfilter motions is examined along the vertical direction, and the vertical profiles show maximum decays at the greatest obstacle height. The subfilter-scale transfer and TKE define the effective eddy viscosity for subfilter-scale motions in the wavelet space. The vertical distribution of effective eddy viscosity indicates the importance of modelling roughness sublayer, especially around the roof level. The probability density functions of effective eddy viscosity reveal a non-negligible amount of negative eddy viscosity commonly omitted in subgrid-scale modelling.
Last, we introduce the roughness eddy viscosity to account for unresolved dynamic effects for the roughness sublayer in the mesoscale meteorological simulation. Using the Weather Research and Forecasting (WRF) model, different SGS viscosity models, which are formulated by the vertical dependence and statistic distribution of the wavelet eddy viscosity, are applied to the urban area to account for the unsolved urban dynamic effects. The application of spatial-dependent eddy viscosity introduces vertical-dependent changes in the velocity field.
This study shows that the wavelet presentation can be a powerful tool for rough-wall turbulence and shows that the TKE budget is related to the obstacle geometries scales inside the canopy layer. The sensitivity analysis of subfilter-scale motions shows promising properties for the SGS turbulence modelling.