Large-eddy simulation of the atmospheric boundary layer: Influence of unsteady forcing, baroclinicity, inversion strength and stability on the wind profile

De største vindmøller i dag når ofte højder, hvor traditionelle modeller for vindhastigheden og dens højdeafhængighed ikke længere kan forventes at gælde. Nøjagtig vurdering af vindenergi-ressourcer og belastninger på vindmøller kræver bedre forståelse af vinden over luftlaget nærmest jordoverfladen (overfladelaget). Kontinuerlige og detaljerede målinger af middelvind og turbulens i sådanne højder er bekostelige og vanskelige at udføre. Computer-simulering af atmosfæriske luftstrømme kan være et attraktivt alternativ eller supplement til virkelige fuldskala eksperimenter.Metoden ”large eddy simulation” (LES) bruges her til at opnå en bedre forståelse af luftstrømmen i det atmosfæriske grænselag. Den primære motivation er at muliggøre forbedring af eksisterende modeller for vindhastigheden over overfladelaget. Den potentielle brug af LES direkte i forbindelse med eksempelvis forudsigelse på kort sigt af vind og turbulens i og omkring vindmølleparker bliver imidlertid også taget i betragtning. To simuleringseksempler baseret på målinger fra et fladt landbrugsområde ved Høvsøre i Danmark og et bebygget område uden for den centrale del af Hamborg i Tyskland viser nødvendigheden af nøjagtig specifikation af den trykgradient, der driver vinden, når LES bruges til forudsigelse af vindprofiler i den virkelige verden. Høvsøre-eksemplet viser god overensstemmelse mellem simulerede og målte vindhastigheder gennem hele det atmosfæriske grænselag, men kun når den påførte kraft følger en højde- og tidsafhængig trykgradient bestemt på grundlag af kontinuerlige LIDAR målinger af vindhastigheden over det atmosfæriske grænselag. Inkludering af trykgradientens tidsafhængighed og baroklinitet (udtryk for en horisontal temperaturgradient) forbedrer også overensstemmelsen mellem målinger og simulering i Hamborg-eksemplet, men ikke ligeså entydigt som i Høvsøre-eksemplet. Det konkluderes at de tilgængelige målinger ikke er tilstrækkelige til nøjagtig bestemmelse af trykgradienten, og at fænomener så som synkende luftmasser og stor-skala advektion også bør inkluderes i simuleringer, hvor målet er at opnå overensstemmelse med målte vindprofiler.En række simuleringer af i højere grad idealiserede forhold er blevet udført med henblik på at undersøge indflydelsen af Brunt Vaisala frekvensen (udtryk for en vertikal temperaturgradient) i den fri atmosfære og baroklinitet på udviklingen og ligevægtstilstanden af neutrale og nær-neutrale atmosfæriske grænselag. En justeringstid på mindst 16 timer findes nødvendig for at opnå en tilnærmelsesvis ligevægtstilstand. De meget idealiserede forhold tillader udviklingen af et lag nær toppen af det atmosfæriske grænselag, hvori vindhastigheden overstiger hastigheden af geostrofvinden. Dette antages at være et sjældent fænomen i den virkelige verden, og der bliver ikke taget højde for det i de modeller af vindhastighedens vertikale gradient, som er inkluderet i denne undersøgelse. Det vises at den vindprofil-model, som indgår i undersøgelsen, kan forbedres ved på passende vis at inkludere den højdeafhængighed af vinden som stammer fra Brunt Vaisala frekvensen i den fri atmosfære og baroklinitet.The largest wind turbines today often reach heights where traditional models of the wind speed and how it varies with height no longer can be expected to apply. For accurate assessment of wind energy resources and loads on wind turbines, there is a need for better understanding of the flow of air above the atmospheric surface layer. Continuous and detailed measurements of mean winds and turbulence above the surface layer are expensive and difficult to obtain. Computational fluid dynamics modelling of the atmospheric flow can be an attractive alternative or supplement to field experiments.In this study, the method of large-eddy simulation (LES) is applied to gain improved insight on the flow in the atmospheric boundary layer (ABL). The primary motivation behind the study has been to facilitate improvement of analytical wind profile models valid above the surface layer, however, the prospect of using LES more directly in applications such as short-term forecasting of the turbulent flow at e.g. wind farm sites is also considered. Two case studies based on measurements from the rural site of Høvsøre, Denmark and a suburban site in Hamburg, Germany demonstrate the need for accurate specification of the large-scale pressure forcing, when using LES for prediction of real-world wind profiles. In the Høvsøre case study, simulated wind speeds agree well with measurements throughout the ABL, but only when the applied forcing follows a height- and time-dependent pressure gradient estimated from continuous LIDAR measurements of the wind speed above the ABL. Including unsteadiness and baroclinic effects in the forcing also improves agreement with measurements in the Hamburg case study, but not as unambiguously as in the Høvsøre case study. It is concluded that the measurements available at and around the site in Hamburg are insufficient for accurate estimation of the driving pressure gradient, and that phenomena such as large-scale subsidence and advection also should be included in the LES for accurate wind profile prediction. A range of simulations of more idealized conditions are performed to study the influence of the free atmosphere Brunt Vaisala frequency and baroclinicity on the development and steady-state structure of neutral and near-neutral ABLs. It is found that an adjustment time of at least 16 hours is needed for the simulated flow to reach a quasi-steady state. The highly idealized conditions facilitate the formation of a super-geostrophic jet near the top of the ABL. It is considered to be a rare phenomena in the real-world ABL, and is not accounted for by the analytical models of the wind shear included in this study. It is furthermore shown that the considered wind profile model can be improved by appropriately accounting for the wind shear due to the free atmosphere Brunt Vaisala frequency and baroclinicity

The effect of unsteady and baroclinic forcing on predicted wind profiles in Large Eddy Simulations: Two case studies of the daytime atmospheric boundary layer

Due to its fine-resolution requirement and subsequent computational demand, Large Eddy Simulation of the atmospheric boundary layer is limited in most cases to computational domains extending only a few kilometers in both the vertical and horizontal directions. Variations in the flow and in relevant atmospheric fields (e.g. temperature) that occur at larger scales must be imposed through boundary conditions or as external forcing. In this work we study the influence of such variations on the wind profile in Large Eddy Simulations of daytime atmospheric boundary layers, by comparing observations with simulations that use progressively more realistic forcing relative to observed large-scale pressure gradients.Two case studies are presented. One is based on measurements from the rural site of Høvsøre in Denmark, and the other on measurements from a suburban site in Hamburg, Germany. The applied domain-scale pressure gradient and its height- and time-dependence are estimated from LIDAR measurements of the wind speed above the atmospheric boundary layer in the Høvsøre case, and from radio soundings and a network of ground-based pressure sensors in the Hamburg case.In the two case studies, LIDAR measurements of the wind speed up to heights between 900 and 1600 m and tower-based measurements up to 100 and 250 m are used to evaluate the performance of the variably-driven Large Eddy Simulations. We find in both case studies that including height- and time-variations in the applied pressure gradient has a significant influence on simulated wind speeds, and improves agreement with measured wind speeds, especially in the Høvsøre case. In the Hamburg case, an overly simplified specification of the height dependence of the forcing, as well as the influence of phenomena such as large-scale subsidence and advection, tend to reduce agreement with measurements, relative to the Høvsøre case. The Hamburg case illustrates that measurements of the surface pressure gradient and relatively infrequent radio soundings alone are not sufficient for accurate estimation of a height- and time-dependent pressure gradient

Comparison of Large Eddy Simulations of a convective boundary layer with wind LIDAR measurements

Vertical profiles of the horizontal wind speed and of the standard deviation of vertical wind speed from Large Eddy Simulations of a convective atmospheric boundary layer are compared to wind LIDAR measurements up to 1400 m. Fair agreement regarding both types of profiles is observed only when the simulated flow is driven by a both time- and height-dependent geostrophic wind and a time-dependent surface heat flux. This underlines the importance of mesoscale effects when the flow above the atmospheric surface layer is simulated with a computational fluid dynamics model