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Recommendations on setup in simulating atmospheric gravity waves under conventionally neutral boundary layer conditions

Wind farm-induced atmospheric gravity waves have been the subject of recent research as they can impact wind farm performance. Pressure variations associated with gravity waves can contribute to the global blockage effect and wind farm wake recovery. Therefore, accurate numerical simulation of flow fields, where wind-farm-induced gravity waves may be produced, is important. Three main considerations in such simulations are the overall domain size, the use of Rayleigh damping near domain boundaries to dampen gravity waves, and advection damping at the inlet to prevent spurious oscillations. Often these considerations are treated ad hoc rather than systematically. This work aims to test and extend the systematic modelling of internal gravity waves proposed in a preliminary investigation to modelling of both internal and trapped gravity waves. The preliminary study identifies the length scales to set the domain and damping layer sizes and the time scale to configure the Rayleigh damping coefficient but under linearly stratified conditions. Large eddy simulations of flow through a wind farm canopy are performed under conventionally neutral boundary layer (CNBL) conditions to test the validity of proposed setups for CNBL conditions. Background atmospheric parameters, such as Froude number (Fr), inversion height (H i ), and inversion layer Froude number (Fr i ) control most of the atmospheric gravity wave characteristics. We validated for CBNL conditions that the effective wavelengths of the internal gravity waves are the correct length scale to configure the domain size and damping layer thickness. Likewise, the optimum damping coefficient to dampen the internal gravity waves relates to the free atmosphere's buoyancy frequency or buoyant perturbations' time scale. We infer that the damping coefficient in the inversion layer may relate to the inversion buoyancy frequency to effectively dampen the trapped gravity waves. Moreover, the advection damping length is linked to the horizontal wavelength of the trapped gravity waves in the inversion layer to prevent spurious waves at the inlet by retaining wave energy accumulation.

17 WIND ENERGY↗

On the interaction of a wind turbine wake with a conventionally neutral atmospheric boundary layer

In this work, we investigate the dynamics of wind turbine tip-vortex breakdown in a conventionally neutral atmospheric boundary layer (ABL). To this end, high-resolution data are collected from large-eddy simulations of a wind turbine operating within a neutral ABL and studied by means of proper orthogonal decomposition (POD) and Fourier analysis. The high resolution of the generated data in both space and time allows us to gain insight into the tip-vortex breakdown mechanisms by (i) capturing the energy modes of the coherent structures, (ii) studying their contribution to the tip-vortex breakdown through their power spectra functions and mean kinetic energy (MKE) flux, and (iii) analysing the growth rate of each contributing perturbation frequency along tip vortices. Our analysis shows that under a fully turbulent scenario, the growth rate of perturbations along the tip vortices is largest for low wave numbers, i.e. long-wave perturbations. Additionally, the MKE flux reaches its highest value at two diameters downstream of the rotor plane, a behaviour that can be attributed to the coexistence of multiple interacting POD modes, with the streamwise vortex roller mode being the primary contributor to the total MKE flux budget, contributing approximately . Finally, comparisons with a laminar, uniform flow scenario subject to a single-frequency perturbation highlight the differences between the two ambient flow conditions. In the non-turbulent, uniform flow scenario, the growth rate attains its maximum value at a wave number corresponding to the out-of-phase mutual-inductance mechanism, whereas the MKE flux exhibits local minima and maxima along the wake and at different downstream locations depending on the perturbation frequency. Our analyses suggest that the breakdown of the wind turbine tip vortices under a fully turbulent neutral ABL inflow is due to complex interactions across a range of excitation frequencies, in which the mutual-inductance instability may not be the dominant one.

17 WIND ENERGY↗

Dependence of wind-farm-induced gravity waves and wind farm performance on non-dimensional atmospheric parameters and simulation configuration

This large-eddy simulation (LES) study examines how wind-farm-induced atmospheric gravity waves (AGWs) and wind farm performance depend on non-dimensional atmospheric parameters and simulation configuration. A hypothetical aligned wind farm of actuator disks is simulated under neutral surface conditions, with a stable capping inversion and a mildly stable free atmosphere, to assess the effects of stratification beyond the atmospheric boundary layer (ABL) on ABL flow. Simulation set-ups fully resolving AGWs are validated to minimize spurious wave generation and reflection from the domain boundaries. The validated set-up is then used to analyze AGW types and characteristics, as well as stratification impacts under conventionally neutral boundary layer (CNBL) conditions. These conditions are governed by four non-dimensional parameters: the Froude numbers of the free atmosphere and capping inversion (Fr, Fr i ), and the aspect ratios of the ABL and wind farm (H̃ i , S h ). Simulation configurations that fully resolve AGWs – capturing at least one wavelength both horizontally and vertically – yield the most realistic stratification effects on ABL flow, whereas partial or unresolved configurations produce non-physical, channel-like behavior. A coherent description of the AGW phenomena is provided, highlighting the central role of capping inversion displacement in linking ABL fluctuations with AGWs. Trapped waves are confined within the capping inversion, while interfacial and internal waves aloft are identified as the AGW types most relevant to wind farm performance. The wavy inversion, analogous to an interfacial wave, forms converging and diverging zones that drive power fluctuations across the farm. The interfacial wavelength, measured over the wind farm, corresponds to one diverging, one converging, and one mildly diverging zone. As the interfacial wavelength decreases with Fr i , multiple convergence–divergence zones develop under sub-critical conditions (Fr i <1.0), while for super-critical conditions (Fr i > 1.0), the wavelength approaches the farm length. Wave amplitude increases with decreasing H̃ i (i.e., shallower capping inversions). Wind farm performance is most sensitive to H̃ i : shallow boundary layers increase blockage and reduce efficiency, while deeper layers enhance efficiency. Increasing Fr and Fr i mitigates blockage, and increasing S h mainly improves wake recovery. Although local power fluctuations arise from AGWs, overall wind farm efficiency remains nearly constant with Fr and Fr i , improving primarily with larger H̃ i and S h .

17 WIND ENERGY↗

Correlations of supersonic boundary-layer transition on cones including effects of large axial variations in wind-tunnel noise

Transition data on sharp tip cones in two pilot low disturbance wind tunnels at Mach numbers of 3.5 and 5 were correlated in terms of noise parameters with data from several conventional wind tunnels and with data from supersonic flight tests on a transition cone. The noise parameters were developed to account for the large axial variations of the free stream noise and the very high frequency noise spectra that occurred in the low disturbance tunnels for some test conditions. The noise could be varied in these tunnels from high levels, approaching those in conventional tunnels, to extremely low levels. The correlations indicated that transition in the low disturbance tunnels was dominated by the local stream noise that was incident on the cone boundary layer unstream of the neutral stability point. The correlation results also suggested that high frequency components of the low disturbance tunnel noise spectra had significant effects on transition when the noise was incident on the boundary layer both upstream and downstream of the neutral stability point.

Chen, F. J.↗

Possible mitigation of tokamak plasma–surface interactions using thermionic divertor plates with inverse sheaths

Recent studies demonstrate that when a plasma-facing surface emits a sufficient flux of electrons, it will form an inverse sheath. In this work, we consider a possibility of using thermionic target plates with inverse sheaths as an innovative divertor operating scenario. We derive an electron heat flux boundary condition for inverse sheaths and show that for given power exhaust into a tokamak scrape-off-layer, an inverse sheath leads to a much lower target plasma electron temperature than a conventional sheath. Low enough target plasma temperatures for radiative divertor detachment could therefore be achieved using inverse sheaths instead of the usual need to inject neutral atoms that compromise the core plasma. Other advantages of inverse sheath detachment over conventional sheath operating scenarios include (a) ion impact energies are as low as possible, minimizing sputtering and tritium implantation, (b) surface recombination heat flux is reduced due to ion flux reduction, and (c) arcs are inhibited due to the sign of the surface electric field. This paper outlines the basic properties of inverse sheath detachment and considers the feasibility of implementation. We offer recommendations for future modeling efforts needed to better understand the effects of thermionic emission in tokamaks and whether inverse sheaths present a viable divertor solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effects of streamwise variations in noise levels and spectra on supersonic boundary-layer transition

Transition data for sharp cones in two quiet wind tunnels at Mach numbers 3.5 and 5.0 have been correlated in terms of noise parameters with data from several conventional wind tunnels and from the flight data for the AEDC transition cone. The noise parameters were developed to account for the large axial variations of the rms stream noise and the high frequency noise spectra that occurred in the quiet tunnels for some test conditions. The correlation results indicated transition in the quiet tunnels was dominated by the local stream noise that was incident on the cone boundary layer upstream of the neutral stability point. The correlation results also suggested that the energy in high frequency components of the quiet tunnel noise spectra had significant adverse effects on transition when the noise was incident on the boundary layer both upstream and downstream of the neutral stability point.

Chen, F.-J.↗

Ocean surface pressure fields from satellite-sensed winds

The University of Washington's planetary boundary layer model is inverted to use remotely sensed satellite scatterometer-derived surface winds as input to calculate maritime surface pressure fields. The analysis of three different synoptic storm situations is performed using the model and is then compared to conventional National Weather Service analyses. Agreement is good. Isolation of the PBL secondary flow, stratification and thermal wind effects in the model revealed that each may be significant under certain conditions. However, the model shows sensitivity to the thermodynamic features only in a general sense and even a neutral stratification solution gives a good approximation. The high density of the scatterometer data produces mesoscale (hundreds of kilometers) dynamic details, which cannot be confirmed by conventional data at this stage.

Brown, Robert A.↗