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At least 91 records · Page 5

Experimental investigation on heat transfer performance of drain water heat recovery heat exchangers

Water heating accounts for 18 % of residential energy consumption, and a substantial portion of this energy can be recovered through drain water heat recovery systems. Here, this paper investigates the heat transfer performance of drain water heat recovery heat exchangers. Two heat exchanger configurations were studied: vertical (gravity film exchanger) and horizontal. The heat recovery performance of the exchangers was quantified using sensible effectiveness and characteristic curves following the ε-NTU approach. Depending on the flow conditions, heat exchangers with a vertical configuration offered higher heat transfer effectiveness compared with the horizontal configuration under similar operating conditions. Furthermore, the results showed that properly designed and sized heat exchangers can effectively recover considerable amounts of waste heat from drains, depending on flow rates. Additionally, in the vertical heat exchanger configuration, low flow rates result in partially wet conditions, resulting in lower heat transfer effectiveness. Therefore, two distributor configurations are proposed to improve the heat transfer performance of vertically configured heat exchangers at low flow rates. The proposed distributor configurations and data presented in this paper will be useful in the design and development of drain water heat recovery systems in building applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

General bounds on holographic complexity

We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal volume slice has nonnegative vacuum-subtracted volume, and the vacuum-subtracted volume vanishes if and only if the spacetime is identically pure AdS. Under the Complexity=Volume proposal, this constitutes a positive holographic complexity theorem. The result features a number of parallels with the positive energy theorem, including the assumption of an energy condition that excludes false vacuum decay (the AdS weak energy condition). Our proof is rigorously established in broad generality in four bulk dimensions, and we provide strong evidence in favor of a generalization to arbitrary dimensions. Our techniques also yield a holographic proof of Lloyd’s bound for a class of bulk spacetimes. We further establish a partial rigidity result for wormholes: wormholes with a given throat size are more complex than AdS-Schwarzschild with the same throat size.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Improvement of registration accuracy in accelerated partial breast irradiation using the point-based rigid-body registration algorithm for patients with implanted fiducial markers

Purpose: To investigate image-registration errors when using fiducial markers with a manual method and the point-based rigid-body registration (PRBR) algorithm in accelerated partial breast irradiation (APBI) patients, with accompanying fiducial deviations. Methods: Twenty-two consecutive patients were enrolled in a prospective trial examining 10-fraction APBI. Titanium clips were implanted intraoperatively around the seroma in all patients. For image-registration, the positions of the clips in daily kV x-ray images were matched to those in the planning digitally reconstructed radiographs. Fiducial and gravity registration errors (FREs and GREs, respectively), representing resulting misalignments of the edge and center of the target, respectively, were compared between the manual and algorithm-based methods. Results: In total, 218 fractions were evaluated. Although the mean FRE/GRE values for the manual and algorithm-based methods were within 3 mm (2.3/1.7 and 1.3/0.4 mm, respectively), the percentages of fractions where FRE/GRE exceeded 3 mm using the manual and algorithm-based methods were 18.8%/7.3% and 0%/0%, respectively. Manual registration resulted in 18.6% of patients with fractions of FRE/GRE exceeding 5 mm. The patients with larger clip deviation had significantly more fractions showing large FRE/GRE using manual registration. Conclusions: For image-registration using fiducial markers in APBI, the manual registration results in more fractions with considerable registration error due to loss of fiducial objectivity resulting from their deviation. The authors recommend the PRBR algorithm as a safe and effective strategy for accurate, image-guided registration and PTV margin reduction.

60 APPLIED LIFE SCIENCES↗

A YOUNG GIANT MOLECULAR CLOUD FORMED AT THE INTERFACE OF TWO COLLIDING SUPERSHELLS: OBSERVATIONS MEET SIMULATIONS

Dense, star-forming gas is believed to form at the stagnation points of large-scale interstellar medium flows, but observational examples of this process in action are rare. We here present a giant molecular cloud (GMC) sandwiched between two colliding Milky Way supershells, which we argue shows strong evidence of having formed from material accumulated at the collision zone. Combining {sup 12}CO, {sup 13}CO, and C{sup 18}O(J = 1-0) data with new high-resolution, three-dimensional hydrodynamical simulations of colliding supershells, we discuss the origin and nature of the GMC (G288.5+1.5), favoring a scenario in which the cloud was partially seeded by pre-existing denser material, but assembled into its current form by the action of the shells. This assembly includes the production of some new molecular gas. The GMC is well interpreted as non-self-gravitating, despite its high mass (M{sub H{sub 2}}∼1.7×10{sup 5} M{sub ⊙}), and is likely pressure confined by the colliding flows, implying that self-gravity was not a necessary ingredient for its formation. Much of the molecular gas is relatively diffuse, and the cloud as a whole shows little evidence of star formation activity, supporting a scenario in which it is young and recently formed. Drip-like formations along its lower edge may be explained by fluid dynamical instabilities in the cooled gas.

79 ASTRONOMY AND ASTROPHYSICS↗

Irrigation system

A gravity irrigation system includes a distribution piping having apertures to distribute water to a field, and a valve located upstream of the distribution piping. The valve limits a pressure of the water being delivered to the distribution piping. The system also includes a sump to receive the water at a lowest elevation of the field, a depth sensor disposed within the sump, and a return pump disposed at least partially within the sump to move the water to an elevated portion of the field. The system also includes a motor to drive the return pump, and a power source coupled to a variable frequency drive that powers the motor and controls a motor speed proportionately to an indication of the depth sensor. The system also includes a transfer piping to bring the water from the return pump to a check valve and to the distribution piping.

Henry, Christopher G.↗

Quantum state reduction: Generalized bipartitions from algebras of observables

Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with the partial-trace map by tracing out part of the quantum state, but in many natural situations this reduction may not be achievable. We investigate the general problem of identifying how the quantum state is reduced given a restriction on the observables. For example, in an experimental setting, the set of observables that can actually be measured is usually modest (compared to the set of all possible observables) and their resolution is limited. In such situations, the appropriate state-reduction map can be defined via a generalized bipartition, which is associated with the structure of irreducible representations of the algebra generated by the restricted set of observables. One of our main technical results is a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras. In our work, we demonstrate the viability of this approach with two examples of limited-resolution observables. The definition of quantum state reductions can also be extended beyond algebras of observables. To accomplish this task we introduce a more flexible notion of bipartition, the partial bipartition, which describes coarse grainings preserving information about a limited set (not necessarily algebra) of observables. We describe a variational method to choose the coarse grainings most compatible with a specified Hamiltonian, which exhibit emergent classicality in the reduced state space. We apply this construction to the concrete example of the one-dimensional Ising model. Our results have relevance for quantum information, bulk reconstruction in holography, and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The first heat: production of entanglement entropy in the early universe

Entanglement entropy (EE) of a spatial region quantifies correlations between the region and its surroundings. For a free scalar in the adiabatic vacuum in de Sitter space the EE is known to remain low, scaling as the surface area of the region. Here, we study the evolution of entanglement after the universe transitions from de Sitter to flat space. We concentrate on the case of a massless minimally coupled scalar. We find numerically that, after the de Sitter stage ends, the EE and the R´enyi entropy rapidly grow and saturate at values obeying the volume law. The final state of the subsystem (region) is a partially thermalized state reminiscent of a generalized Gibbs ensemble. We comment on application of our results to the question of when and how cosmological perturbations decohere.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Basin and Range Investigation for Developing Geothermal Energy: Exploration Data

This data package includes exploration material from the Basin & Range Investigation for Developing Geothermal Energy [in Hidden Systems] project (BRIDGE), which is part of a broader initiative to advance the exploration of hidden geothermal resources in the Basin & Range Province of the western U.S. Data modalities include a helicopter-borne time-domain electromagnetic survey, magnetotellurics, 2-meter temperature measurements, ground-based gravity and legacy aeromagnetic surveys, geochemistry, geologic mapping, LiDAR analysis, 3D models, associated geospatial data, and a bibliography of existing data and references utilized in prospect characterization and conceptual modeling. Key files are in CSV, Geosoft, and Geotools formats. Please refer to READMEs for dataset-specific information. Where applicable, acquisition data and inversion models for a particular prospect or area of interest are organized separately. This BRIDGE data package is the product of a collaboration led by Sandia National Laboratories with partners from Geologica Geothermal Group, Inc., the U.S. Navy Geothermal Program Office, and consultants Steven Sewell (Australis Geoscience Ltd) and William Cumming (Cumming Geoscience). The project's areas of interest (AOIs) are based off priority areas of interest in the southwestern portion of the Nevada Play Fairway map, distribution across tectonic provinces, accessibility, and the project team's extensive experience in the region. AOIs cover about a dozen basins that include unexplored prospects, partially explored prospects, and some developed analogue resources that provide validation cases. Many unexplored and partially explored prospects are on U.S. Department of Defense (DoD) land, though adjacent lands are included as well.

15 GEOTHERMAL ENERGY↗

Lagrangian flows within reflecting internal waves at a horizontal free-slip surface

In this paper sequel to Zhou and Diamessis [“Reflection of an internal gravity wave beam off a horizontal free-slip surface,” Phys. Fluids 25, 036601 (2013)], we consider Lagrangian flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking Lagrangian fluid particles in direct numerical simulation (DNS) datasets of the Eulerian flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that Eulerian mean flow due to wave-wave interaction and wave-induced Stokes drift cancels each other out completely at the second order in wave steepness A, i.e., O(A{sup 2}), implying zero Lagrangian mean flow up to that order. However, high-accuracy particle tracking in finite-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A{sup 2}) is not complete. This partial cancelation significantly weakens the mean Lagrangian flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean Lagrangian drifts on O(A{sup 2}) and thus particle dispersion on O(A{sup 4}). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

EBS Task Force: Task 9/FEBEX Modeling Final Report: Thermo-Hydrological Modeling with PFLOTRAN

This report outlines Sandia National Laboratories modeling studies applied to Stage 1 and Stage 2 of the Full-scale Engineered Barriers Experiment in Crystalline Host Rock (FEBEX) in situ test for the SKB EBS Task Force Task 9. The FEBEX test was a full-scale test conducted over ~18 years at the Grimsel, Switzerland Underground Research Laboratory (URL) managed by NAGRA. It involved emplacing simulated waste packages, in the form of welded cylindrical heaters, inside a tunnel in crystalline granitic rock and surrounded by a bentonite barrier and cement plug. Sensors emplaced within the bentonite monitored the wetting-up, heating, and drying out of the bentonite barrier, and the large resulting data set provides an excellent opportunity for validation of multiphysics Thermal-Hydrological (TH), Thermal-Hydrologic-Chemical (THC), and Thermal-Hydrological-Mechanical (THM) modeling approaches for underground nuclear waste storage and the performance of engineered bentonite barriers. The present status of the EBS Task Force is finalizing Task 9, which follows years of modeling studies of the FEBEX test, by many notable modeling teams (Gens et al., 2009; Sanchez et al. 2010; 2012; Samper et al., 2018). These modeling studies generally use two-dimensional axisymmetric meshes, ignoring threedimensional effects, gravity and asymmetric wetting and dry out of the bentonite engineered barrier. This study investigates these effects with use of the PFLOTRAN THC code with massively parallel computational methods in modeling FEBEX Stage 1 and Stage 2 results. The PFLOTRAN numerical code is an open source, state-of-the-art, massively parallel subsurface flow and reactive transport code operating in a high-performance computing environment (Hammond et al., 2014). Section 2 describes the applied partial differential equations describing mass, momentum and energy balance used in this study, considerations derived by assuming phase equilibrium between gas and liquid phases, constitutive equations for granite, cement plug, and bentonite domains, and specific approaches for use inthe PFLOTRAN code. Section 3 describes the geometry, meshing, and model set-up. Section 4 describes modeling results, Section 5 compares modeling results to field testing data, and Section 6 gives conclusions. The Appendix provides detailed information required by the EBSTask Force for final reporting.

42 ENGINEERING↗

The discrete Green's function paradigm for two-way coupled Euler-Lagrange simulation

We outline a methodology for the simulation of particle-laden flows whereby the dispersed and fluid phases are two-way coupled. The drag force which couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. The method is general in that it can be extended to other partial differential equations which may be associated with particle-laden flows, such as the thermal energy equation or Maxwell's equations. In this work, we demonstrate the method of discrete Green's functions by obtaining these functions for the Navier-Stokes equations at low particle Reynolds number in a two-plane channel geometry. We perform verification at low and finite particle Reynolds number for the case of a point-particle settling under gravity parallel to a plane wall, for different wall normal separations. In comparing to other point-particle schemes the discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations and is the most accurate in the near wall region at finite Reynolds number. We discuss how the accuracy away from the wall at finite Reynolds number could be improved by appealing to Oseen-like discrete Green's functions. Finally we demonstrate that the discrete Green's function approach can have important implications on statistics of particle-laden turbulent channel flow.

42 ENGINEERING↗

Stellar Characterization and Radius Inflation of Hyades M-dwarf Stars from the APOGEE Survey

We present a spectroscopic analysis of a sample of 48 M-dwarf stars (0.2 M ⊙ < M < 0.6 M ⊙ ) from the Hyades open cluster using high-resolution H-band spectra from the Sloan Digital Sky Survey/Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. Our methodology adopts spectrum synthesis with LTE MARCS model atmospheres, along with the APOGEE Data Release 17 line list, to determine effective temperatures, surface gravities, metallicities, and projected rotational velocities. The median metallicity obtained for the Hyades M dwarfs is [M/H] = 0.09 ± 0.03 dex, indicating a small internal uncertainty and good agreement with optical results for Hyades red giants. Overall, the median radii are larger than predicted by stellar models by 1.6% ± 2.3% and 2.4% ± 2.3%, relative to a MIST and DARTMOUTH isochrone, respectively. We emphasize, however, that these isochrones are different, and the fractional radius inflation for the fully and partially convective regimes have distinct behaviors depending on the isochrone. Using a MIST isochrone there is no evidence of radius inflation for the fully convective stars, while for the partially convective M dwarfs the radii are inflated by 2.7% ± 2.1%, which is in agreement with predictions from models that include magnetic fields. For the partially convective stars, rapid rotators present on average higher inflation levels than slow rotators. The comparison with SPOTS isochrone models indicates that the derived M-dwarf radii can be explained by accounting for stellar spots in the photosphere of the stars, with 76% of the studied M dwarfs having up to 20% spot coverage, and the most inflated stars with ~20%–40% spot coverage.

79 ASTRONOMY AND ASTROPHYSICS↗

TU-CD-304-04: Scanning Field Total Body Irradiation Using Dynamic Arc with Variable Dose Rate and Gantry Speed

Purpose: Enable a scanning field total body irradiation (TBI) technique, using dynamic arcs, which is biologically equivalent to a moving couch TBI. Methods: Patient is treated slightly above the floor and the treatment field scans across the patient by a moving gantry. MLC positions change during gantry motion to keep same field opening at the level of the treatment plane (170 cm). This is done to mimic the same geometry as the moving couch TBI technique which has been used in our institution for over 10 years. The dose rate and the gantry speed are determined considering a constant speed of the moving field, variations in SSD and slanted depths resulting from oblique gantry angles. An Eclipse (Varian) planning system is commissioned to accommodate the extended SSD. The dosimetric foundations of the technique have been thoroughly investigated using phantom measurements. Results: Dose uniformity better than 2% across 180 cm length at 10cm depth is achieved by moving the gantry from −55 to +55 deg. Treatment range can be extended by increasing gantry range. No device such as a gravity-oriented compensator is needed to achieve a uniform dose. It is feasible to modify the dose distribution by adjusting the dose rate at each gantry angle to compensate for body thickness differences. Total treatment time for 2 Gy AP/PA fields is 40–50 minutes excluding patient set up time, at the machine dose rate of 100 MU/min. Conclusion: This novel yet transportable moving field technique enables TBI treatment in a small treatment room with less program development preparation than other techniques. Treatment length can be extended per need, and. MLC-based thickness compensation and partial lung blocking are also possible.

60 APPLIED LIFE SCIENCES↗

Sodium Extraction from Full-Length Fermi-1 Blanket Assembly

Enrico Fermi Nuclear Generating Station is a nuclear power plant on the shore of Lake Erie. On October 5, 1966, Fermi 1, a prototype fast breeder reactor, suffered a partial fuel meltdown (no radioactive material was released). As a result, 34 metric tons of sodium-bonded blanket material from the decommissioned Fermi-1 reactor were shipped to and are currently stored at the Idaho Nation Lab (INL). This material is currently awaiting removal from the state of Idaho by 2035. In its current state, the Fermi-1 material is not suitable for disposal due to the reactive characteristic of its bond sodium. This work demonstrates removal of bond sodium from an entire full-length unirradiated Fermi-1 outer radial blanket assembly using a gravity assisted melt-drain-evaporate (MEDE) treatment process. Quantitative and qualitative analyses were performed to characterize the extent of sodium removal from the blanket material following MEDE treatment.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the N = 6 solution

We compute the set of all extreme rays of the 6-party subadditivity cone that are compatible with strong subadditivity. In total, we identify 208 new (genuine 6-party) orbits, 52 of which violate at least one known holographic entropy inequality. For the remaining 156 orbits, which do not violate any such inequalities, we construct holographic graph models for 150 of them. For the final 6 orbits, it remains an open question whether they are holographic. Consistent with the strong form of the conjecture in [1], 148 of these graph models are trees. However, 2 of the graphs contain a “bulk cycle”, leaving open the question of whether equivalent models with tree topology exist, or if these extreme rays are counterexamples to the conjecture. The paper includes a detailed description of the algorithm used for the computation, which is presented in a general framework and can be applied to any situation involving a polyhedral cone defined by a set of linear inequalities and a partial order among them to find extreme rays corresponding to down-sets in this poset.

AdS-CFT correspondence↗

Evaluation of a semiautomated lung mass calculation technique for internal dosimetry applications

Purpose: The authors sought to evaluate a simple, semiautomated lung mass estimation method using computed tomography (CT) scans obtained using a variety of acquisition techniques and reconstruction parameters for mass correction of medical internal radiation dose-based internal radionuclide radiation absorbed dose estimates.Methods: CT scans of 27 patients with lung cancer undergoing stereotactic body radiation therapy treatment planning with PET/CT were analyzed retrospectively. For each patient, free-breathing (FB) and respiratory-gated 4DCT scans were acquired. The 4DCT scans were sorted into ten respiratory phases, representing one complete respiratory cycle. An average CT reconstruction was derived from the ten-phase reconstructions. Mid expiration breath-hold CT scans were acquired in the same session for many patients. Deep inspiration breath-hold diagnostic CT scans of many of the patients were obtained from different scanning sessions at similar time points to evaluate the effect of contrast administration and maximum inspiration breath-hold. Lung mass estimates were obtained using all CT scan types, and intercomparisons made to assess lung mass variation according to scan type. Lung mass estimates using the FB CT scans from PET/CT examinations of another group of ten male and ten female patients who were 21–30 years old and did not have lung disease were calculated and compared with reference lung mass values. To evaluate the effect of varying CT acquisition and reconstruction parameters on lung mass estimation, an anthropomorphic chest phantom was scanned and reconstructed with different CT parameters. CT images of the lungs were segmented using the OsiriX MD software program with a seed point of about −850 HU and an interval of 1000. Lung volume, and mean lung, tissue, and air HUs were recorded for each scan. Lung mass was calculated by assuming each voxel was a linear combination of only air and tissue. The specific gravity of lung volume was calculated using the formula (lung HU − air HU)/(tissue HU − air HU), and mass = specific gravity × total volume × 1.04 g/cm{sup 3}.Results: The range of calculated lung masses was 0.51–1.29 kg. The average male and female lung masses during FB CT were 0.80 and 0.71 kg, respectively. The calculated lung mass varied across the respiratory cycle but changed to a lesser degree than did lung volume measurements (7.3% versus 15.4%). Lung masses calculated using deep inspiration breath-hold and average CT were significantly larger (p < 0.05) than were some masses calculated using respiratory-phase and FB CT. Increased voxel size and smooth reconstruction kernels led to high lung mass estimates owing to partial volume effects.Conclusions: Organ mass correction is an important component of patient-specific internal radionuclide dosimetry. Lung mass calculation necessitates scan-based density correction to account for volume changes owing to respiration. The range of lung masses in the authors’ patient population represents lung doses for the same absorbed energy differing from 25% below to 64% above the dose found using reference phantom organ masses. With proper management of acquisition parameters and selection of FB or midexpiration breath hold scans, lung mass estimates with about 10% population precision may be achieved.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

High Energy Theory and Cosmology Workshops at the Leinweber Center for Theoretical Physics at the University of Michigan

This award partially supported a workshop and a summer school held at the Leinweber Center for Theoretical Physics at the University of Michigan in Ann Arbor. Funds were primarily used to support the travel of external participants. The programs were substantially delayed owing to the pandemic. The symposium was initially slated for Spring 2020. The 2023 Michigan Cosmology Summer School was held June 5-9 2023 in Ann Arbor Michigan. There were about 150 in-person international participants (of whom about 35Nine external lecturers listed below delivered a series of lectures ranging on topics from “Measuring and Mapping Cosmic Shear” to “Dark Dark Energy and Modified Gravity.” Many archived version of the slides and videos of the lectures may be found at https://johannesulf.github.io/cosmology-school-2023/program.html

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗