Horizontal Flow Components Research Articles

Effect of climate warming on subsurface temperature in basins with topography-driven groundwater flow

Climate warming has caused increased air temperature as well as increased subsurface temperature. Many previous studies on subsurface warming simplified heat advection by neglecting the horizontal component of regional groundwater flow or even neglected heat advection accompanying groundwater flow. In this study, the simultaneous control of heat advection and conduction on subsurface warming is numerically investigated in a 2D hypothetical basin cross section. By calculating the increment of subsurface temperature, we find that heat advection could accelerate subsurface warming. In a given basin, subsurface warming in the recharge area with downward groundwater flow is more significant than that in the discharge area with upward groundwater flow. By using a 1D model with vertical groundwater flow only for comparison, we find that in any part of a basin, even if the horizontal flux is very small compared with the vertical flux, neglecting the horizontal flux would underestimate the propagation depth of climate warming. This implies that when the propagation depth of climate warming is a priori known variable, existing 1D models would overestimate downward groundwater flux or underestimate upward groundwater flux. Moreover, we find pumping would cause deeper propagation depths of climate warming by accelerating groundwater circulation, whereas basin-scale heterogeneity and anisotropy of hydraulic conductivity would cause shallower propagation depths of climate warming because of the relative dominance of horizontal flow. By demonstrating the importance of 2D groundwater flow on subsurface warming, the results provide new insight into understanding the regulation of temperature among the atmosphere, the hydrosphere and the lithosphere.

S3DCN-OLSR: A shallow 3D CNN method for online learning state recognition

The repeated recurrence of COVID-19 has significantly disrupted learning for students in face-to-face instructional settings. While moving from offline to online instruction has proven to be one of the best solutions, classroom management and capturing students' learning states have emerged as important challenges with the increasing popularity of online instruction. To address these challenges, in this paper we propose an online learning status recognition method based on shallow 3D convolution (S3DC-OLSR) for online students, to identify students' online learning states by analysing their micro-expressions. Specifically, we first use the data augmentation method proposed in this paper to decompose the students' online video file into three features: horizontal component of optical flow, vertical component of optical flow and optical amplitude. Next, the students' online learning status is recognised by feeding the processed data into a shallow 3D convolution neural network. To test the performance of our method, we conduct extensive experiments on the CASME II and SMIC datasets, and the results indicate that our method outperforms the other state-of-the-art methods considered in terms of recognition accuracy, UF1 and UAR, which demonstrates the superiority of our method in identifying students’ online learning states.

Hydrogeochemical controls and recharge-flow system of groundwater in the lowland of the Fukui-Ohno Basin, central Japan, based on carbon isotopic signatures

• River water mixing and CO 2 dissolution in groundwater was modeled with δ 13 C tracers. • Decomposition of both C3 and lacustrine organic matter was related to CO 2 dissolution. • Modeling identified similar amounts of vertical and horizontal groundwater recharge. Carbon stable isotopic compositions of dissolved inorganic carbon (δ 13 C DIC ) and chemical compositions of groundwater were used to investigate the processes of supply of DIC to groundwater in the lowland area of the Fukui-Ohno Basin and to examine constraints on the groundwater recharge-flow system. The groundwater in the basin is dominantly of Ca-HCO 3 type with relatively high concentrations of Ca 2+ and HCO 3 − and lower concentrations of Mg 2+ ; this groundwater chemistry can be attributed to weathering within the aquifer of mainly anorthite and some pyroxene at partial pressures of CO 2 that are typical of soils. The δ 13 C values of the CO 2 gas initially equilibrated with DIC in the groundwater were calculated to be −28.6‰ to −22.8‰, indicating that the groundwater in the lowland basin has two main sources of carbon: (1) C3 organic matter (δ 13 C ≈ −29‰), distributed mainly in mountains surrounding much of the basin and in aquicludes within the basin; and (2) organic matter in shallow lacustrine deposits within the lowland basin (δ 13 C ≈ −20‰). The results of modeling accounting for these two sources demonstrated that roughly equal proportions (50 ± 20%) of DIC in the groundwater are sourced from lacustrine deposits and C3 organic matter. The distributions of these types of organic matters in and around the lowland basin suggest that there are two major and roughly equal components of groundwater recharge: a vertical component of downward percolation of precipitation in the lowland area and a mainly horizontal component of groundwater flow originating in the mountains around the study area and flowing through aquifers into the lowland basin.

The effect of boundary conditions on the single-well push-pull test in a partially penetrated well

Boundary conditions of well screen are critical formodeling reactive transport around a partially penetrated well in a single-well push–pull (SWPP) test. Previous SWPP test models often assumed that water flux was uniformly distributed along the well screen of the partially penetrated well, named the uniformly distributed flux boundary condition (UFBC). To investigate the influence of such an assumption on reactive transport in the SWPP test, we develop a new finite-difference numerical model under a flow field with a finite hydraulic diffusivity in this study, considering the wellbore storage. The uniformly distributed head boundary condition (UHBC) is employed for both groundwater flow and reactive transport across the well screen. The dispersion coefficients are in a tensor form, depending on both horizontal and vertical flow components. The results show that the UFBC model may cause non-negligible errors when modeling reactive transport in the SWPP test with a partially penetrated well. Such errors are obvious at the early stage of the extraction phase, but become negligible at late stage of the extraction phase. The UHBC solution for reactive transport is smaller than the UFBC solution at the middle of the well screen, but greater than the UFBC solution at the top or bottom of the well screen. Using the SWPP test to investigate the reactive transport in subsurface, in addition to the breakthrough curves (BTCs), the information of the flow field (like well geometry information and the observed time-drawdown data) is necessary and could be used to calibrate the model. Field application demonstrates that the UHBC model performs better than the UFBC model when interpreting BTCs of the SWPP test in the extraction phase. The findings of this study can help for better understanding of reactive transport in the SWPP test.

On the nonlocal boundary value problem of geophysical fluid flows

This paper proposes a nonlocal formulation regarding the modeling of Antarctic Circumpolar Current by introducing flow functions to encode horizontal flow components without considering vertical motion. Using topological degree, zero exponent theory and fixed point technique, we show the existence of positive solutions to nonlocal boundary value problems with nonlinear vorticity.

Mapping Subsurface Seepage Flow Patterns in Proximity to a Coal Combustion Residual Landfill Using Electrical Resistivity Tomography

Electrical resistivity tomography data were acquired in proximity to the coal combustion residual landfill in an effort to image and analyze seepage pathways through the shallow residual soil and underlying karsted limestone bedrock. The water table is at a depth of more than 45 m. The most prominent subsurface seepage pathways identified on the acquired electrical resistivity tomography data are located immediately adjacent to the toe of the landfill and are attributed to stormwater run-off. The moisture content of the limestone appears to decrease gradually with increasing distance from the toe of the landfill, suggesting there is also a horizontal component of moisture flow in the subsurface. Shallow limestone with higher moisture content generally underlies or is in close proximity to anthropogenic features such as drainage ditches and clay berms that are designed to channel run-off. At one location, electrical resistivity tomography data were acquired along essentially the same traverse at different times of the year, and the resistivity of shallow limestone overall was lower on the data acquired after heavy rains.

Spatial–temporal variation of treatment performance and bacterial community diversity in a hybrid constructed wetland

A hybrid pilot-scale constructed wetland (HSSF-FWS) with three horizontal flow components and a free water surface in series (HF-CW1 + HF-CW2 + HF-CW3 + FWS) was designed and investigated to evaluate seasonal wastewater treatment performance, the microbial diversity and community structure. The HF-CW1 component was planted with Scirpus holoschoenus and Cyperus papyrus; HF-CW2 was unplanted, whereas HF-CW3 was planted with Scirpus validus. In FWS, the wastewater was covered with Lemna minor and Daphnia magna. HSSF-FWS has a great potential to reduce chemical oxygen demand (COD), biochemical oxygen demand (BOD5), total suspended solids (TSS), fecal coliforms (FC) and fecal streptococci (FS), while the removal efficiencies of nitrate nitrogen (NO3−) and orthophosphorus (PO43−) were relatively low. The best removal efficiency was achieved in spring for COD and BOD5, in summer for TSS, in autumn for NO3− and in winter for PO43−, while no seasonal difference was found for the removal of FC and FS. The seasonal treatment performance is generally less influenced by the plant species than by the presence or absence of vegetation. HF-CW3 and FWS had different influences on treatment parameters; the FWS component improved the removal of TSS and PO43− during winter and the removal of COD and NO3− during spring season. Seasonal changes affect the microbial diversity and community structure throughout the hybrid constructed wetland and are enhanced by the presence of plants, with diversity changing with different plant species. Cluster analysis indicated that bacterial community structure from influent and FWS samples was closely related in autumn.

Digging deeper: The influence of historical mining on Glasgow's subsurface thermal state to inform geothermal research

Studies of the former NE England coalfield in Tyneside demonstrated that heat flow perturbations in boreholes were due to the entrainment and lateral dispersion of heat from deeper in the subsurface through flooded mine workings. This work assesses the influence of historical mining on geothermal observations across Greater Glasgow. The regional heat flow for Glasgow is 60 mW m −2 and, after correction for palaeoclimate, is estimated as c . 80 mW m −2 . An example of reduced heat flow above mine workings is observed at Hallside ( c . 10 km SE of Glasgow), where the heat flow through a 352 m deep borehole is c . 14 mW m −2 . Similarly, the heat flow across the 199 m deep GGC01 borehole in the Glasgow Geothermal Energy Research Field Site is c . 44 mW m −2 . The differences between these values and the expected regional heat flow suggest a significant component of horizontal heat flow into surrounding flooded mine workings. This deduction also influences the quantification of deeper geothermal resources, as extrapolation of the temperature gradient above mine workings would underestimate the temperature at depth. Future projects should consider the influence of historical mining on heat flow when temperature datasets such as these are used in the design of geothermal developments. Supplementary material : Background information on the chronology of historical mining at each borehole location and a summary of groundwater flow in mine workings beneath Glasgow are available at https://doi.org/10.6084/m9.figshare.c.4681100 Thematic collection: This article is part of the ‘Early Career Research’ available at: https://www.lyellcollection.org/cc/SJG-early-career-research

Comparison of time–distance inversion methods applied to SDO/HMI Dopplergrams

Context. The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) satellite has been observing the Sun since 2010. The uninterrupted series of Dopplergrams are ideal for studying the dynamics of the upper solar convection zone. Within the Joint Science Operations Center (JSOC) the time–distance inversions for flows and sound-speed perturbations were introduced. The automatic pipeline has produced flow and sound-speed maps every 8 h. We verify the results of JSOC inversions by comparing the data products to equivalent results from inverse modelling obtained by an independent inversion pipeline. Aims. We compared the results from the JSOC pipeline for horizontal flow components and the perturbations of the speed of sound at set of depths with equivalent results from an independently implemented pipeline using a different time–distance inversion scheme. Our inversion pipeline allows inversion for all quantities at once while allowing minimisation of the crosstalk between them. This gives us an opportunity to discuss the possible biases present in the JSOC data products. Methods. For the tests we used the subtractive optimally localised averaging (SOLA) method with a minimisation of the cross-talk. We compared three test inversions for each quantity at each target depth. At first, we used the JSOC setup to reproduce the JSOC results. Subsequently, we used the extended pipeline to improve these results by incorporating more independent travel-time measurements but keeping the JSOC-indicated localisation in the Sun. Finally, we inverted for flow components and sound-speed perturbations using a localisation kernel with properties advertised in the JSOC metadata. Results. We successfully reproduced the horizontal flow components. The sound-speed perturbations are strongly affected by the high level of the cross-talk in JSOC products. This leads to larger amplitudes in the inversions for the sound-speed perturbations. Different results were obtained when a target function localised around the target depth was used. This is a consequence of non-localised JSOC averaging kernels. We add that our methodology also allows inversion for the vertical flow.

Combined helioseismic inversions for 3D vector flows and sound-speed perturbations

Context. Time–distance helioseismology is the method of the study of the propagation of waves through the solar interior via the travel times of those waves. The travel times of wave packets contain information about the conditions in the interior integrated along the propagation path of the wave. The travel times are sensitive to perturbations of a variety of quantities. The usual task is to invert for the vector of plasma flows or the sound–speed perturbations separately. The separate inversions may be polluted by systematic bias, for instance, originating in the leakage of vector flows into the sound–speed perturbations and vice versa (called a cross-talk). Information about the cross-talk is necessary for a proper interpretation of results. Aims. We introduce an improved methodology of the time-distance helioseismology which allows us to invert for a full 3D vector of plasma flows and the sound–speed perturbations at once. Using this methodology one can also derive the mean value of the vertical component of plasma flows and the cross-talk between the plasma flows and the sound–speed perturbations. Methods. We used the Subtractive Optimally Localised Averaging method with a minimisation of the cross-talk as a tool for inverse modelling. In the forward model, we use Born approximation travel-time sensitivity kernels with the Model S as a background. The methodology was validated using forward-modelled travel times with both mean and difference point-to-annulus averaging geometries applied to a snapshot of fully self-consistent simulation of the convection. Results. We tested the methodology on synthetic data. We demonstrate that we are able to recover flows and sound–speed perturbations in the near-surface layers. We have taken the advantage of the sensitivity of our methodology to entire vertical velocity, and not only to its variations as in other available methodologies. The cross-talk from both the vertical flow component and the sound–speed perturbation has only a negligible effect for inversions for the horizontal flow components. Furthermore, this cross-talk can be minimised if needed. The inversions for the vertical component of the vector flows or for the sound–speed perturbations are affected by the cross-talk from the horizontal components, which needs to be minimised in order to provide valid results. It seems that there is a nearly constant cross-talk between the vertical component of the vector flows and the sound–speed perturbations.

VALIDATING FORWARD MODELING AND INVERSIONS OF HELIOSEISMIC HOLOGRAPHY MEASUREMENTS.

Here we use synthetic data to explore the performance of forward models and inverse methods for helioseismic holography. Specifically, this work presents the first comprehensive test of inverse modeling for flows using lateral-vantage (deep-focus) holography. We derive sensitivity functions in the Born approximation. We then use these sensitivity functions in a series of forward models and inversions of flows from a publicly available magnetohydrodynamic quiet-Sun simulation. The forward travel times computed using the kernels generally compare favorably with measurements obtained by applying holography, in a lateral-vantage configuration, on a 15-hour time series of artificial Dopplergrams extracted from the simulation. Inversions for the horizontal flow components are able to reproduce the flows in the upper 3Mm of the domain, but are compromised by noise at greater depths.

Numerical Simulation of Dynamic Stall Characteristics for Wind Turbine under Yawed Condition

When a horizontal axis wind turbine rotor works under yawed condition, a cyclic variation of Angle of Attack (AOA) at blades will causes dynamic stall phenomenon and accordingly increases the fatigue load. In order to relate the yawed condition with dynamic stall characteristic, a 3D and time-accurate Computational Fluid Dynamics (CFD) is used for the simulations of flow-field and dynamic stall characteristic on the National Renewable Energy Laboratory (NREL) Phase VI wind turbine rotor at yaw 30 degrees. The local AOA and airfoil aerodynamics, i.e., lift coefficient Cl and drag coefficient Cd, are computed based on CFD results. The results show that the horizontal component of yawed inflow and unsteady flow around sections of blade will delay the formation of separation vortex and also the occurrence of stall. The dynamic load accompanied with dynamic stall phenomenon is significantly increased on blade, and the hysteresis characteristic of airfoil lift and drag is more remarkable at the inboard blade sections. The derived results are helpful to develop more reliable aerodynamic models for wind turbine design codes, and also can provide theoretical guidance for the optimal design of a wind turbine.

Modelling aeolian sand transport using a dynamic mass balancing approach

Knowledge of the changing rate of sediment flux in space and time is essential for quantifying surface erosion and deposition in desert landscapes. Whilst many aeolian studies have relied on time-averaged parameters such as wind velocity (U) and wind shear velocity (u⁎) to determine sediment flux, there is increasing field evidence that high-frequency turbulence is an important driving force behind the entrainment and transport of sand. At this scale of analysis, inertia in the saltation system causes changes in sediment transport to lag behind de/accelerations in flow. However, saltation inertia has yet to be incorporated into a functional sand transport model that can be used for predictive purposes. In this study, we present a new transport model that dynamically balances the sand mass being transported in the wind flow. The ‘dynamic mass balance’ (DMB) model we present accounts for high-frequency variations in the horizontal (u) component of wind flow, as saltation is most strongly associated with the positive u component of the wind. The performance of the DMB model is tested by fitting it to two field-derived (Namibia's Skeleton Coast) datasets of wind velocity and sediment transport: (i) a 10-min (10Hz measurement resolution) dataset; (ii) a 2-h (1Hz measurement resolution) dataset. The DMB model is shown to outperform two existing models that rely on time-averaged wind velocity data (e.g. Radok, 1977; Dong et al., 2003), when predicting sand transport over the two experiments. For all measurement averaging intervals presented in this study (10Hz–10min), the DMB model predicted total saltation count to within at least 0.48%, whereas the Radok and Dong models over- or underestimated total count by up to 5.50% and 20.53% respectively. The DMB model also produced more realistic (less ‘peaky’) time series of sand flux than the other two models, and a more accurate distribution of sand flux data. The best predictions of total sand transport are achieved using our DMB model at a temporal resolution of 4s in cases where the temporal scale of investigation is relatively short (on the order of minutes), and at a resolution of 1min for longer wind and transport datasets (on the order of hours). The proposed new sand transport model could prove to be significant for integrating turbulence-scale transport processes into longer-term, macro-scale landscape modelling of drylands.

Karst groundwater source protection based on the time-dependent vulnerability assessment model: Crnica springs case study, Eastern Serbia

The implementation of sanitary protection zones is one of the most widely used approaches for preventive groundwater protection. Current regulations are usually based on the determination of the horizontal groundwater travel time component, while the vertical component is commonly neglected. Karst aquifers are especially sensitive to contamination through the unsaturated zone, and consequently numerous methods for determining intrinsic vulnerability have been developed. Many of these methods take into account the effects in the unsaturated zone, but mostly by indirect means. Vulnerability assessment methods do not fully reflect the component of groundwater residence time, making groundwater delineation zoning more difficult, with possible ambiguous and subjective results. Therefore, a method that incorporates the two equally important components (horizontal and vertical) is needed to facilitate groundwater protection zoning. The time-dependent model represents a redesigned vulnerability assessment method, created for karst aquifers, to incorporate the travel time component. This model incudes horizontal and vertical groundwater flow components and also considers a surface component toward ponor zones. The baseline for groundwater travel time through the unsaturated zone was adopted from the Time–input method. The estimation of the horizontal travel time component was based on the conceptual duality of flow in karst aquifers, which has fast and slow components. For the allogenic part of the karst aquifer catchment area (subcatchments of the ponor zone) travel time components were estimated according to different influencing factors e.g. slope, soil type, vegetation, and rainfall intensity. This methodology was tested on the case example of the Crnica karst source located at the western part of the Kucaj anticline in Eastern Serbia. The methodology was shown to be more accurate and appropriate for the delineation of the groundwater protection zones than existing approaches.

Kinetic Energy Budget during the Genesis Period of Tropical Cyclone Durian (2001) in the South China Sea

Abstract A set of kinetic energy (KE) budget equations associated with four horizontal flow components was derived to study the KE characteristics during the genesis of Tropical Cyclone (TC) Durian (2001) in the South China Sea using numerical simulation data. The genesis process was divided into three stages: the monsoon trough stage (stage 1), the midlevel mesoscale convective vortex (MCV) stage (stage 2), and the establishment stage of the TC vortex (stage 3). Analysis showed that the KE of the symmetric rotational flow (SRF) was the largest and kept increasing, especially in stages 2 and 3, representing the symmetrization process during TC genesis. The KE of the SRF was mainly converted from the KE of the symmetric divergent flow (SDF), largely transformed from the available potential energy (APE). It was found that vortical hot towers (VHTs) emerged abundantly, aggregated, and merged within the MCV region in stages 1 and 2. From the energy budget perspective, massive moist-convection-produced latent heat was concentrated and accumulated within the MCV region, especially in stage 2, and further warmed the atmosphere, benefiting the accumulation of APE and the transformation from APE to KE. As a result, the midlevel circulation (or MCV) grew strong rapidly. In stage 3, the intensity and number of VHTs both decreased. However, affected by increasing lower-level inward radial wind, latent heat released by the organized convection, instead of disorganized VHTs in the first two stages, continuously contributed to the strengthening of the surface TC circulation as well as the warm core.

Hydrochemical and 14C constraints on groundwater recharge and interbasin flow in an arid watershed: Tule Desert, Nevada

Summary Geochemical data deduced from groundwater and vein calcite were used to quantify groundwater recharge and interbasin flow rates in the Tule Desert (southeastern Nevada). 14 C age gradients below the water table suggest recharge rates of 1–2 mm/yr which correspond to a sustainable yield of 5 × 10 −4 km 3 /yr to 1 × 10 −3 km 3 /yr. Uncertainties in the applied effective porosity value and increasing horizontal interbasin flow components at greater depths may bias these estimates low compared to those previously reported using the water budget method. The deviation of the groundwater δ 18 O time-series pattern for the Pleistocene–Holocene transition from that of the Devils Hole vein calcite (which is considered a proxy for local climate change) allows interbasin flow rates of northerly derived groundwater to be estimated. The constrained rates (75.0–120 m/yr) are slightly higher than those previously calculated using Darcy’s Law, but translate into hydraulic conductivity values strikingly similar to those obtained from pump tests. Data further indicate that production wells located closer to the western mountainous margin will be producing mainly from locally derived mountain-system recharge whereas wells located closer to the eastern margin are more influenced by older, regionally derived carbonate groundwater.

Effects of a Shielding Skirt for Prevention of Sea Lice on the Flow Past Stocked Salmon Fish Cages

The effect of a shielding skirt, a tarpaulin mounted from the surface down to 5 m depth around a net cage, on the flow pattern at a commercially stocked salmon cage was investigated. Dye was used as a tracer for water movement and the dye spreading was monitored using aerial images. Current meters were employed to investigate the flow close to the net inside and outside the cage. Tests were conducted with and without the shielding skirt. The focus was on the effectiveness of the shielding skirt to deflect water around the cage. This study shows that a shielding skirt can reduce horizontal flow components significantly inside a cage, which is related to a reduction of water exchange. The flow toward a cage is divided by a shielding skirt, i.e., some of the water is transported around the cage, while some is passing underneath the shielding skirt. Some water entering the fish cage from underneath the tarpaulin is transported toward the surface inside the cage. The use of a shielding skirt might not prevent interaction of the upper water layers inside and outside of a fish cage completely, but it has the potential to reduce the inflow of surface water into the cage, if deployed properly.

A 3D analysis algorithm to improve interpretation of heat pulse sensor results for the determination of small-scale flow directions and velocities in the hyporheic zone

The hyporheic zone is strongly influenced by the adjacent surface water and groundwater systems. It is subject to hydraulic head and pressure fluctuations at different space and time scales, causing dynamic and heterogeneous flow patterns. These patterns are crucial for many biogeochemical processes in the shallow sediment and need to be considered in investigations of this hydraulically dynamic and biogeochemical active interface. For this purpose a device employing heat as an artificial tracer and a data analysis routine were developed. The method aims at measuring hyporheic flow direction and velocity in three dimensions at a scale of a few centimeters. A short heat pulse is injected into the sediment by a point source and its propagation is detected by up to 24temperature sensors arranged cylindrically around the heater. The resulting breakthrough curves are analyzed using an analytical solution of the heat transport equation. The device was tested in two laboratory flow-through tanks with defined flow velocities and directions. Using different flow situations and sensor arrays the sensitivity of the method was evaluated. After operational reliability was demonstrated in the laboratory, its applicability in the field was tested in the hyporheic zone of a low gradient stream with sandy streambed in NE-Germany. Median and maximum flow velocity in the hyporheic zone at the site were determined as 0.9×10−4 and 2.1×10−4ms−1 respectively. Horizontal flow components were found to be spatially very heterogeneous, while vertical flow component appear to be predominantly driven by the streambed morphology.

Subsurface Supergranular Vertical Flows as Measured Using Large Distance Separations in Time–Distance Helioseismology

As large-distance rays (say, 10 – 24°) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows within a few Mm of the solar surface. All previous analyses of supergranulation have used smaller separations and have been hampered by the difficulty of separating the horizontal and vertical flow components. We find that the large-separation travel times associated with supergranulation cannot be studied using the standard phase-speed filters of time–distance helioseismology. These filters, whose use is based upon a refractive model of the perturbations, reduce the resultant travel-time signal by at least an order of magnitude at some distances. More effective filters are derived. Modeling suggests that the center–annulus travel-time difference [δt oi] in the separation range Δ=10 – 24∘ is insensitive to the horizontally diverging flow from the centers of the supergranules and should lead to a constant signal from the vertical flow. Our measurement of this quantity, 5.1±0.1 seconds, is constant over the distance range. This magnitude of the signal cannot be caused by the level of upflow at cell centers seen at the photosphere of 10 m s−1 extended in depth. It requires the vertical flow to increase with depth. A simple Gaussian model of the increase with depth implies a peak upward flow of 240 m s−1 at a depth of 2.3 Mm and a peak horizontal flow of 700 m s−1 at a depth of 1.6 Mm.

On the generation and evolution of numerically simulated large-amplitude internal gravity wave packets

Numerical simulations of internal gravity wave (IGW) dynamics typically rely on wave velocity and density fields which are either generated through forcing terms in the governing equations or are explicitly introduced as initial conditions. Both approaches are based on the associated solution to the inviscid linear internal wave equations and, thus, assume weak-amplitude, space-filling waves. Using spectral multidomain-based numerical simulations of the two-dimensional Navier–Stokes equations and focusing on the forcing-driven approach, this study examines the generation and subsequent evolution of large-amplitude IGW packets which are strongly localized in the vertical in a linearly stratified fluid. When the vertical envelope of the forcing terms varies relatively rapid when compared to the vertical wavelength, the associated large vertical gradients in the Reynolds stress field drive a nonpropagating negative horizontal mean flow component in the source region. The highly nonlinear interaction of this mean current with the propagating IGW packet leads to amplification of the wave, a significant distortion of its rear flank, and a substantial decay of its amplitude. Scaling arguments show that the mean flow is enhanced with a stronger degree of localization of the forcing, larger degree of hydrostaticity, and increasing wave packet steepness. Horizontal localization results in a pronounced reduction in mean flow strength mainly on account of the reduced vertical gradient of the wave Reynolds stress. Finally, two techniques are proposed toward the efficient containment of the mean flow at minimal computational cost. The findings of this study are of particular value in overcoming challenges in the design of robust computational process studies of IGW packet (or continuously forced wave train) interactions with a sloping boundary, critical layer, or caustic, where large wave amplitudes are required for any instabilities to develop. In addition, the detailed description of the dynamics of the wave generation region may offer a first probe into the underlying physics of disruptive near-source nonlinearities observed in laboratory experiments of persistently forced IGW beams. Finally, the question arises as to whether a highly vertically compact IGW packet, which has propagated far from its source but still maintains its original structure and amplitude, can indeed occur in nature.