Interactions between Gravity Waves and Cold Air Outflows in a Stably Stratified Uniform Flow

Abstract. Gravity waves play a significant role in driving the semiannual oscillation (SAO) of the zonal wind in the tropics. However, detailed knowledge of this forcing is missing, and direct estimates from global observations of gravity waves are sparse. For the period 2002–2018, we investigate the SAO in four different reanalyses: ERA-Interim, JRA-55, ERA-5, and MERRA-2. Comparison with the SPARC zonal wind climatology and quasi-geostrophic winds derived from Microwave Limb Sounder (MLS) and Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) satellite observations show that the reanalyses reproduce some basic features of the SAO. However, there are also large differences, depending on the model setup. Particularly, MERRA-2 seems to benefit from dedicated tuning of the gravity wave drag parameterization and assimilation of MLS observations. To study the interaction of gravity waves with the background wind, absolute values of gravity wave momentum fluxes and a proxy for absolute gravity wave drag derived from SABER satellite observations are compared with different wind data sets: the SPARC wind climatology; data sets combining ERA-Interim at low altitudes and MLS or SABER quasi-geostrophic winds at high altitudes; and data sets that combine ERA-Interim, SABER quasi-geostrophic winds, and direct wind observations by the TIMED Doppler Interferometer (TIDI). In the lower and middle mesosphere the SABER absolute gravity wave drag proxy correlates well with positive vertical gradients of the background wind, indicating that gravity waves contribute mainly to the driving of the SAO eastward wind phases and their downward propagation with time. At altitudes 75–85 km, the SABER absolute gravity wave drag proxy correlates better with absolute values of the background wind, suggesting a more direct forcing of the SAO winds by gravity wave amplitude saturation. Above about 80 km SABER gravity wave drag is mainly governed by tides rather than by the SAO. The reanalyses reproduce some basic features of the SAO gravity wave driving: all reanalyses show stronger gravity wave driving of the SAO eastward phase in the stratopause region. For the higher-top models ERA-5 and MERRA-2, this is also the case in the lower mesosphere. However, all reanalyses are limited by model-inherent damping in the upper model levels, leading to unrealistic features near the model top. Our analysis of the SABER and reanalysis gravity wave drag suggests that the magnitude of SAO gravity wave forcing is often too weak in the free-running general circulation models; therefore, a more realistic representation is needed.

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 (Hi ), and inversion layer Froude number (Fri ) 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.

Understanding how wind turbines interact with large-scale atmospheric phenomena is an increasingly important issue for wind farm developers. With the latest 15 MW turbines reaching heights of 270 m, several studies have predicted that farms of these turbines will be able to induce Atmospheric Gravity Waves (AGWs). These buoyancy-driven waves are triggered as a result of a farm vertically deflecting thermally stratified flow above the turbine array. In particular, as the temperature inversion above the North Sea is typically located at heights near the top of a 15 MW turbine, farms in this region may be especially susceptible to generating AGWs. Hence, with most European offshore wind farms based in the North Sea, understanding the interactions with, and impact of, these waves is vital for yield prediction.Recent studies have shown that AGWs cause a redistribution of flow at the farm scale, altering wind farm power production. As a result, AGWs provide a new challenge for wind farm planning and raise questions about whether farm design can influence how the AGW is triggered, and if these AGWs also have impacts at the turbine scale. To address these questions, large eddy simulations using actuator line turbine representations were undertaken. These simulations replicated the typical atmospheric turbulence, Coriolis force and thermal parameters seen in the North Sea.First, the middle turbine of an infinitely wide row was simulated. The turbine triggered an AGW, and the flow field was compared to a wave-free case. The AGW was found to cause upstream flow deceleration, accelerate bypass flow above the turbine wake, and cause pockets of acceleration within the wake itself at AGW troughs. Overall, this led to faster wake recovery than in a wave-free case.Following this, simulations were conducted using two turbines aligned in the streamwise direction, each representative of the middle turbine in an infinitely wide row. Introducing a second turbine triggered stronger AGWs, magnifying their effects on the flow. Furthermore, by varying the position of the downstream turbine, it was possible to both amplify and dampen the AGW produced, along with causing a shift in the wave phase. The power of the second turbine was found to vary sinusoidally with the change in turbine position. When in line with an AGW trough, the second turbine even outperformed the first despite sitting in its wake. However, the increased power came at the cost of a higher mean blade loading and an increase in cyclic loading.This work demonstrates that AGWs can impact intra-farm flows and turbine performance. Additionally, it confirms an interdependence between AGWs and wind farm turbine spacing. Given the variation in the AGW with spacing, it may become an important factor in design which considers both intra-farm and farm-to-farm scale flows.

Background: UV occultations measured by Voyager 2 during its flyby of Uranus in 1986 detected a warm stratosphere and extremely hot thermosphere [1, 2], far in excess of solar irradiance [3, 4] or internal heating [5]. These measurements imply that Uranus has the coldest lower stratosphere and yet the hottest thermosphere of any Solar System planet [6] (see Figure 1, dashed line). Uranus has the weakest internal heat of any of the giant planets [5]. The fundamental lack of understanding about the energy balance of Uranus is an example of the “giant planet energy crisis” [7].Furthermore, the Voyager 2 UV occultation measurements and models were in stark tension with Earth-based stellar occultations observed between 1977 and 1996. In [8] and [9], we present the results of reprocessing 26 archival occultations using modern techniques. While stratospheric tensions have decreased, thermospheric tensions remain, calling into question the Voyager 2 findings. In [9], we present a new 1-D atmospheric model that successfully reproduces these results. Aims: We present a new representative temperature-pressure profile for the atmosphere of Uranus from reprocessed stellar occultation observations and 1-D atmospheric modeling [8, 9]. We discuss the energy inputs to the thermosphere, circulation necessary to explain the new profiles, and the significant, potential magnetosphere-ionosphere-thermosphere interactions at Uranus. We describe critical measurements from a likely Uranus Orbiter and Probe (UOP) mission as well as from Earth beforehand that would enable the study of the energy inputs to Uranus. Prior Results & Conclusions: We reprocessed 26 archival Uranus stellar occultations, which produced temperature-pressure profiles inconsistent with Voyager 2 UVS profiles [8, 9]. A 1-D atmospheric model comprised of radiative-convective and conduction models was developed for Uranus based on these reprocessed profiles. The model reproduces the profiles and suggests a heat sink exists in the lower thermosphere. Figure 1 shows the new reference temperature-pressure profile for Uranus in comparison to the Voyager 2 profile and profiles for other planets.We conclude that the mesopause of Uranus is likely significantly higher in altitude (~10-4 mbar) than suggested from Voyager 2 profiles (~1 mbar), consistent with the mesopause levels of the other giant planets [9, 10]. We find that the stratosphere of Uranus likely contains a nearly isothermal region, again, consistent with those of the other giant planets [9, 10]. Last, we find that the required thermospheric energy flux is tens of times the solar EUV flux, underscoring the energy crisis and motivating detailed study of energy sources in the Uranian system. Ongoing Work: Measurements of Jupiter and Saturn have identified an energy crisis similar to that of Uranus. The emerging solution involves gravity waves activity that facilitates heating of the thermospheres by inducing Rayleigh drag in the polar regions. This breaks down the Coriolis force and enables meridional transport of strong auroral [11, 12] heating. While it is likely that Uranus has significant gravity wave activity [13, 14], it is possible that the auroral inputs to Uranus occur around the entire planet and are not limited to the poles [15, 16]. Much work is underway to better understand the shape and behavior of the magnetosphere of Uranus. Gravity waves may also provide the dynamical transport needed to create the heat sink observed in our new 1-D model.Therefore, additional observations of the prevalence and properties of gravity waves are critical to extending recent modeling work from Jupiter and Saturn to Uranus. While UOP may make many such observations in the 2050s, we outline Earth-based observations that can be made prior. Upcoming Stellar Occultations: In [17], we predicted Uranus and Neptune occultations 2025 – 2035 that could be observed from the ground and/or from low-Earth orbit. Additional predictions can be found in [18]. The most promising Uranus events occur in 2025, 2031, and 2032. We will describe how we intend to observe the 2025 occultation from ground-based and airborne assets, as well as other upcoming observing campaigns. We will present simulated results for temperature profiles of Uranus as well as gravity wave detections. The Shadow Chaser: In [17], we outlined the case for a low-Earth orbit small satellite to observe stellar occultations to better constrain the temperature and density profiles of the upper atmosphere of Uranus and to detect gravity waves. This mission concept, called the Shadow Chaser, is being explored at NASA Langley Research Center. By observing above the atmosphere, the Shadow Chaser could observe during the day and would not be impacted by scintillation, greatly increasing signal-to-noise. We will present simulations showing the Uranus profiles that would result from the Shadow Chaser observing the 2031 Uranus event, during which Uranus will occult a 4th magnitude K-band star. 

Field observations imply that accumulation and advection of invertebrate larvae and other plankton by propagating fronts provides an efficient mechanism for the cross‐shelf transport and subsequent coastal settlement of larvae and plankton. Gravity currents propagating into a heavier, uniform‐density fluid are known to have near‐surface velocities u that exceed the propagation speed c of the gravity current nose. It is shown by simple dam‐break laboratory experiments and through corresponding numerical solutions of two‐dimensional stratified flow and Lagrangian particle advection that this characteristic of gravity currents can lead to accumulation in the gravity current nose of particles that originate well behind the gravity current head. However, efficient particle accumulation and transport with the speed c only occurs for particles with sufficient vertical buoyancy or vertical swimming capability. Weakly buoyant or neutral particles are swept down and back away from the gravity current head by the circulation in this region. A dam break into an ambient fluid with stratification (two‐layered) could result in the transport of some particles that are initially trapped in the forepart of the leading disturbance, an undular bore. However, this situation does not result in significant accumulation of particles at the leading edge of the disturbance. The numerical solutions show that particles that originate in the dense fluid ahead of the gravity current are much less likely to be accumulated at the gravity current nose. A simple scaling criterion for the minimum vertical buoyancy velocity for efficient accumulation and transport of buoyant particles based on the gravity current and particle characteristics is developed and compares favorably with the numerical results. The implications of these results for transport of larvae in coastal environments are discussed.

Gravity currents modify their flow characteristics by entraining ambient fluid, which depends on a variety of governing parameters such as the initial density, Δρ, the total initial height of the fluid, H, and the slope of the terrain, α, from where it is released. It is imperative to study the entrainment dynamics of a gravity current in order to have a clear understanding of mixing transitions that govern the flow physics, the velocity mixing layer thickness, δu, and the density mixing layer thickness, δρ. Experiments were conducted in a lock-exchange facility in which the dense fluid was separated from the ambient lighter fluid using a gate. As the gate is released instantaneously, an energy conserving gravity current is formed, for which the only governing parameter is the Reynolds number defined as Re=Uhν, where U is the front velocity of the gravity current and h is the height of the current. In our study, the bulk Richardson number (inverse of Froude number, Fr), Rib = g′HUb2 = 1, takes a constant value for all the experiments, with Ub being the bulk velocity of the current defined as Ub = g′H. Simultaneous particle image velocimetry and planar laser induced fluorescence measurement techniques are employed to get the velocity and density statistics. Using the buoyancy conservation equation, a new flux-based method was formulated for calculating the entrainment coefficient, EF, near the front and head of the propagating gravity current for a Reynolds number range of Re ≈ 485-12 270 used in our experiments. At the head of the current, the results show a mixing transition at Re ≈ 2700 that is attributed to the flow transitioning from weak Holmboe waves to Kelvin-Helmholtz instabilities, in the form of Kelvin-Helmholtz vortex rolls. Following this mixing transition, the entrainment coefficient continued to increase with increasing Reynolds number owing to the occurrence of three-dimensional Kelvin-Helmholtz billows that promote further small-scale local mixing. Such a mixing transition indicates that a fully turbulent state is not reached even at Re = 12 270 and the amount of entrainment and ensuing mixing depends on the type of flow instability and presence of small-scale secondary structures. The entrainment dynamics were further substantiated using the ratio of δu and δρ. It was observed that δuδρ decreases with increasing Re and reaches a constant value of δuδρ≈ 1 at high values of Re. This trend is in contrast to the entrainment coefficient EF, which never reaches a constant value even at high enough Re. This disparity could be explained by the fact that EF accounts for small-scale scalar mixing, which is not captured by the ratio of mixing layer thicknesses. Experimentally, it was also observed that the EF value near the front of gravity current was 2-9 times higher than the head value depending on the value of the Reynolds numbers. At low Reynolds numbers, the entrainment near the front is an order of magnitude higher than the head and the value decreases with increasing Re. This could be attributed to different modes of entrainment near the front (dominated by vortical structures) and the head (dominated by turbulent flux exchange triggered by the nature of the flow instability). The results from this study improve our understanding of entrainment dynamics and would be useful in developing empirical parameterizations for mixing in stratified flows.

Suspended particle transport is inherent in a wide range of industrial and environmental flows, from energy generation to manufacturing and from marine to atmospheric systems. Such flows are inherently stratified where varying concentration of particulates changes the mean density of the fluid; however, the role of stratification on particle suspension is poorly understood. Here the suspension of sediments in a channel (plane Poiseuille) flow is resolved using numerical simulation where the flow is stably thermally stratified and the particles passive. This set up enables quantification of stratification controls sediment transport processes. Sediment suspension is resolved for settling velocities of V s = 0.005 , V s = 0.01 , and V s = 0.02 , made dimensionless by the friction velocity u τ . Our results show that stratification generates flow-scale mixing processes, which invalidate extant models of sediment suspension that have been used for over 100 years. For stratified flows, the dimensionless collapse of flow scalars and turbulent statistics is poor near the core of the channel, where large concentration gradients coincide with large-scale mixing events. Here the differences between vertical turbulent diffusivities of sediment and temperature increase with increasing V s , reaching 15 % for V s = 0.02 . Discrepancies arise due to a breakdown of the linear gradient diffusion hypothesis. Predictions using the gradient diffusion hypothesis are expected to worsen with increasing settling velocity, indicating that classical models poorly predict dilute particle transport in strongly stratified flows, which are common in a range of environmental and industrial settings. Further, in stratified flows a feedback loop is established that generates strong buoyancy forces in the core of the duct, having the profound impact of building a self-reinforcing two-layer sediment concentration profile. These results highlight that classical sediment transport models may underpredict the amount of turbulent mixing, and therefore the capability of flows to suspend material, where flow-scale mixing events occur. They further reveal mechanisms for the formation of a barrier to mixing which significantly reduces suspended load capacity in flows with an internal velocity maximum, such as ducts, pipes, gravity currents, and jets.

Convective generation and vertical propagation of fast gravity waves on Mars: One- and two-dimensional modeling

The basic processes of time-dependent nonlinear horizontal convection caused by differential bottom cooling in a two-dimensional stratified Boussinesq fluid are investigated both theoretically and numerically. The fluid is initially at rest, and horizontal convection is induced by suddenly cooling one half of the bottom boundary. It is shown that three distinct flow regimes exist according to the nondimensional elapsed time and the nondimensional stratification parameter: diffusion regime, gravity current regime, and gravity wave regime. In each regime, existence of a self-similar solution is predicted theoretically, and its realizability is confirmed by a numerical experiment. The vertical length scale of the circulation in each regime is given by the diffusion length scale. The horizontal length scales of the circulation in the diffusion, gravity current, and gravity wave regimes are determined by the diffusive spread, horizontal propagation of the gravity current, and horizontal propagation of the gravity wave, respectively. The presence of a self-similar solution for each flow regime gives a useful perspective about the development process and dynamics of horizontal convections in the atmosphere. For example, the formation process of a steady heat/cool island circulations is understood as a merging of two horizontal convection initiated from both ends of the heat/cool island. In fact, this interpretation is proved to give correct estimates for the vertical scale of the circulation as well as the time required for the formation of the steady heat/cool island circulation.

Detailed synoptic-scale map analysis and diagnosis for all six low-level jet (LLJ) cases that occurred during the Taiwan Area Mesoscale Experiment (TAMEX) were made to study the structure and the development of the LLJs. It was shown that the development of these LLJs was closely linked to the development of a lee trough to the cast of the Tibetan Plateau. Seasonal change had a profound influence on the secondary circulation across the jet-front system. Before the seasonal transition, the formation of a lee trough with closed isobars in low levels east of the Tibetan Plateau occurred as an upstream short-wave trough moved eastward with strengthening westerlies over the Tibetan Plateau in upper levels. After the development of the lee trough, the southwest flow appeared in the southeast quadrant of the Ice trough. As the upstream trough moved farther eastward, it merged with the lee trough, and the low-level southwesterly flow intensified. For most cases, a midlatitude deep trough was present to the north or northeast at this time; the northwesterlies behind the midlatitude trough brought in the cold air to the rear of the merged trough. The upper-level jet ahead of the merged trough strengthened. The secondary circulation across the jet-front system was characterized by a thermally direct circulation across the baroclinic zone, with warm air rising within the southwest monsoon flow, cold air sinking in the postfrontal northeasterlies, and a weak thermally indirect circulation to the south. After the seasonal transition, the major baroclinic zone shifted northward, and the upper-level south Asian high pressure cell moved over the Tibetan Plateau. The Tibetan high dominated the upper-level circulations with easterlies along the southern China coast, preventing baroclinic disturbances from moving into southern China. At 1200 UTC 22 June 1987, an orographically induced lee trough formed in the lee side of the Tibetan Plateau. An LLJ was observed during 0000 UTC 23 June-0000 UTC 25 June 1987 over the southern China coast as a southwest vortex developed within the lee trough. The formation of the vortex was driven by latent heat release in a barotropic environment. The secondary circulation associated with the LLJ was characterized by a rising motion northwest of the LLJ axis and a broad sinking motion to the south.

Gravity currents are of high interest both for their relevance in natural scenarios and because varying horizontal buoyancy presents a canonical problem in fluid mechanics [Huppert, “Gravity currents: A personal perspective,” J. Fluid Mech. 554, 299–322 (2006)]. In this paper, attention is directed to gravity currents with a full-depth lock release propagating into a linearly stratified ambient fluid. For the case of an unstratified ambient, similarity solutions are known to capture the evolving height profile of the gravity current. We will compare this solution class with numerical data from high fidelity simulations. The presence of ambient stratification (quantified by the stratification intensity, S) introduces internal gravity waves that interact with the propagating current head, which will inhibit Kelvin–Helmholtz billows, decelerate current propagation, and smooth the shape of the current head. We perform direct numerical simulations of planar two- and three-dimensional gravity currents released into stratified ambient fluid of varying S and analyze the gravity current kinematics. Our analysis complements existing findings from performed laboratory and numerical experiments [Dai et al., “Gravity currents propagating at the base of a linearly stratified ambient,” Phys. Fluids 33, 066601 (2021)] that show a stratified ambient modifies the current front velocity. Previous literature employed has inconsistent Reynolds numbers and boundary conditions, complicating interpretations. In the present numerical campaign, a closer analysis clarifies influence of the top boundary condition choice on formation and structure of the internal gravity waves. While acknowledging there is no available choice for a high-accuracy simplified numerical representation of a free-surface, a family of profiles for internal wave formation emerges varying with buoyancy Reynolds number and top boundary condition selection. The subsequent results appraise similarity solutions for the distribution of the heavy fluid in the gravity current. Our results show that for unstratified and low stratification ambient fluid, height profiles permit a similarity solution but higher values of S are less amenable; these profiles suggest a continuing time dependency on the traveling internal wave.

The impact of mesh adaptivity on the gravity current front speed in a two-dimensional lock-exchange

This report of the Task Committee on Preparation of Sedimentation Manual, part of their proposed Report on Sedimentation Engineering, deals with the density currents, defined as the movement under gravity of a stream of fluid under, through, or over another fluid, the density of which differs by a small amount from that of the primary current. The basic principles presented are mainly those concerned with the mechanics and sedimentation characteristics of sediment-laden under-flows as found in reservoirs. Means of determining certain basic relationships among the major variables such as velocity, depth, slope, density difference, and the boundary conditions of the underflow are presented. Resistance laws for uniform underflows are examined. The stability and mixing in stratified flows as well as the transportation of sediment by density currents are considered.

A series of numerical simulations of tropical cyclones in idealized large-scale environments is performed to examine the effects of vertical wind shear on the structure and intensity of hurricanes. The simulations are performed using the nonhydrostatic Pennsylvania State University–National Center for Atmospheric Research fifth-generation Mesoscale Model using a 5-km fine mesh and fully explicit representation of moist processes. When large-scale vertical shears are applied to mature tropical cyclones, the storms quickly develop wavenumber one asymmetries with upward motion and rainfall concentrated on the left side of the shear vector looking downshear, in agreement with earlier studies. The asymmetries develop due to the storm's response to imbalances caused by the shear. The storms in shear weaken with time and eventually reach an approximate steady-state intensity that is well below their theoretical maximum potential intensity. As expected, the magnitude of the weakening increases with increasing shear. All of the storms experience time lags between the imposition of the large-scale shear and the resulting rise in the minimum central pressure. While the lag is at most a few hours when the storm is placed in very strong (15 m s−1) shear, storms in weaker shears experience much longer lag times, with the 5 m s−1 shear case showing no signs of weakening until more than 36 h after the shear is applied. These lags suggest that the storm intensity is to some degree predictable from observations of large-scale shear changes. In all cases both the development of the asymmetries in core structure and the subsequent weakening of the storm occur before any resolvable tilt of the storm's vertical axis occurs. It is hypothesized that the weakening of the storm occurs via the following sequence of events: First, the shear causes the structure of the eyewall region to become highly asymmetric throughout the depth of the storm. Second, the asymmetries in the upper troposphere, where the storm circulation is weaker, become sufficiently strong that air with high values of potential vorticity and equivalent potential temperature are mixed outward rather than into the eye. This allows the shear to ventilate the eye resulting in a loss of the warm core at upper levels, which causes the central pressure to rise, weakening the entire storm. The maximum potential vorticity becomes concentrated in saturated portions of the eyewall cloud aloft rather than in the eye. Third, the asymmetric features at upper levels are advected by the shear, causing the upper portions of the vortex to tilt approximately downshear. The storm weakens from the top down, reaching an approximate steady-state intensity when the ventilated layer can descend no farther due to the increasing strength and stability of the vortex at lower levels.

Downslope winds and lee gravity waves are common features of mountainous environments. A similar weather type at Mt. Parnassos in Arachova, Greece is known as “Katevatos” and has devastating results for the population and visitors at the local touristic resorts. In this study, we analyze three incidents of this atmospheric pattern at local scale resolution (1 × 1 km) with WRF model. This is the first study of this local weather hazard, and the following key factors are identified. (I) The main synoptic forcing is the propagation of an upper-level trough from central Europe towards the Balkans. (II) The associated generation of a surface low-pressure system over the Aegean Sea results in a northeast flow in the lower troposphere that is perpendicular to the main topographic ridge of Mt. Parnassos. (III) Generation of gravity waves and downward reflection of wave energy at the critical level between the upper level flow and the undercutting northeast current result in the formation of “Katevatos” downslope wind at the lee side of the mountain. This hurricane-scale wind is accompanied with horizontal transport of frozen rain and snow from the mountain tops towards the village of Arachova. This wind pattern appeared also during the battle of Arachova in November 1826 between the Greek and Ottoman forces resulting in enormous casualties due to the adverse weather conditions.