1. Introduction
In thunderstorm cloud systems, once a strong downdraft hits the ground, it forms strong destructive winds that diverge into the surrounding areas. This type of downdrafts, which induces catastrophic gales at or near the surface, was first defined as a downburst by Fujita and Byers (1977). Downbursts are mostly generated in mature and strong thunderstorms, which usually correspond to strong localized depressions. The wind speed induced by downbursts exceeds 17.9 m s−1, and the ground wind field exhibits a divergent pattern with disastrous gales (Fujita 1985; Holmes 2002). According to the spatial scale and duration of downbursts, they can be divided into macrodownbursts and microdownbursts (Fujita 1985). The maximum horizontal outflow scale of a macrodownburst is more than 10 km and its duration is longer than 10 min. For microdownbursts, the maximum horizontal outflow scale is less than 4 km and the duration is less than 10 min (Wilson et al. 1984; Fujita 1985).
Downbursts threaten the aviation industry, building structure, agricultural production, and power transmission, as well as many other fields, and they cause unpredictable serious disasters because of the large low-level wind shear (Lombardo et al. 2014; Mahale et al. 2016). In addition, low-level wind shear is characterized by short duration and high intensity, it is difficult to accurately observe and forecast downbursts. Therefore, early warning and forecasting of wind shear remains a challenging issue in operational weather forecasting (Solari et al. 2015). Owing to the importance of downbursts and their associated weather phenomena (e.g., haboob dust formed by downburst winds) (Miller et al. 2008), a great deal of attention has been paid to the study of downbursts (Wang et al. 2013). Field studies, including the Northern Illinois Meteorological Research on Downbursts (NIMROD) (Fujita 1985), the Joint Airports Wind Shear (JAWS) (McCarthy et al. 1982; Wilson et al. 1984), the Federal Aviation Administration (FAA)/Lincoln Laboratory Operational Weather Studies (FLOWS) (Wolfson et al. 1985), and the Microburst and Severe Thunderstorm (MIST) projects (Dodge et al. 1986; Atkins and Wakimoto 1991), have been conducted to understand the physical properties of downbursts (Alahyari and Longmire 1995). The properties of airflow within the downburst were measured through those field experiments. The characteristics of typical downburst width, asymmetric outflows and deeper microburst storms, etc., are presented in Wilson et al. (1984) and Atkins and Wakimoto (1991). However, the details of the downburst structure and its formation mechanism were not deeply understood. The results of the observation studies have helped to promote the numerical studies of dust storms induced by downbursts.
Several numerical simulations have been performed to model the structure and evolution of downbursts, and they were initiated by imposing a cooling source in the upper level of the model domain (Anderson et al. 1992; Orf et al. 1996) or by specifying a precipitation distribution at the top boundary of the model (Hjelmfelt 1982; Proctor 1988, 1989; Straka and Anderson 1993). The k-epsilon turbulence model has been used to study the influence of thunderstorm downdrafts on the wind speed and the features of the kinetic energy and momentum budgets of traveling microbursts in unidirectional sheared environments (Panneer Selvam and Holmes 1992; Orf and Anderson 1999). Kim and Hangan (2007) employed computational fluid dynamics (CFD) software to investigate the time-dependent evolution of an impinging jet for various Reynolds numbers. A large-eddy model was employed by Anabor et al. (2011) and Huang et al. (2018) to simulate the turbulent characteristics of the cold pool outflow associated with a microburst-producing downdraft. Cloud simulations have also been used to evaluate the thermodynamic cooling in a downburst-producing thunderstorm cloud (Oreskovic et al. 2018). The Weather Research and Forecasting (WRF) Model with a high spatiotemporal resolution has been used to perform a detailed analysis of the variables and structure of the microburst (Bolgiani et al. 2020). These field programs and simulation studies have helped us understand the features of the structure and evolution of downbursts. However, those studies were performed over homogenous surfaces. The effects of surface dynamics on the downburst evolution and the turbulence in cold pool are still unclear.
The cooling source method introduced by Anderson et al. (1992) is an idealized numerical approach, which attempts to reproduce the thermodynamic processes in a thunderstorm cloud system by adopting a spatially and temporally dependent cooling source that grows in the atmosphere (Oreskovic et al. 2018). In this method, a cooling source with a spatially and temporally varying cooling rate is added to a dry adiabatic atmosphere. Vermeire et al. (2011) used a large-eddy model to simulate a downburst and proposed that a cooling source model can simulate the features of such an event. It has been confirmed that an idealized cooling source model is a practical simplification method to describe the thermodynamic cooling in a natural thunderstorm cloud system since the various parameters of the source itself can be modified (Lin et al. 2007). But the factors that affect downburst intensity and the turbulence in cold pool are not fully understood. In addition, the influence of the topography on the structure and intensity of turbulent vortex during a downburst remains unclear (Wood et al. 2001). The turbulence characteristics (such as turbulence intensities, length scales) are essential to the development of downburst (Aboshosha et al. 2015). Homar et al. (2003) pointed out that the complex terrain greatly increased the destructiveness of the storm. Thus, the goal of this work is to explore the occurrence and development of a downburst via the cooling source method and further probe the effects of an isolated hill on turbulence in cold pool.
This paper is organized as follows. Section 2 describes the data and experimental design. Section 3a discusses the structure, development, and average kinetic energy of the downburst. Section 3b briefly examines the effects of the width and height of the hill on the structure and evolution of the downburst. The summary and conclusions are presented in section 4.
2. Model setup and methods
The numerical model used in this study is the Met Office boundary layer model, Boundary Layer Above Stationary, Inhomogeneous Uneven Surface (BLASIUS) model, which has been described by Wood and Mason (1991, 1993). This model is nonhydrostatic and employs a terrain-following coordinate system (Mason and Sykes 1982; Mason 1987). The BLASUIS model based on the ensemble averaged Navier–Stokes equations can be used to simulate either laminar or turbulent flow. This is achieved by adding together the turbulent viscosity and the molecular or constant laminar viscosity (Clark 1977). The model using terrain-following coordinate transformation was coded to be periodic in both horizontal directions. Thus, the BLASIUS model has been widely used in the study of turbulence separation behind steep slopes, boundary layer turbulence over different underlying surfaces, cold air accumulation and atmospheric rotation in valleys, and terrain-induced gravity waves (Tian and Parker 2002a,b; Tian et al. 2003; Lewis et al. 2008; Vosper and Brown 2008; Wang et al. 2011).
The numerical experiments in this study were all three-dimensional, and the domain size was 50 km × 50 km × 10 km. According to Bolgiani et al. (2020), high-resolution numerical models are more appropriate for the simulation of downbursts. The model’s horizontal resolution was 0.25 km, and the vertical mesh was stretched and contained 30 points with a high vertical resolution in the surface layer. A periodic lateral boundary condition was used. To minimize the reflection of the internal gravity waves, an artificial Rayleigh damping layer was applied to the top half of the model domain. Each simulation experiment covered a 3-h period with a time step of 0.01 s. This study focused on the evolution of the density flow after the downburst occurred and the effects of the terrain on the turbulence of the downbursts. We used idealized simulations of a density current, which had properties that were generally consistent with those obtained from observations rather than simulations of any particular downburst event. According to the study of Orf and Anderson (1999), a sinking density flow can be generated by specifying a cooling source in the model, and the wet process related to water vapor condensation was not considered in this study.
The temporal function of the cooling rate g(t) is shown in Fig. 1a. Figure 1b shows the distribution of the spatial function R(x, y, z) at y = 25 km, which has a maximum of 1.0 in the cooling center, with the magnitude decreasing to zero at the edge of the cooling source (i.e., the potential temperature is equal to that of the ambient air).
Dimensionless (a) temporal [g(t)] and (b) spatial [R(x, y, z)] modulations of the maximum intensity of the cooling function.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
Schematic diagram showing a hill and the projection of the cooling center at the model surface. The red dot represents the projection of the cooling center, and the shaded area is the hill.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
The configurations of the hill top (km) and hill width (km) for the different runs. The same model parameters have been used for all sensitivity runs. The configuration/sensitivity runs are defined in section 3b.
Previous studies have shown that a deep dry adiabatic mixed layer favors the formation of a thunderstorm density flow (Knippertz et al. 2007; Roberts and Knippertz 2012; Huang et al. 2018). The model was initialized with a sounding profile characterized by an approximately 4-km-deep mixed layer with a stable layer above (Fig. 3). The profile is from a field experiment conducted by the Urumqi Institute of Desert Meteorology, China Meteorological Administration, in the hinterland of the Taklimakan Desert on 27 July 2016 (observational duration from 1 to 31 July) (Yin et al. 2021). To simulate the evolution of the downburst, perturbations in the model were generated by adding a cooling bubble and a hill in the model’s domain.
Vertical distributions (y–z) of the (a) potential temperature (K) at 66 min and (b) wind vector (m s−1) at 70 min from the standard run SNH.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
The vertical distribution of the potential temperature at 66 min shows that the largest cooling rate occurred in the cooling center with the lowest potential temperature (Fig. 3a). The cooling rate gradually decreased from the cooling center and was equal to the temperature of the ambient atmosphere at the edge of the cooling bubble. As can be seen from Fig. 3b, the density flow reached the ground and produced a sinking divergent current with a pair of clockwise and counterclockwise turbulent vortexes at a height of about 1 km near y = 21 and 29 km at 70 min, respectively, which is similar to the results of Orf et al. (1996) and Huang et al. (2018). Therefore, the method of adding a cooling source in the BLASUIS model to form a density flow in the standard run can be adopted to further simulate and analyze the effects of the terrain on the structure and evolution of a downburst.
3. Model results
Since the background wind and the environmental turbulence were not considered in the numerical experiments conducted in this study, the downburst simulation results are quasi-symmetrical in the horizontal direction. Some slight random disturbances were also ignored. In addition, to avoid the splashing effect caused by the sinking cooling air touching the ground, the following analysis of the downburst was conducted along the positive direction of the y axis starting at 28 km from the center of the model’s bottom to the edge.
a. Analysis of standard run
1) The development of a downburst
The development of a downburst based on the BLASIUS model is presented in Fig. 4. Figure 4a shows that after 76 min (at this time the cooling is already over), the density flow reaches the model’s surface and diverges to the surrounding areas, forming a cold pool, this result is consistent with previous study proposed by Mueller and Carbone (1987). At a distance of 8 km from the center of the model, the divergent airflow forms a counterclockwise turbulent vortex in the vertical direction, which is also called the head of the density flow (hereinafter referred to as the head). The potential temperature difference between the coldest area in the cooling center and the ambient environment is about 6 K, which is within the observed range of 2–14 K (Flamant et al. 2007; Engerer et al. 2008; Marsham et al. 2013; Provod et al. 2016). The height and width of the head are about 1.3 and 2.3 km, respectively. Behind the head, a secondary surge (secondary turbulent vortices) forms at a height of around 0.4 km, with a width of about 1 km. The average potential temperature of the secondary surge is lower than that of the head. The maximum wind speed in the cold pool is about 34.1 m s−1 at a height of 16 m and y = 32.3 km, while the average wind speed near the surface of the cold pool is about 15.0 m s−1. The similar maximum wind speed records are also observed in numerical simulation of extreme winds in Chen and Letchford (2007). In their study, based on discrete values at observation positions, mode mean speed time functions were estimated. Their results show that during downbursts, the maximum wind speed can reach 40 m s−1. Note that small eddies occur behind the secondary surge (e.g., at y < 30.5 km).
Vertical distributions (y–z) of the potential temperature (K; shading) and wind field (m s−1; vectors) for the standard run at (a) 76, (b) 80, (c) 84, and (d) 96 min. The red lines denote the potential temperature of 312 K.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
The height of the density current head decreases due to the relatively strong mixing between the head and its environment. By 80 min, the height of the head decreases to 0.81 km, and the movement speed of the leading edge is 8.8 m s−1 (Fig. 4b). It should also be noted that the distance between the secondary surge and the density current head is larger than at 76 min. The height of the secondary surge has decreased by about 20 m, and its width has increased by 0.4 km. The depth of the turbulent layer behind the secondary surge increases due to the occurrence of more cold air flowing underneath and the blocking of the downdraft from the secondary surge. The average wind speed near the ground decreases to 7.9 m s−1, with a maximum speed of 27.2 m s−1 in the density current head. By 84 min (Fig. 4c), the secondary surge becomes indistinct due to the turbulent mixing in the cold pool, and the isothermal surface of 312 K tends to be flatter behind the head. The density current head tends to be warmer and lower due to more warm ambient air being entrained into it. These results are consistent with those of Knippertz and Todd (2010). The turbulence behind the secondary surge in the cold pool tends to be weaker. The potential temperature in the density current tail (left of 29 km) is similar to that of the ambient air. By 96 min (Fig. 4d), the height of the head has decreased to about 70 m, with a strong downdraft separating the cold air from the head and tail. In addition, the average wind speed near the ground is about 2.5 m s−1, with a maximum speed of 12.7 m s−1 behind the head.
Figure 5 shows the temporal and spatial distributions of the potential temperature at a height of 5 m above the surface. At the initial moment, the cold pool is located within the range of 25–31 km. The head is located at about 32 km in the y direction, with the secondary surge behind it. When compared with the location of the head centered at a height of 10–80 m (Fig. 4a), the head centered at 5 m is about 1 km behind. This illustrates that the movement speed of the cold pool near the ground is lower than that at a higher altitude due to the friction at the surface, which is consistent with the observation results of Flamant et al. (2007). Figure 5 also shows that the head and the secondary surge move at different speeds, with the secondary surge moving slower because of the obstruction of the downdraft from the head. The bottom of the head tends to be colder because the cold air flows into it from the secondary surge after 84 min. At 102 min, the leading edge of the head is located at 43.5 km in the y direction.
Spatial–temporal distribution of the potential temperature (K) at a height of 5 m above the ground.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
2) Analysis of total kinetic energy
Figure 6 illustrates the temporal changes in the maximum wind speed, total kinetic energy, and movement speed of the head during the evolution of the downburst. Here, the maximum wind speed refers to the maximum value at the output time obtained from the BLASUIS model. The total kinetic energy is the sum of the average kinetic energy in the area within the downburst range (y > 28 km) where the wind speed is greater than 0.5 m s−1. The moving speed of the head refers to the speed of the head with an isopotential temperature of 312 K within the height range of 30–90 m. It can be seen that the total kinetic energy and the maximum wind speed increase rapidly before 75 min due to the formation of a density flow. After that, the total kinetic energy of the downburst, the maximum wind speed, and the movement speed of the density current head decrease significantly due to the effects of surface friction and entrainment of the ambient warm air. In addition, after about 80 min, the total kinetic energy and the movement of the leading edge begin to fluctuate, which are related to the colder air surging into the head from the cold pool. Figure 6 also shows that the decrease in the movement speed of the head slows down after 80 min because the cold pool warms as air from the ambient atmosphere is entrained (Fig. 5). The decrease in the temperature gradient between the cold pool and the ambient atmosphere leads to a reduction in the horizontal pressure gradient force between them, which reduced the movement speed of the head (Anabor et al. 2011).
Temporal changes in the maximum wind speed (for areas of y > 28 km) (m s−1; red line), total kinetic energy (m2 s−2; black line), and movement speed of the density current head (m s−1; blue line). The black dotted line represents the end of the cooling.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
b. Effects of a hill on the downburst
1) The structure and evolution of the downburst
The vertical distribution of the potential temperature and the wind field from the run with a hill are shown in Fig. 7. It can be seen that the density current tends to be asymmetric when a hill is implanted in the model domain. Similar vertical and radial velocity structures are found in the simulation results by Aboshosha et al. (2015). The potential temperature in the cold pool increases significantly, with a warmer density current head in the side with a hill. Figure 7a shows that the head is lifted over the hill, and the head is slimmer relative to that in the side without the hill. The cold pool behind the head in the side with the hill is warmer than that in the side without the hill, and the average potential temperature is about 0.5 K warmer than that of the standard run [sensitivity run with no hill (SNH)]. Note that cold air flows out of the cold pool due to the turbulence caused by the hill (e.g., y = 36 km). Figure 7b shows that the cold air in the head flows along the slope, and the height of the head decreases significantly. By 84 min, the head has moved to the right-hand side of the hill, with a higher altitude and larger potential temperature relative to that on the opposite side. Figure 7d shows that the difference in the potential temperature between the cold pool and the environment decreases because the cold air moves divergently due to the entrainment of warm air. The turbulent mixing initiated by the hill in the model probably enhances the exchange between the cold air of the downburst and the warm ambient air, which contributes to the warming of the cold pool. In addition, when compared with the simulation of the standard run SNH (Fig. 4a), the height of the secondary surge from the sensitivity run with hill (SH) is larger because of the stronger downdrafts of the head (maximum downdrafts of 10.55 m s−1). Yan et al. (2022) modeled downburst outflows under different terrain conditions and found that in the near-ground regions, rough terrain played a significant role on the downburst winds. In the test SH, at 76 min, due to the lifting effect of the hill, the height of the head is about 0.5 km higher than that in the standard test SNH without hill. At 80 min, after the head of the downburst encounters the peak of the hill, there is not much difference between the height of the head in test SH and test SNH. In summary, the cold pool tends to become warmer due to the entrained warm air and the enhanced turbulent mixing caused by the hill. In addition, the head intensity decreases significantly with the maximum wind speed in area y > 28 km and the maximum wind speed at a height of 5 m at 76 min being 37.4 and 32.8 m s−1, respectively. The average wind speed at the same time in run SH is about 2.6 m s−1, which is 4.7 m s−1 lower than that in run SNH. Similarly, the average surface wind speed at a height of 5 m is about 4.1 m s−1 lower in run SH.
Vertical distributions (y–z) of the potential temperature (K; shading) and wind field (m s−1; vectors) from run SH at (a) 76, (b) 80, (c) 84, and (d) 88 min. The red lines denote the potential temperature of 312 K.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
The head moving speed (at 76 min) (HMS; m s−1), Froude number Fr, and averaged wind speed U (m s−1) in the cold pool (for areas of y > 28 km) for different runs.
2) Influence of the hill width on the downburst
To analyze the influence of the horizontal scale of the hill on the structure and strength of the downburst, simulations were performed in which the height of the hill (0.5 km) was kept constant while varying the width of the hill [hill width 1.5 km (SHW15), 2 km (SHW2), 3 km (SHW3), and 3.5 km (SHW35) in Table 1]. The vertical distributions of the potential temperature and the wind field at 76 min are shown in Fig. 8. Figure 8 shows that the height of the cooling pool’s head also changes with the hill width. The height of the head reaches up to 1.27 km for a hill width of 3.5 km, but it is onlyabout 0.98 km when the width of the hill is 2.0 km. The width of the head tends to decrease due to the obstruction of the hill, which leads to a smaller head. These results are consistent with those of Mason et al. (2010). The region with a potential temperature of <312 K, especially the colder area with a potential temperature of <309 K, is significantly reduced. The potential temperature of the cold pool behind the head decreases as the hill width increases. For example, the potential temperatures in the cold pool are 308.05 and 307.26 K for runs SHW15 and SHW35, respectively. These results confirm that a large hill width more efficiency weakens the intensity of the downburst (Yamaguchi et al. 2003). Moreover, Table 2 shows that small changes in Fr occur for the runs with different hill widths, in which the maximum variation in Fr is about 0.3 (Fr = 1.92, 2.14, 1.81, and 1.87 for runs SHW15, SHW2, SHW3, and SHW35, respectively). This indicates that the hill width has less effect on the downburst passing over the hill, but wider hills tend to weaken the intensity of the downburst. In addition, the movement speed of the cooling pool head decreases as the hill becoming wider (the center locations of the head are 33.2, 33.4, 32.9, and 32.6 km in the horizontal direction for runs SHW15, SHW2, SHW3, and SHW35, respectively), which indicates that a larger hill width more effectively blocks the downburst (Cao et al. 2012; Mason et al. 2010).
Vertical distributions (y–z) of the potential temperature (K; shading) and wind field (m s−1; vectors) at 76 min for runs with hill widths of (a) 1.5, (b) 2.0, (c) 2.5, and (d) 3.0 km. The red lines denote the potential temperature of 312 K.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
Figure 9 shows that the maximum wind speed and the maximum wind speed near the ground (height of 5 m) in the cold pool (y > 28 km) increase significantly with increasing hill width (i.e., the hill slope decreases), in which the maximum wind speeds occur over the windward slope. Similar results were reported by Mason et al. (2010). Previous numerical studies of the hill slope’s influence on downbursts have revealed that the wind speed increases significantly during its movement process from the foot to the top of the hill (Mason et al. 2007, 2010; Q. Yang et al. 2021). The maximum wind speeds for the runs with different slopes are relatively close, and the maximum wind speeds are slightly larger in the small slope runs than in the large slope runs.
Maximum wind speed (m s−1; solid lines) and maximum wind speed at a height of 5 m (m s−1; dotted line) (for areas of y > 28 km) for runs with various hill widths at 76 (black), 80 (blue), 84 (red), and 90 (green) min.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
3) Influence of the hill height on the downburst
To further analyze the influences of the hill height on the structure and development of downbursts, tests with different hill heights and a constant hill width (2.5 km, the same as in run SH) were performed [hill top 0.4 km (SHT04), 0.45 km (SHT045), 0.55 km (SHT055), and 0.6 km (SHT06)]. Relative to run SNH, the average potential temperature of the cold pool increases significantly (about 1.09 K) at 76 min, which is attributed to the effect of the topographic obstruction (EI-Sayed et al. 2018). As is shown in Fig. 10, the blocking effect of the hill on the head gradually strengthens with increasing hill height, which results in intensified transport of cold air to the head via the rear secondary surge. As a result, the area of the colder head (where the potential temperature is lower than 309 K) increases. Figure 10a shows that the 309 K isothermal line in the secondary surge reaches a height of about 0.27 km for a hill height of 0.4 km at 76 min. At this time, there is a large warm gap between the secondary surge and the head of the downburst because the cold air is blocked by the strong downdraft of the head’s eddy. It should be noted that the intensity of the head’s eddy decreases with increasing hill height. Moreover, the maximum wind speed in the cold pool behind the head (28–31.25 km) increases (27.1, 27.2, 29.7, and 29.9 m s−1 for runs SHT04, SHT045, SHT055, and SHT06, respectively) with increasing hill height. This leads to an indistinct warm gap between the secondary surge and the head. It was also found that the height of the head decreased to about 1.4 km above the model’s surface in the run with a hill height of 0.6 km (Fig. 10d) (EI-Sayed et al. 2018). The blocking effect of the hill on the downbursts increases with increasing hill height. In addition, the maximum wind speed and the near-surface maximum wind speed decrease slightly with increasing hill height at 76 min (black lines in Fig. 11). The similar results can be obtained for the runs with a higher hill (hill height are 1.0 and 1.2 km, respectively) (figures not shown). The maximum magnitudes occurred over the windward slope of the hill between 31 and 32 km in the y direction in runs SHT04, SHT045, SHT055, and SHT06. This implies that the hill height does not affect the maximum wind speed as much as the hill width.
Vertical distributions (y–z) of the potential temperature (K; shading) and wind field (m s−1; vectors) at 76 min for runs with hill heights of (a) 0.4, (b) 0.45, (c) 0.55, and (d) 0.6 km. The red lines denote the potential temperature of 312 K.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
As in Fig. 9, but for runs with different hill heights.
Citation: Journal of Applied Meteorology and Climatology 61, 8; 10.1175/JAMC-D-21-0243.1
4. Conclusions and discussion
In this study, the observational data obtained from the Boundary Layer Comprehensive Observational Experiment, which was conducted in Tazhong, China, in the hinterland of the Taklimakan Desert on 27 July 2016, were used as the driving field for the high-resolution boundary layer model (i.e., BLASIUS). The BLASIUS model was used to simulate the structure and evolution of downbursts by specifying a cooling source in the model. The downburst occurred in a deep convective boundary layer (about 4 km). An isolated hill was implanted on the model’s surface to investigate the effects of the hill’s height and width on the downburst’s structure, turbulence intensity, and wind speed.
The BLASIUS model can simulate the structure and evolution characteristics of downbursts that have been observed in previous studies. A cold pool forms as the cold air diverges along the surface with symmetric turbulent vortices in the cold pool’s head. The intensity and scale of the turbulent vortices are relatively large, with the maximum horizontal wind speed mostly occurring in the head at the model’s surface. The turbulence intensity becomes weaker away from the head in the cold pool. The movement speed of the cold pool near the ground is lower than that at higher altitudes due to the friction at the surface. A colder secondary surge forms because of the obstruction of the head’s downdraft. Owing to the entrainment of the ambient air, the head moves slower than the secondary surge. This subsequently causes the secondary surge and the head to gradually merge together.
The cold pool becomes warm if an isolated hill is implanted in the model under the same model conditions. Both the movement speed of the head and the average wind speed of the downburst decrease, while the maximum wind speed increases. The downburst passes over the hill with a Froude number of 2.00, which implies that it is easy for the downburst to climb and cross an isolated hill with the height and width less than 0.6 and 3.5 km, respectively.
The scale of the hill affects the dynamic and thermodynamic structure of the downburst through obstruction and entrainment mixing. In this study, sensitivity tests with different hill widths (from 1.5 to 3.5 km) and hill heights (from 0.4 to 0.6 km) were performed under the same conditions as test SNH and the SH. The maximum wind speed occurred on the windward slope and the downburst passed over the hill in the various tests with a hill. The head of the cold pool became narrower and taller as the hill width increased. The downburst’s insensitivity decreased and its movement speed decreased with increasing hill width owing to the enhanced entrainment of the ambient air. However, the maximum wind speed at the surface and the areas of y > 28 km increased with the increasing of hill width. The height of the downburst head decreased as the hill height increased. The blocking effect on downbursts increased as the maximum wind speed increased, and the maximum wind speed at the surface decreased slightly. The Froude number generally decreased as the height of the hill increased, but the downburst could pass over the hill. The turbulence intensity in the downburst head was strongly related to the height of the hill and the evolution of the downburst.
In the simulation results, the effects of hill on downburst structure, cold pool, and near-ground maximum wind speed were discussed. However, it is noticed that an isolated hill is used to explore the effects of terrain on the convective cold pool in this study, which may have significant implications for the entrainment processes between the density currents and the ambient air. In addition, because of the lack of the observation downbursts data, the properties of the cold pool for the standard run (SNH) and the characteristics of the density currents’ wind speeds have been compared with those from the previous simulations results rather than observations. Further work is needed to more accurately assess the effects of terrain disturbances on the convective outflows.
Acknowledgments.
This work was supported by the National Natural Science Foundation of China (42175088, 41775013, 41875046) and Supercomputing Center of Lanzhou University.
Data availability statement.
The sounding data used as the initial field for BLASIUS model in this research are included in F. Yang et al. (2021). The numerical model simulations upon which this study is based are too large to archive or to transfer. The model results and boundary condition files can be obtained from the corresponding author.
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