On the Features of Thermal Convection in a Compressible Gas

The fully nonlinear equations of gas dynamics are solved in the framework of a numerical approach in order to study the stability of the steady mode of Rayleigh-Bénard convection in compressible,viscous and heat-conducting gases encapsulated in containers with no-slip boundaries and isothermal top and bottom walls.An initial linear temperature profile is assumed.A map of the possible convective modes is presented assuming the height of the region and the value of the temperature gradient as influential parameters.For a relatively small height,isobaric convection is found to take place,which is taken over by an adiabatic mode when the height exceeds the critical value,or by a super-adiabatic mode in case of a relatively high temperature gradient.In the adiabatic mode,convective flow develops due to adiabatic processes given a stable initial stratification.An analytic formula for the critical height of the region is derived taking into account and neglecting the dependence of the gas viscosity on the temperature.Moreover,an analytic formula is obtained for the upper boundary of the region of applicability of the Boussinesq approximation for incompressible gases.These models for compressible gases are relevant to practical situations such as the study of convective flows in spatially extended gas mixtures when dealing with safety issues related to hydrocarbons stored in gas stations.A dangerous situation arises when the tank is almost empty but some hydrocarbon is left at the bottom of the tank.In the presence of convective flows,the vaporized fuel is mixed with the oxidizer(air)forming a gas-vapor medium.However,if the volumetric concentration of fuel vapor(hydrocarbon)is in the interval between the lower and upper concentration limits of ignition,then the gas-vapor mixture becomes explosive and any accidental spark is sufficient to cause an emergency.

A Numerical Study of the Severe Heavy Rainfall Associated with Typhoon Haitang (2005)

Typhoons landing in the central and north of Fujian Province often seriously impact Zhejiang Province. Much attention has been given to exceptionally torrential rain in the South/North Yandang mountainous regions in the southeast of Zhejiang Province associated with typhoon-landing. Typhoon Haitang （2005） is a typical case of such a category, which landed in Huangqi Town of Lianjiang County in Fujian Province, and meanwhile greatly impacted Southeast Zhejiang. A numerical simulation has been performed with the PSU/NCAR non-hydrostatic model MM5V3 to study the torrential rain associated with Typhoon Haitang. The comparison of simulated and observed rainfalls shows that the MM5V3 was able to well simulate not only the intensity but also the locations of severe heavy rain of Typhoon Haitang, especially the locations of the south/north heavy rain center areas in the South/North Yandang mountainous regions. Meanwhile, the diagnostic analysis has been also carried out for better understanding of the severe heavy rain mechanism by using the model output data of high resolution. The diagnostic analysis indicates that the westward tilt of the axis of vorticity from lower layer to upper layer over the south heavy rain center area and the coupled structure of convergence in the lower layer and divergence in the upper level over the north heavy rain center area, were both propitious to stronger upward motion in the layers between the mid and upper atmosphere, and the secondary circulation induced by the vertical shear of the ambient winds further strengthened the upward motion in the heavy rain areas. After Haitang passed through Taiwan Island into the Taiwan Strait, the water vapor east of Taiwan Island was continuously transferred by typhoon circulation towards South Wenzhou, leading to the torrential rainfall in the South Yandang mountainous region south of Wenzhou. Subsequently~ Haitang moved northwards, the water vapor belt east of Taiwan Island slowly advanced northwards, the precipitation rate obviously enhanced in the North Yandang mountainous region north of Wenzhou. After landing in Fujian Province, Haitang moved northwestwards, the water vapor belt coming from the Taiwan Strait merged into the strong water vapor belt from the ocean surface east of Taiwan Island, and passed through the north of Wenzhou, resulting in the torrential rainfall in the north of Wenzhou. The specific moisture transport passage offered abundant water vapor condition for torrential rainfalls associated with Haitang. The unstable stratification at the middle and lower layers over rainstorm areas also provided favorable thermal condition for torrential rainfall. The sensitivity simulation experiments of terrain effect on Haitang＇s heavy rain were also conducted. The moisture flow derived by Haitang＇s southeast flow, which was perpendicular to the South and North Yandang Mountain ranges, played an important role in the torrential rainfall associated with Haitang. The experimental results show that orographic lifting contributed greatly to the enhancement of precipitation, and made the distribution of precipitation more uneven. Some causes for typhoon heavy rainfalls in the south and north of Wenzhou are common, but some causes different. The common aspects are strong ascending motion forced by vertical wind shear, sustained unstable stratification, and amplification effect of orography on precipitation, while different aspects are dynamic structure, conditions for maintenance of unstable stratification, and moisture transport condition.