On The Spatio-Temporal Evolution Of Dust Storms:Theoretical And Numerical Modelling

Dust storms are extreme weather events that usually occur in arid and semi-arid regions.Dust particles suspended in the air can greatly affect the hydrological cycle,ecological system,air quality,human health,and agriculture.A systematic and comprehensive investigation of the spatio-temporal evolution and the underlying physical mechanism is of great importance for predicting and controlling dust storms.The downburst outflow which gives rise to local convective sandstorms is essentially a gravity current.A volume of air cooled by the evaporation and sublimation of precipitation in the cloud descends and collides with the earth's surface,spreading longitudinally in the ambient.Over arid ground,large amounts of aerosols carried by the strong wind can form a dust wall at the leading edge of the gravity current,which is referred to as a convective dust storm.On one hand,the existing CFD(computational fluid dynamics)analysis of the convective dust storms is rare and limited to coarse grids.Thus,the impact of the turbulent motions on the spatiotemporal evolution of local convective dust storms is unclear.On the other hand,the modelling of the downburst outflow lacks a sophisticated theory and an appropriate scaling approach,and barely concerns the front features.The atmospheric boundary layer is a high Reynolds number wall turbulence,which is the basic flow of regional dust storms.The main characteristics of the high Reynolds number atmospheric boundary layer are large-and very-large-scale motions,and the effect of the related coherent structures on the spatio-temporal evolution of the regional dust storm is scarcely studied.Therefore,based on the basic governing equations for incompressible flows and the Eulerian representation for dust concentration,through theoretical and numerical approaches,we develop models that can track the spatio-temporal evolution of the dust storm and the relevant turbulent flow.Theoretical models for the gravity current are improved for a suitable description of the downburst outflow.Utilizing DNS(direct numerical simulations)and LES(large-eddy simulations)can capture the complex turbulent structures and the spatio-temporal distribution of dust concentration.The following work has been carried out:First of all,a theoretical study of the downburst outflow is conducted.An integral model considering a continuous velocity transition across the density interface that does not need any empirical constants is proposed to predict the front velocity of the gravity current.Through analyzing the mass,density,momentum,and the single-value pressure field encompassing the front,we find that the Froude number is governed by the front depth and the relative thickness of the lower velocity transition layer,and introducing the latter leads to a larger Froude number.By combining the feature of the discontinuity that travels back to the lock,the new integral model is applied in the lock-release gravity current.The Froude number as a function of the front depth nearly coincides with the vortex-wake model,implying that the influence of the lower velocity transition layer is negligible in the lock-release gravity current.In conjunction with the conditions in the cooling source region,the new integral model is able to correlate the front characteristics with the thermodynamic and geometric parameters of the cooling source.An unambiguous scaling approach incorporating the properties of the cooling source is proposed.The scaling laws of the downburst outflow are obtained by the box model and dimensional analysis.Under the inertial-buoyancy balance,the cooling source prevents the gravity current from slowing down,resulting in a steady moving front.Under the viscousbuoyancy balance,the decaying trend of the front velocity is much gentler than that in the lock-release gravity current.Secondly,direct numerical simulations of the downburst outflow and the dispersion of suspended particles in it are implemented to examine the applicability of the theoretical models and to obtain the spatio-temporal evolution of the convective sandstorm.Results show that the box model can provide a satisfying prediction of the scaling laws in the viscous phase.A good estimate of the relationship between the front features and the geometric parameters of the cooling source in the inertial phase is offered by the integral model.Both theory and numerical results suggest that the dimensionless front velocity and the front depth are governed by the center height and the longitudinal radius of the cooling source,and the influence of the vertical radius of it is very limited.The turbulent mixing in the gravity current plays an important role in the downburst outflow,which accelerates the propagation,and previous integral models fail to capture this unique feature.The front velocity nondimensionalized by the scaling method of the liquid drop release varies with the geometric parameters of the cooling source.The Froude number based on the center height of the cooling source is found to maintain around unit and to merely rely on the geometric parameters of the cooling source.The downburst outflow manifests common features of the gravity current: Kelvin-Helmholtz instability emerges in the density interface and breaks up into three-dimensional lobe-and-cleft structures.The vortex dynamics reveal that in the viscous phase,owing to the impact of the cooling source,the spanwise vortices continue to form in the downburst outflow.The instantaneous concentration fields show that a high concentration layer is moving longitudinally along the wall,the average propagation of which nearly coincides with the gravity current.The lobe-and-cleft structures of the front also reveal a strong correlation.The thickness of the high concentration layer is increasing along the longitudinal direction and reaches the highest vertical position at the front.The formation of the inclined concentration interface is correlated with the balance between the vertical net flux and the longitudinal convection.The thickness of the high concentration layer at the front keeps rising with time if the settling effect is not obvious,and is limited by the particle settling.The new integral model and the Froude number based on the center height of the cooling source are both utilized to make a rough estimate of the characteristics of the dust storm,achieving a good agreement with fields measurements.Thirdly,numerical simulations of the dust transport in a neutral atmospheric surface layer based on an Eulerian modeling approach and a large-eddy simulation technique are performed to investigate the coherent structure of dust concentration.The instantaneous fields confirm the existence of very long meandering streaks of dust concentration,with alternating high-and low-concentration regions.A strong negative correlation between the streamwise velocity and concentration and a mild positive correlation between the vertical velocity and concentration are observed.The spatial length scales of the concentration structures are smaller than their flow counterparts,accompanied by larger inclination angles.High-and low-concentration events are correlated with a pair of counter-rotating quasi-streamwise vortices,with a downwash inside the low-concentration region and an upwash inside the highconcentration region.It is indicated that the vertical dust transport is closely related to the large-scale roll modes,and ejections in high-concentration regions are the major mechanisms for the upward motion of dust particles.