On The Dynamics Of Gravity Waves Generated In Directional Shear Flows Over Three-dimensional Circular Bell-shaped Mountains

Orographic gravity waves(OGWs),which are very common in the atmosphere,are generated as stably stratified airflow goes over the mountains.OGW activities are related to many weather phenomena,such as clear air turbulence,downslope windstorms,and atmospheric vortex street,etc.Vertically propagating OGWs are capable of transporting the momentum upward from the ground.When OGWs break,the momentum carried by them is deposited onto the mean flow,thus influencing the momentum budgets of the atmospheric general circulation.Therefore,studies on the dynamics of OGWs can help improve the understanding and forecast of related weather phenomena.It can also lay a theoretical foundation for the parameterization of subgrid-scale OGWs in large-scale numerical models,which is benefical to the development of numerical models.Based on linear wave theory,this work analytically solves gravity waves generated in adiabatic,inviscid,and irrotating Boussinesq flows over three-dimensional(3D)circular bell-shaped mountains.The general formulae of wave momentum flux(WMF,i.e.,wae stress)and its vertical derivative are derived for hydrostatic flows of linear-type vertical wind shear.Then the structural features of OGWs and their vertical transport of momentum are investigated in detail.Lastly,a series of idealized numerical experiments are performed by use of the ARPS(Advanced Regional Prediction System)model.These numerical simulations,for one thing,aim to verify the results obtained from linear wave theory;for another,they are intended to examine the characteristics of nonlinear OGWs forced by large-amplitude mountains in directional shear flows.The main results of this study are summarized as follows.For mountain waves generated in directional shear flows over 3D circular bell-shaped obstacles,the perturbation fields of vertical velocity and potential temperature at the surface are symmetrically distributed about the surface wind,while those of pressure and horizontal velocity are not.As the height increases,the whole wave field undergoes a rotation in the same direction as the ambient wind,exhibiting an asymmetric structure.At each height,a wake region forms downstream of the local mean flow,particularly evident in the fields of potential temperature and horizontal velocity.These structural features of OGWs are then explained at length by analyzing the power spectra and phase of the wave variables.The directional wind shear has a great impact on the vertical transport of gravity wave momentum.In the presence of directional shear,vertically propagating OGWs are continuously absorbed by the mean flow(i.e.,selective critical level absoprtion),which results in a decrease of the WMF with height.The height decay of the WMF is largely determined by the maximum turning angle of the ambient wind with height(i.e.,?).In the case of large ?,the WMF decreases rapidly with height,that is,OGWs are basically trapped in the lower atmosphere.On the contrary for small ?,the WMF exhibits a weak decay with height such that the wave momentum can be transported to the middle/upper atmosphere.In addition,the wave stress vector turns with height in the same direction of the ambient wind but at a relatively slow rate.Consequently,the wave stress is usually misaligned with the mean wind at high altitudes.The vertical shear of the WMF due to selective critical level absoprtion is always perpendicular to the mean flow,which is thus named "lift force".Lift force is oriented toward the left(right)of the ambient flow that backs(veers)with height.The magnitude of lift force is always equal to zero at the surface.It first increases and then decreases with height,vanishing again at the infinite height.The altitude where the lift force peaks is found proportional to the surface wind speed,but inversely proportional to the vertical wind shear intensity,increasing as the wind maximum turning angle(i.e.,?)increases.The magnitude of the peak lift force also increases with the wind maximum turning angle,but it in general decreases as the ambient wind Richardson number increases.The above linear wave theory results are successfully verified by the numerical experiments performed using the ARPS model.For linear gravity waves forced by small amplitude mountains,the simulated WMFs and their vertical shear are in good agreement with their linear analytic counterparts.However,for nonlinear gravity waves forced by large amplitude mountains,the height variation of the mean wind speed has an important influence on the wave structure and the WMF.Specifically,even the OGWs generated in directional shear flows of the same surface-wind based Froude number(Fr),they may be in opposite drag state(i.e.,high drag versus low drag).Therefore,unlike the constant-flow case,the wave drag state in directional shear flows cannot be determined from the surface wind-based Froude number alone.Additionally,at small Froude number(e.g.,Fr=0.4),the directional wind shear may trigger vortex shedding in the wake flow region,which eventually gives rise to the formation of atmospheric vortex street.