Abstract
The Bernoulli equation is applied to an air parcel which originates at a low level at the inflow region, climbs adiabatically over a mountain with an increase in velocity, then descends on the lee side and forms a strong downslope wind. The parcel departs from hydrostatic equilibrium during its vertical motion. The air parcel can be noticeably cooler than the temperature calculated from adiabatic lapse rate, which allows part of enthalpy to be converted to kinetic energy and produces a stronger wind at mountain peak and a severe downslope wind on the lee side. It was found that the hydrostatic assumption tends to suppress the conversion from enthalpy to kinetic energy. It is also shown that the Froude number defined in the atmosphere is equal to the ratio of kinetic energy to the potential energy, same as in Boussinesq fluid. But in the atmosphere, the Froude number cannot be used to determine whether a parcel can move over a mountain or not, unless the vertical motion is weak and the system is near hydrostatic equilibrium. Numerical simulations confirm that except in highly turbulent areas, the potential temperature and Bernoulli function are almost conserved along the streamline, as well as the change of kinetic energy comes from the change of enthalpy instead of potential energy.
Highlights
Severe downslope winds on the lee sides of mountains have been observed frequently around the world
The hydraulic jump was originally derived from shallow-water equations; (b) superposition of upward- and downward-propagating waves: Klemp and Lilly (1975) suggested that strong downslope winds occur when the atmosphere has a multilayer structure that produces an optimal superposition of upward- and downward-propagating waves; (c) wave breaking and enhancement of downslope winds by the energy trapped by the wave-breaking region in the upper layer and/or wave-induced critical layer
The analytical solutions reveal that when an air parcel moves over a mountain, the change of kinetic energy comes from the change of enthalpy instead of from the potential energy, which invalids the popular theory of hydraulic jump based on the conversion between potential energy and kinetic energy
Summary
Severe downslope winds on the lee sides of mountains have been observed frequently around the world. Because the numerical simulations with a nonslip surface could not simulate the longlasting severe windstorms observed in Boulder from the conventional theories, Sun (2013) has proposed a new theory: (d) geostrophic adjustment of the geostrophic-unbalanced upper-level jet introducing a convergence in the upper layer and enhancing the downslope wind. Sun’s numerical simulations reproduced a long-lasting, strong downslope wind (~50 m s−1) on the lee side over a nonslip surface. The numerical simulations confirm that, over a free-slip surface, the Bernoulli equation holds well for an isentropic flow over a mountain before it reaches high-turbulence regions on the lee side. Numerical results show that conservations of Bernoulli function (which is related to the total energy of an air parcel and is defined as B in Methods) and potential temperature hold quite well before the flow encounters highly turbulent regions on the lee side of the mountain. Above the surface frictional layer, the simulated B, potential temperature, and streamlines are near-parallel, and Bernoulli function and potential temperature conservation hold quite well
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