Bernoulli equation and flow over a mountain

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.

The vortex moving toward Taiwan and the influence of the central mountain range

“…Surface friction is important to the flow over mountains (Peng and Thompson 2003;Sun and Hsu 2005;Sun and Chern 2006;Sun 2013;Sun and Sun 2015). Previously, it is also believed that surface friction is secondary; therefore, it is not included in Lin et al (2005); Huang and Lin (2008), and other studies.…”

Mountaintop winds as representatives of low‐level jets and precursors of downstream precipitation over Eastern China

“…Mountains can dynamically accelerate low‐level winds. Sun and Sun () used the theoretical derivations and numerical simulations to demonstrate that a severe downslope wind can develop as a result of the conversion of heat energy to kinetic energy. The thermal effects induced by mountains can also affect LLJs.…”

A geomorphodiversity map of the Soutpansberg Range, South Africa

“…Mountainous regions generally experience more precipitation and wind turbulence affecting the geomorphic behaviour of both water and wind (Banta, Cotton 1981, Barry 2008, Peattie 2013, Stoelinga et al 2013, Sun, Sun 2015. The geomorphic behaviour depends on differences in ground surface characteristics such as roughness, slope, vegetation cover, and soil characteristics (Uzun et al 2017).…”

“…Its east-west orientation creates a huge and unique earth atmosphere interaction in the region. The orientation of the mountain range creates a landscape that influences rainfall distribution due to its effect on both large and small scale atmospheric circulation systems (Ka-banda 2004, Oettli, Camberlin 2005, Smith 2007, Barry 2008, Zardi, Whiteman 2013, Sun, Sun 2015, Rodrigues et al 2016. Moist south easterly prevailing winds from the Indian Ocean are forced to rise over the southern scarp of the range (Kabanda 2004) resulting in rainfall on the south facing slopes while the air dissipates in valleys, creating dryness.…”