A Theory of Topographically Bound Balanced Motions and Application to Atmospheric Low-Level Jets

Abstract

The response of a stratified fluid to forcing from the lower boundary is studied both analytically and numerically. The lower boundary forces a flow field through orographic obstacles and potential vorticity anomalies. It is argued that these mechanisms contribute to the maintenance of low-level jets (LLJs) that are observed regularly in the vicinity of the Rocky Mountains and the Andes. Low-level jets function as one of the primary mechanisms through which topography and surface heating influence regional and global climates.On the f -plane a horizontal transform of the governing equation for potential vorticity leads to a vertical structure equation that is solved using Green's functions. On the sphere a vertical transform of this system leads to a horizontal structure equation that is solved using spheroidal harmonics. These analytic solutions lead to a conceptually simple picture of the fluid response to forcing. However, these derivations only lead to closed analytic solutions for the case of an isentropic lower boundary. When the lower boundary is not isentropic a massless layer must be included in the domain and the solution is then found iteratively. For the cases including a massless layer the system is approximated using finite differences and solved with an over-relaxation procedure.Solutions are presented for the geostrophically balanced, steady response of the fluid to three idealized lower boundaries. An isentropic ridge is studied to determine the role non-heated orography plays on the wind field. Then a flat heated lower boundary and a non-isentropic ridge are ii studied. The cases with a heated lower surface result in a cyclonic wind field that is anchored over the topography. Observations show a prominent cyclonic wind field centered on both the Rocky Mountains and the Andes. The idealized cases studied in this work allow for the examination of fluid systems analogous to the Great Plains LLJ and the South American LLJ. Both the mean behavior of these jets and their variability have important climatological and economic impacts on the plains regions of North and South America.

Observational study of the South American low‐level jet during the SALLJEX

“…From the analysis presented in this work, a weakening of the maximum wind speed is observed from stations near the Andes to stations eastward over the plains. This suggests a possible mechanical effect of the Andes on centring the SALLJ geographical core, in agreement with previous studies (Byerle and Paegle, 2002; Campetella and Vera, 2002; Silvers and Schubert, 2012). The analysis shows a poleward decrease of the maximum wind speed height AGL along the jet stream.…”

A Dynamical Explanation of the Topographically Bound Easterly Low‐Level Jet Surrounding Antarctica

“…In Figure 6 the lower boundary is isentropic: the isentropes parallel the surface both along the plateau and the slope. However, as shown by Eliassen (1980) and further explored by Silvers and Schubert (2012), with higher or steeper terrain it is possible for the topography to puncture the lower isentropes. For example, Figure 7 shows the flow obtained for a steeper plateau (top) and a higher plateau (bottom).…”

“…The reference state is taken to be which gives Π linear in θ and buoyancy frequency inversely proportional to θ . This is the same reference state as used by Silvers and Schubert (), and is shown in their Figure 5. Unless otherwise specified, the constants are given by θ B =260 K and θ T =370 K, with Π B and Π T based on p B = p 0 =1,000 hPa and p T =100 hPa.…”

“…The approach is based on a zonally symmetric potential vorticity invertibility principle and includes vertical structure and more accurate versions of potential vorticity, dynamical balance, and the lower boundary condition. The theoretical basis for this approach was given by Eliassen (), who studied the topographically bound, balanced response of a rotating, stratified fluid to orography, and by Silvers and Schubert (), who applied these ideas to the low‐level flows surrounding the Andes. Here we extend the latter analysis to the Antarctic region and thereby demonstrate that the Antarctic easterly LLJ can be interpreted as a balanced flow attributed—through the potential vorticity invertibility principle—primarily to the distribution of topography, to the fact that potential temperature varies little along this topography, and to the PV anomaly that resides just above the elevated ice sheet.…”

Analytical solutions of the potential vorticity invertibility principle

“…[30] In the analysis presented here we have neglected the effects of topography and surface gradients of potential temperature. Recently, Silvers and Schubert [2012] have shown how these effects are crucial in understanding the low-level jets that are topographically bound to the Andes. Inclusion of topography and surface gradients of potential temperature in the present analysis would provide a framework for studying the flow fields that result when upper level and surface PV anomalies interact with elevated terrain.…”