Mountain-induced stagnation points in hydrostatic flow

Abstract

The Bernoulli and hydrostatic relations are used to derive an exact diagnostic equation relating wind speed to the integral of vertical displacement aloft. The form of this equation does not support the "kinetic energy" concept of flow stagnation proposed by Sheppard (1956). Linear theory estimates of the displacement integral are used to predict the occurrence of stagnation points as a function of hill shape and ambient shear. For a long ridge perpendicular to a weakly sheared flow, stagnation begins aloft, thus allowing wave breaking and transition to a severe state. For a ridge aligned with the flow, waves dispersively weaken aloft and stagnation occurs first on the surface. This allows density surfaces to intersect the ground and the low-level flow to split around the hill.

Supplement to “Numerical Simulation of Lee-Wave Events over the Pyrenees”

“…His diagram indicates that mountains of high aspect ratio (>5) act as a two-dimensional wall. Using a hydrostatic numerical model, Stein (1992) examined non-linear effects on critical mountain height for stagnation and confirmed the diagram of Smith (1989).…”

“…Dietze (1981, 1982) solved mountainwave equations over multiple elliptical mountains in a shear flow and calculated the momentum flux. Smith (1989) showed a diagram of critical mountain height for stagnation as a function of horizontal aspect ratio using the linear theory. His diagram indicates that mountains of high aspect ratio (>5) act as a two-dimensional wall.…”

The effect of indiscriminate nudging time on large and small scales in regional climate modelling: Application to the Mediterranean basin

“…Indeed, when low-level flow splitting or wave breaking occurs, dissipative processes in the turbulent regions generate PV that streams downwind in 'PV banners' (e.g. Smith, 1989;Smith et al, 2007). For instance, the mistral is qualified as a primary PV banner Guénard et al, 2006), contrary to smaller streams of vorticity which wrap up into pairs of eddies of opposite signs due to the irregular peak and pass structure of the mountain ridges forming eventually multiple PV banners (Aebischer and Schär, 1998;Schär et al, 2003;Flamant et al, 2004).…”

Disentangling the Forcing Mechanisms of a Heavy Precipitation Event along the Alpine South Side Using Potential Vorticity Inversion

“…The inverse Froude number, 5 NH 0 /U (Smith 1989), is used here to determine whether or to what degree the southerly flow toward the Alps was blocked by the latter or directed over them. By doing so, many processes that are important for a detailed assessment of the interaction of the flow with the topography are neglected.…”

“…Studies determining the flow response have mainly focused on idealized flow over idealized topography (e.g., Schä r and Davies 1988;Smith 1989;Ó lafsson and Bougeault 1997). Reinecke and Durran (2008) investigated different methods to characterize nonuniform flows using the inverse Froude number.…”