Boussinesq dynamics of an idealized tropopause

Boussinesq dynamics of an idealized tropopause Olivier Asselin, Peter Bartello and David Straub McGill University olivier.asselin@mail.mcgill.ca Abstract The near-tropopause flow has been interpreted using quasigeostrophic (QG) theory. Asselin et al. (2016) showed that this simplified dynamical framework is inconsistent. In the vicinity of rapid changes in stratification such as those characterizing the tropopause, QG flows develop statically unstable conditions. In this paper, a simple yet self-consistent Boussinesq model of the near-tropopause flow is proposed. As expected, the Boussinesq model reduces to the QG model in the limit where the Rossby number is much smaller than , the nondimensional height scale characterizing the stratification change. In the more relevant case where the Rossby number is larger than but still smaller than unity, analysis and numerical simulations suggest that Boussinesq dynamics inhibit the development of statically unstable density profiles. Additionally, tropopause displacements are to found to scale with the Rossby number. Introduction The quasigeostrophic (QG) approximation has been used extensively to model tropo- spheric dynamics at mid-latitudes. Under such balanced conditions, the potential vortic- ity distribution can be inverted to deduce all the other dynamical variables (eg. Hoskins et al. (1985)). Tropopause motion plays a crucial role in the dynamics, because potential vorticity anomalies are generally strongest there. Blumen (1978) considered a simplified configuration whereby the tropopause is treated as a rigid lid overlying a semi-infinite domain with uniform potential vorticity. In this surface quasigeostrophic (SQG) model, the flow is everywhere determined by the distribution of temperature anomalies at the tropopause. Tulloch and Smith (2006) showed that the finite-depth version of Blumen’s model produces an energy spectrum similar to that observed near the tropopause (eg. Nastrom and Gage (1985)). The SQG model can also be derived as a limit of QG in which the stratification profile undergoes a discontinuous jump (eg. Juckes (1994), Held et al. (1995)). The rigid-lid approximation is thus not formally required and the strato- spheric flow may be taken into account. More recently, Plougonven and Vanneste (2010) and Smith and Bernard (2013) examined the more realistic case of a rapid yet continuous transition in the stratification profile. Asselin et al. (2016) showed that only very weak QG flows are self-consistent near the tropopause. In the presence of a sharp transition in the stratification profile, QG dynam- ics produce comparably sharp vertical gradients of perturbation buoyancy. These small vertical scales imply locally large Froude numbers. For realistic atmospheric parameters, not only does QG break down, but statically unstable conditions also develop. In this con- tribution we describe a simple yet self-consistent Boussinesq model of the near-tropopause flow. In the next section, we analyze near-tropopause Boussinesq dynamics in the limit of low Rossby number and compare them to the QG case. Leading order dynamics sug- gest that Boussinesq flows have a lessened tendency to static instability and tropopause displacements scale with the Rossby number. In Section 3, we use numerical simulations to confirm our analysis. Section 4 briefly discusses the results. VIII th Int. Symp. on Stratified Flows, San Diego, USA, Aug. 29 - Sept. 1, 2016