A51O-0300
A study of convective instability in the shallow troposphere: a non-Boussinesq approach

Friday, 18 December 2015
Poster Hall (Moscone South)
Babu Ram Tiwari, INPE National Institute for Space Research, Sao Jose dos Campos, Brazil
Abstract:
In this work, we present a simulation study of the convective instability (CI) which is excited in the presence of a negative temperature gradient in the dry troposphere. Using incompressible-inviscid hydrodynamic equations and laws of thermodynamics, we derive a growth equation for the wind wy, explicitly containing a growth term with frequency equals to the modified Brunt-Vaisala frequency (ωb) and a non-local term. A general expression for the modified Brunt-Vaisala frequency is derived for the dry-shallow troposphere, retaining the diabatic compression and non-linearity of the density (Diabatic-non-Boussinesq, DNB). This expression is also analyzed under adiabatic compressibility for two approaches: without the density linearizatin (Adiabatic-non-Boussinesq, ANB) and with the density linearization (Boussinesq, OB). The DNB approach is desirable in the dry troposphere where the environmental lapse rate (γe) is weaker than the adiabatic lapse rate (γad). Under the DNB approach, ωb is found to be modified from its OB counterpart such that stabilizing γad is replaced by a modified lapse rate (η-1) γac. Here, (γac,η) are the auto-convective lapse rate and the ratio of hydrostatic density to the total density. It is shown that under ANB approach, η becomes equal to the ratio of specific heats (γ). We show by simulation of the CI that as η increases from unity towards γ within a heated fluid parcel, the CI changes from DNB to ANB type and γe approaches toward γad. Notably, the CI growth remains positive during DNB phase for the initial temperature profile having γe < γad. The present study, thus, proposes an alternative mechanism for the positive growth of the CI under an initial adiabatically stable dry troposphere.