## 1. Introduction

[2] Over the years several experiments to advance our understanding of the stratospheric circulation have been performed with super-pressure balloons (SPBs) drifting on constant density surfaces [e.g., *Hertzog and Vial*, 2001; *Hertzog et al.*, 2007]. In this framework perturbation quantities *ψ*′ are necessarily defined with respect to averages on constant density surfaces. The relationships between wave perturbation quantities defined in this manner can be different from the relations that apply when means and deviations are defined with respect to isosurfaces of other parameters. For example, the linearized ideal gas law when means and perturbations are defined on constant *density* surfaces is since *ρ*′ ≡ 0, whereas when means and perturbations are defined on constant height surfaces for typical waves [*Walterscheid et al.*, 1987]. Here *ρ* is density, *p* is pressure, *T* is temperature, overbars denote basic state quantities, and primes denote wave-caused deviations therefrom. Other relationships such as those for momentum, continuity and heat, and others derived from these, such as flux relations, can also be different.

[3] Our principal objectives in this study are twofold. First, we introduce gravity wave relations in constant density coordinates. Second, we use these relations to calculate gravity wave momentum fluxes and sensible heat fluxes over in the lower stratosphere over Antarctica using data from SPBs released in the southern hemisphere polar vortex during the VORCORE campaign of the STRATÉOLE program. Log-density coordinates are the natural coordinates to infer wave fluxes using data obtained on isopycnal surfaces.

[4] *Vincent et al.* [2007], *Hertzog et al.* [2008], and *Boccara et al.* [2008] have inferred momentum fluxes in the lower stratosphere above Antarctica from the SPBs launched during the VORCORE campaign. These authors modify gravity wave relations based on constant height coordinates. The relations derived by *Vincent et al.* [2007] are no less valid than those obtained here, but as we shall show, they require more reliance on gravity wave relations (hence make more redundant use of information) and are more difficult to apply.

[5] This paper is organized as follows: In section 2 we derive gravity wave relations in constant density coordinates: in section 3 we derive flux relations; in section 4 we describe a wavelet-based analysis of VORCORE data for wave fluxes, in section 5 we show results of an analysis of VORCORE data; in section 6 we discuss the results; and in section 7 we summarize our main findings.