[Paper Review] Consistent Static Models of Local Thermospheric Composition Profiles

J. M. Picone, J. T. Emmert+1 more|arXiv (Cornell University)|Jul 12, 2016

Gas Dynamics and Kinetic Theory18 references3 citations

TL;DR

This paper proposes physically consistent, static models for local thermospheric composition profiles by solving the nondriven multifluid equations of motion. It identifies three altitude regions—lower thermosphere (z < ~100 km) with composite fluid flow, upper thermosphere (z > ~200 km) with uncoupled species flows, and a transition zone—showing that hydrostatic balance, not diffusive equilibrium, provides truly stationary composition profiles.

ABSTRACT

The authors investigate the ideal, nondriven multifluid equations of motion to identify consistent (i.e., truly stationary), mechanically static models for composition profiles within the thermosphere. These physically faithful functions are necessary to define the parametric core of future empirical atmospheric models and climatologies. Based on the strength of interspecies coupling, the thermosphere has three altitude regions: (1) the lower thermosphere (herein z &lt; ~100 km), in which all species move together at the composite fluid velocity with an effective particle mass equal to the average particle mass of the composite fluid; (2) the upper thermosphere (herein z &gt; ~200 km), in which the species flows are approximately uncoupled; and (3) a transition region in between, where the effective species particle mass and the effective species vertical flow interpolate between the solutions for the upper and lower thermosphere. We place this view in the context of current terminology within the community, i.e., a fully mixed (lower) region and an upper region in diffusive equilibrium (DE). The latter condition, DE, currently used in empirical composition models, does not represent a truly static composition profile in the presence of finite thermal diffusion. Rather, species by species hydrostatic balance is a consistent (i.e., stationary) static representation of vertical thermospheric composition profiles.

Motivation & Objective

• To develop physically faithful, stationary models for thermospheric composition profiles that are consistent with the underlying fluid dynamics.
• To resolve inconsistencies in current empirical models that rely on diffusive equilibrium, which does not represent true static states under finite thermal diffusion.
• To define a parametric core for future empirical atmospheric models and climatologies based on first principles of momentum and mass conservation.
• To clarify the mechanical behavior of thermospheric species across three distinct altitude regimes: lower, upper, and transition regions.
• To establish hydrostatic balance as the correct representation of stationary composition profiles, replacing the commonly used but physically inconsistent diffusive equilibrium.

Proposed method

• Solves the ideal, nondriven multifluid equations of motion to identify mechanically consistent, stationary solutions.
• Applies effective particle mass and flow velocity concepts to model interspecies coupling in the lower thermosphere (z < ~100 km).
• Uses separate species flow solutions for the upper thermosphere (z > ~200 km), where species are approximately uncoupled.
• Interpolates effective particle mass and vertical flow between lower and upper regions in the transition zone (~100–200 km).
• Compares the physical consistency of diffusive equilibrium (currently used) with hydrostatic balance as a stationary solution.
• Derives analytical expressions for species-specific hydrostatic balance to represent truly stationary composition profiles.

Experimental results

Research questions

• RQ1 What are the physically consistent, stationary solutions for thermospheric composition profiles under the assumption of no external forcing?
• RQ2 How does interspecies coupling vary across the thermosphere, and what defines the transition between coupled and uncoupled regimes?
• RQ3 Why is the widely used assumption of diffusive equilibrium not a true stationary solution in the presence of thermal diffusion?
• RQ4 What is the correct physical representation of vertical composition profiles in the thermosphere that satisfies mechanical equilibrium?
• RQ5 How can hydrostatic balance be used as a foundation for future empirical atmospheric models and climatologies?

Key findings

• The lower thermosphere (z < ~100 km) behaves as a single composite fluid with an effective particle mass equal to the average mass of the mixture.
• In the upper thermosphere (z > ~200 km), species flows are approximately uncoupled, allowing individual species to be treated independently.
• The transition region (~100–200 km) exhibits interpolated behavior in both effective particle mass and vertical flow velocity between lower and upper regimes.
• Diffusive equilibrium, currently used in empirical models, is not a consistent stationary solution due to finite thermal diffusion effects.
• Species-by-species hydrostatic balance is identified as the only physically consistent, truly stationary representation of vertical thermospheric composition profiles.
• The study provides a theoretical foundation for replacing diffusive equilibrium with hydrostatic balance in the parametric core of future empirical atmospheric models.