Explanation by Dr. Douglas R. Christie, Research School of Earth Sciences - The Australian National University, given on 2007 Feb. 20.

Comments on the Long Period Event Observed on Feb. 5, 2007 at the EXL Infrasonic Array

The long period, slowly propagating disturbance observed on Feb 5, 2007 at the EXL Infrasonic Array is almost certainly the signature of a surface based density current (or gravity current). This will not be obvious unless the data is first corrected for the instrument response of the EXL differential microbarometers. This can be done, to a good approximation, by simply integrating the trace (or, more formally by deconvolving the response if the response is known accurately). At long periods, a differential microbarometer simply differentiates the surface pressure distribution. After removing the instrument response, it will be clear that the real surface pressure trace exhibits a pressure jump followed by oscillations corresponding to density-current induced turbulence.

The details on the basic response of a differential microbarometer along with numerous examples are given in :

• Christie et al. (1978), On Solitary Waves in the Atmosphere, J. Atmos. Sci., 35, 805-825.

Density currents are very commonly observed at IS07 in Northern Australia at certain times of the year. They most commonly occur as thunderstorm downdraft-outflow density currents (at distances of up to 40 km from the parent storm), but may also be associated with katabatic flows, sea-breeze frontal systems (in the earlier stages) and on a larger scale, synoptic scale cold fronts. The event recorded at EXL is probably a thunderstorm outflow density current or an evolving sea-breeze front.

Density currents have other diagnostic characteristics. The micropressure signature will normally be accompanied by a sharp drop in surface temperature shortly after the initial pressure increase corresponding to the arrival of dense cold air at the surface. This drop in temperature will also be accompanied by a sudden shift in wind direction and an increase in wind speed. The higher frequency micropressure fluctuations behind the 'head' of the density current are caused by normal wind-induced turbulence and turbulence associated with Kelvin-Helmholtz instabilities that develop on the elevated interface behind the head of the density current.

Density currents may also take the form of elevated intrusions propagating along the top of a colder stable layer at the surface. In this case, the sudden drop in surface temperature may not be present. Indeed, the surface temperature may exhibit a transient increase in temperature as turbulence in the wake of the head of the intrusion mixes warmer air from aloft into the surface layer.

This is just the start of a rather long but fascinating story. Density currents that propagate into a stably-stratified atmosphere will slowly evolve into a highly nonlinear wave system. It is quite easy to distinguish with certainty a wave from a density current by looking at the flow in a relative coordinate system that moves with the disturbance. The relative flow behind the leading edge of a density current is towards the front at the surface and away from the front aloft. This means that the wind speed at the surface behind the head of density current will exceed the propagation speed of the front. In contrast, the winds behind the front in a nonlinear wave disturbance will be away from the front at all levels and the wind speeds will be less, at all altitudes, than the propagation speed (ignoring small regions of recirculating fluid as described below).

Density currents that propagate into a stable layer will slowly evolve into a fairly smooth bore wave (which may contain regions of trapped recirculating fluid). As time passes, the (finite-length) smooth bore wave will steepen along the leading edge and slowly evolve into a nonlinear undular bore wave. Each leading undulation will gradually grow in amplitude and separate from the disturbance as a distinct solitary wave. The leading amplitude-ordered solitary waves may be followed by a weak dispersive nonlinear wave group which will decrease in amplitude and disappear. Eventually, the disturbance will comprise only one or more highly stable solitary waves (solitons) which may (in contrast to a density current) propagate over great distances (sometimes in excess of 500 km) as long as stable waveguide conditions persist at the surface. It is also worth noting (in contrast with more familiar linear waves) that each individual solitary wave may transport fluid in a recirculating cell trapped in the interior of the wave.

The theoretical framework for the description of these disturbances is fairly complex. To first order, the evolution of nonlinear waves in the lower atmosphere is described by the Benjamin-Davis-Ono (BDO) equation (a nonlinear integral-differential equation). This equation and various solutions to this equation are described in

• Christie (1989), Long nonlinear waves in the lower atmosphere, J. Atmos. Sci., 46, 1462-1491.

This equation does not describe highly nonlinear waves with regions of closed circulation. A more accurate theoretical description of the morphology of solitary waves is given by the Dubreil-Jacotin-Long equation, a nonlinear partial differential elliptic equation. This equation is very difficult to solve, but accurate numerical solutions that describe all of the features of highly nonlinear waves in the lower atmosphere have been found. These results are given in

• Brown and Christie (1998), Full nonlinear solitary waves in continuously stratified incompressible Boussinesq fluids, Physics of Fluids, 10, 2569-2586.

All of the above cited papers contain references to other papers on the subject.

It is worth noting that the outstanding example of highly nonlinear waves in the lower atmosphere is the Morning Glory of the Gulf of Carpentaria. This spectacular phenomenon takes the form of one or more very large amplitude visible solitary waves created in the collision of two intense density currents (in this case intense tropical sea-breeze fronts) over the Cape York Peninsula. The properties of Morning Glory solitary waves are summarized in the following review article:

• Christie (1992), The Morning Glory of the Gulf of Carpentaria: a Paradigm for Nonlinear Waves in the Lower Atmosphere, Aust. Met. Mag., 41, 21-60.

Again, a large number of relevant references can be found in this paper.

As with density currents, highly nonlinear undular bore waves and solitary waves are very frequently observed at IS07 Warramunga. Indeed, since conditions are nearly ideal in outback Australia, disturbances of this type may be more common at IS07 than at any other IMS station in the global network. Some recent examples observed at IS07of the uncorrected micropressure signatures of density currents, the earlier stages of a density current- nonlinear wave system and a well developed highly nonlinear amplitude-ordered solitary wave group are shown in the accompanying diagrams.

Density current observed at IS07 on 2006, Oct. 28. IS07 is an infrasound array in Australia and part of the International Monitoring System (IMS) for the Comprehensive Nuclear-Test-Ban Treaty (CTBT).

Density current and bore wave observed at IS07 on 2006, Oct. 20.

Nonlinear undular bore wave observed at IS07 on 2006, Oct. 08.

Density current observed at IS07 on 2006, Oct. 14.