Atmospheric Solitary Waves Research Articles

Solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere

By introducing a new transformation, a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system, which extends Fan's direct algebraic method to the case when r > 4. The solutions of a first-order nonlinear ordinary differential equation with a higher degree nonlinear term and Fan's direct algebraic method of obtaining exact solutions to nonlinear partial differential equations are applied to the combined KdV–mKdV–GKdV equation, which is derived from a simple incompressible non-hydrostatic Boussinesq equation with the influence of thermal forcing and is applied to investigate internal gravity waves in the atmosphere. As a result, by taking advantage of the new first-order nonlinear ordinary differential equation with a fifth-degree nonlinear term and an eighth-degree nonlinear term, periodic wave solutions associated with the Jacobin elliptic function and the bell and kink profile solitary wave solutions are obtained under the effect of thermal forcing. Most importantly, the mechanism of propagation and generation of the periodic waves and the solitary waves is analysed in detail according to the values of the heating parameter, which show that the effect of heating in atmosphere helps to excite westerly or easterly propagating periodic internal gravity waves and internal solitary waves in atmosphere, which are affected by the local excitation structures in atmosphere. In addition, as an illustrative sample, the properties of the solitary wave solution and Jacobin periodic solution are shown by some figures under the consideration of heating interaction.

Observations of Atmospheric Solitary Waves in the Urban Boundary Layer

The simultaneous operation of a three-axis Doppler sodar system in the centralurban area of Rome and two similar systems in the suburban area, forming atriangle about 20 km on each side, provided evidence of solitary-type wavesin the urban boundary layer. Three events, each lasting from a few minutes toabout 30 min, and ranging in depth from the minimum range of the sodar (39 m) to over 500 m, are reported here. Two events were recognizable onall three sodar records while the third event could be observed at the urbanlocation only. Time-height acoustic echo intensity records showed no-echoregions within the wave indicating transport of trapped recirculating air.This is typical of large amplitude solitary waves. The time series plots ofsodar-derived vertical wind velocity revealed a maximum peak-to-peakvariation of about 5 m s-1 during periods of wave-associated disturbance.The vertical velocity is found to increase with height up to the top of the closedcirculation within the wave and decreases further above. The normalisedamplitude-wavelength relationship for the two events indicates that theobserved waves are close to a strongly nonlinear regime.

Ocean Internal Wave Observations Using Space Shuttle and Satellite Imagery

Space shuttle photographs and satellite radar (SAR) images provide an excellent view of high‐contrast ocean features such as internal waves, fronts, eddies, oil slicks, and cloud patterns which contain the signatures of atmospheric processes. Since ocean internal waves generate local currents which modulate surface wavelets and slicks, we have been able to detect packets of internal waves in space shuttle photographs and radar imagery of the Atlantic, Pacific, and Indian Oceans. A global database on internal waves has been developed at our center with support from ONR and NASA, and is accessible on the Internet. The database includes visible and radar imagery. To test the database, digitally orthorectified images were used for dynamic and statistical analysis of internal waves. In the deep ocean we found the wavelength distribution to be Gaussian while in the coastal ocean it is Rayleigh. Results have also been applied to non‐linear evolution studies of ocean internal waves, atmospheric solitary waves and to estimate ocean currents.

Interactions of atmospheric solitary waves of different modes

The interactions of atmospheric solitary waves with different modes are investigated by a perturbation method. The model considered in this paper consists of a lower layer with exponential density profile and an infinitely deep upper layer with constant density. The analysis show that the waves obey the Benjamin-Ono equation before and after interaction, and the main effect of the interaction is the phase shifts for each wave.

Atmospheric solitary waves: some applications to the morning glory of the Gulf of Carpentaria

A mathematical model is proposed to describe atmospheric solitary waves at the interface between a ‘shallow’ layer of fluid near the ground and a stationary upper layer of compressible air. The lower layer is in motion relative to the ground, perhaps as a result of a distant thunderstorm or a sea breeze, and possesses constant vorticity. The upper fluid is compressible and isothermal, so that its density and pressure both decrease exponentially with height. The profile and speed of the solitary wave are determined, for a wave of given amplitude, using a boundary-integral method. Results are discussed in relation to the ‘morning glory’, which is a remarkable meteorological phenomenon evident in the far north of Australia.

Solitary Waves in the Atmosphere

The weakly nonlinear theory for internal solitary waves is reviewed, and theoretical results of the vertical and horizontal structure of temperature, vertical displacements, and vertical and horizontal perturbations to the wind field associated with steadily propagating solitary waves are presented in two idealized atmospheric configurations. One configuration is representative of solitary waves observed in the lower troposphere and the other of solitary waves that occupy the entire troposphere. The important results of the theory are presented in a form that can be readily used by observationalists. The results obtained are then analyzed using actual rawinsonde data for two well-documented observations of atmospheric solitary waves, which are analogous to the two idealized configurations. The importance and difficulties of properly identifying the waveguide within which the solitary wave is confined are discussed. The fundamental role of a critical level in ducting the disturbances and thus in defining the thickness of the waveguide is illustrated in the example dealing with the solitary wave occupying the entire troposphere. Together, these two examples illustrate the decisions and compromises that must be made in applying the theory to the real atmosphere.

A Thunderstorm-Generated Solitary Wave Observation Compared with Theory for Nonlinear Waves in a Sheared Atmosphere

Abstract The theory of internal nonlinear waves in a motionless medium is extended to waves in sheared flow to provide a basis for the interpretation of atmospheric solitary waves. It is shown that if the Scorer parameter is zero in a semi infinite upper region, the integro-differential equation [i.e., the Benjamin-Davis-Ono (BDO) equation] defining the evolution of nonlinear waves in sheared flow is independent of shear and stability in the upper layer. A new type of evolution model is presented, based on the numerical solution of the BDO equation, for the generation of solitary waves by a thunderstorm moving at supercritical speeds. The results of a thorough study of observations of a thunderstorm-generated solitary wave are presented in detail. These observations show that some of the storm's outflow, which was denser than the environment through which the wave propagated, was trapped in the interior of the wave. It is hypothesized that the Coriolis force then caused this denser air to flow along the a...

Evidence of very-large-amplitude solitary waves in the atmosphere

ATMOSPHERIC solitary waves are gravity waves that retain their integrity over long periods because of a near balance between nonlinearity and dispersion. They have been observed on various scales in many regions of the world1–3, but we present here detailed measurements of solitary waves with amplitudes comparable to the scale height of the lower troposphere. Two such waves were generated downstream of intense mid-tropospheric pressure troughs over the central United States. They propagated over 1,000km (several times their wavelength) with no appreciable change in structure within a 'waveguide' formed by surface inversion and a middle tropospheric critical level. Fluctuations in surface pressure associated with the two waves exceeded 6 mbar and 10 mbar. The waves caused banded patterns of precipitation and significantly influenced other meteorological phenomena. The restoration of balance between pressure-driven air flow and the Coriolis force ('geostrophic adjustment') seems to have a prominent role in the formation of these solitary waves.

The wavefront shape, position, and evolution of a great solitary wave of translation

Doppler radar mapped the evolution of a pair of atmospheric solitary waves emanating from a thunderstorm complex. The 100-km-long curved wavefront and position of these few-kilometer-wide waves are hypothesized to be a result of an amplitude-dependent wave speed. The observed unfolding is compared with a solution of the nonlinear integro-differential equation governing the evolution of finite amplitude disturbances in stratified media.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Atmospheric Solitary Waves

We show that the hydrodynamic equations which govern the propagation of acoustic gravity waves can have shock-like solutions.

Internal Solitary Waves in an Atmosphere with Thermal Inversion

Abstract This paper reports a study of solitary waves in a compressible atmosphere with a layer of cold air underneath a layer of warmer air of infinite height. The temperature of each layer is uniform. Two critical speeds and the first-order solitary wave solutions for both layers are obtained in terms of the temperature and mass flux ratios. The internal solitary wave may be a wave of elevation or depression, or may not appear at all. The amplitude of a wave of elevation (depression) increases (decreases) with the height and reaches a maximum (minimum) at the inversion interface, then stays at the maximum (minimum) value in the upper layer. The wave speed is found greater than the corresponding critical speed, and no solitary wave appears when the temperature of the atmosphere becomes uniform.

Solitary Waves in an Atmosphere with Arbitrary Wind and Density Profiles

Solitary waves in a compressible atmosphere of finite or infinite height with arbitrary wind and density profiles are studied. Explicit expressions for the critical speed and the first-order solution of the internal solitary waves are obtained by a perturbation scheme applied to the nonlinear equations and are expressed in terms of simple integrals of velocity and density profiles of the atmosphere in the state of equilibrium. The slope of the density profile at the bottom surface plays an important role in determining the signature of the wave, and solitary waves do not appear when the parameters involved in the solitary wave solution assume certain critical values. The results obtained cover many of the existing solitary wave solutions as special cases.

The Atmospheric Solitary Wave

Solitary waves have been observed in shallow water. In the present paper some evidence is presented for the existence of similar phenomena in the atmosphere. A possible mechanism for the formation of atmospheric solitary waves is described, and a case study is discussed in support of this mechanism. Some speculations are made about some possible effects of these disturbances on the local weather.