Modelling the morning glory of the Gulf of Carpentaria

Abstract

The morning glory is a meteorological phenomenon which occurs in northern Australia and takes the form of a series of roll clouds. The morning glory is generated by the interaction of nocturnal seabreezes over Cape York Peninsula and propagates in a south-westerly direction over the Gulf of Carpentaria. In the present work, it is shown that the morning glory can be modelled by the resonant flow of a two-layer fluid over topography, the topography being the mountains of Cape York Peninsula. In the limit of a deep upper layer, the equations of motion reduce to a forced Benjamin–Ono equation. In this context, resonant means that the underlying flow velocity of the seabreezes is near a linear long-wave velocity for one of the long-wave modes. The morning glory is then modelled by the undular bore (simple wave) solution of the modulation equations for the Benjamin–Ono equation. This modulation solution is compared with full numerical solutions of the forced Benjamin–Ono equation and good agreement is found when the wave amplitudes are not too large. The reason for the difference between the numerical and modulation solutions for large wave amplitude is also discussed. Finally, the predictions of the modulation solution are compared with observational data on the morning glory and good agreement is found for the pressure jump due to the lead wave of the morning glory, but not for the speed and half-width of this lead wave. The reasons for this are discussed.

Dispersive shock waves in viscously deformable media

“…equation for atmospheric phenomena (Porter & Smyth 2002). Due to its experimental relevance, the viscous fluid conduit system deserves further theoretical study in the large amplitude regime.…”

Unsteady undular bores in fully nonlinear shallow-water theory

“…Importantly, it also represents a universal mechanism for the generation of the solitary waves, which can be realized in several different fluid flow contexts. For instance, it occurs in the generation of solitary waves in trans-critical flow over topography (see [17], [18]), and in the formation of internal solitary waves in the coastal ocean [3] and atmosphere [5]. If the amplitude of the initial difference between the two basic states (e.g.…”

“…Undular bores also arise in other fluid flow contexts; for instance they can occur as internal undular bores in the density-stratified waters of the coastal ocean (see, for instance, [2], [3]), and as striking wave-forms with associated cloud formation in the atmospheric boundary layer (see, for instance, [4], [5]). They can also arise in many other physical contexts, and in plasma physics for instance, are usually called collisionless shocks.…”

“…For sufficiently large transitions, the front of the bore is often turbulent, but as noted in the classical work of Benjamin and Lighthill [1], transitions of moderate amplitude are accompanied by wave trains without any wave breaking, and are hence called undular bores. Well-known examples are the bores on the River Severn in England and the River Dordogne in France.Undular bores also arise in other fluid flow contexts; for instance they can occur as internal undular bores in the density-stratified waters of the coastal ocean (see, for instance, [2], [3]), and as striking wave-forms with associated cloud formation in the atmospheric boundary layer (see, for instance, [4], [5]). They can also arise in many other physical contexts, and in plasma physics for instance, are usually called collisionless shocks.…”

Approximate Techniques for Dispersive Shock Waves in Nonlinear Media

“…These bores arise due to narrowing estuaries enhancing strong tides so that the tide breaks with dispersion then resolving the breaking wave form into a bore. Bores also occur in the atmosphere, the most well known being glory waves [2,3,4,5], and as internal waves in the ocean [6]. Fluid bores can be of two types, viscous and undular bores, depending on whether viscosity or dispersion, respectively, dominate the evolution [1,7,8].…”