Travelling Waves and Bores in the Lower Atmosphere:

The ‘Morning Glory’ and Related Phenomena

Roger K. Smith

Presented by:

Andi Syahid MuttaqinRiza Adriat

Terencio Fernandes MonizKrismianto

Outline

o Introductiono The Morning Gloryo Theoretical Backgroundo Laboratory and Numerical

Experimentso Related Phenomenao Conclusion

Introduction(Section 1)

o The last ten years have seen a burgeoning interest in large amplitude waves and bores generated on a stably-stratified layer in the lower atmosphere.

o The ‘morning glory’ is the name given to a spectacular low roll cloud or succession of roll clouds that occur early in the morning.

o It is now known that they are associated with solitary wave disturbances at the leading edge of an undular bore that propagates on a low-level stable layer.

o Solitary wave disturbances in the low atmosphere, including the morning glory, may give rise to significant low-altitude wind shear which make them a particular hazard to low-flying aircraft.

Schematic of the simplest solitary wave

o When waves travel at different speeds, the disturbance must spread over time unless some other mechanism intervenes.

o In a solitary wave, dispersion and nonlinear steepening exactly balance create a wave which propagates without change of shape.

The Morning Glory(Section 2)

Brief descriptiono Not all morning-glory bore waves are

accompanied by cloud.o For that reason, morning-glory

phenomenon refer to: wind squall, wind surge.

o The origin and structure of these phenomenon have been determined mainly on the basis of observational experiments in the years 1978-1984.

o Morning-glory disturbances have two preferred directions of travel (in northern Australia): Northeasterly morning glory (most common type) Southerly morning glory (less frequent type)

o While the structure of northeasterly and southerly morning glories is similar, the mechanism of generation must differ considerably.

o Northeasterly morning glories: Moved from sector about 60 deg. and 67 deg. Mean speed about 10.2 ms-1 and 10.6 ms-1

o Southerly morning glories: Moved from sector 140-220 deg. (mean dir. 180 deg) The speed in the range 6-17 ms-1 (mean speed 11.6 m)

Structure

Genesis of northeasterly glories

Demise of disturbanceso A few hours after

sunrise, the low-level stable layer is destroyed over the land by convective mixing.

o But, disturbances can continue to propagate inland in some form for considerable distances during the day.o Indeed, it has been suggested that some of the nocturnal solitary-wave-dominated disturbances are the remnants of northeasterly morning glories generated on the previous night: if this is the case, the disturbances would have to

propagate on an upper level wave-guide, perhaps the capping inversion at the top of the

mixed layer, and there would have to be an effective mechanism

for suppressing the vertical radiation of wave energy.o At this stage, the precise mechanisms associated with the

daytime transformation and decay of disturbances are unknown.

Southerly morning glorieso On the day after 1979 morning-glory experiment had ended it was

considerable surprise to observe a significant-amplitude morning glory, oriented east-west and moving from the south.

o Mechanism possibilities, include: The northeastwards movement of a front or frontal trough over central

Australia into the developing nocturnal inversion ahead of it, The interaction between the inland nocturnal low-level jet and the deeply

penetrating sea breeze from the southern gulf coast, Katabatic drainage from the Barkly Tablelands northwards to this coast.

o However, the data are inadequate to assess the relative importance of katabatic drainage.

o There is circumstantial evidence that a few surges are generated by the motion of a front, but this does not appear to be the most usual mechanism.

o Precursor to a southerly surge at Burketown is a marked increase in the southerly component of the low-level wind at Mount Isa during the late evening and early morning, following some hours later by an increase in the easterly component, a feature indicative of a nocturnal low-level jet (Mount Isa wind signature).

Theoretical Background(Section 3)

o For disturbance on a water surface the theories fall into two classes: those relating to steady bores; and those relating to transient, but in some sense, long lived bores which evolve from rather general initial disturbance

o Numerical solutions of the initial-value problem for the Korteweg-de Vries (KdV) equation, the equatin appropriate to transient finite amplitude disturbance, indicate that an initial surge with an abrupt rise in water level propagating on water of uniform depth at rest will subsequently develop wave-type undulations at its leading edge.

Korteweg de Vries (KdV) Equation

Where : = horizintal coordinate in the direction of

propagation = linear long wave phase speed

= the coeffisient of the nonlinier= dispersive terms = relatively shallow stable layer

03

3

0

x

A

x

AA

x

Ac

t

A

x0c

A

o In the deep fluid case where a relatively shallow stable layer of depth h underlies a much deeper layer of neutrally stable fluid, finite amplitudo disturbance with amplitudo a are governed to a fisrt approximation in a/h by the so called Benjamin-Davis-Ono (BDO) equation rather than the Kdv equation.

Benjamin Davis Ono (BDO) Equation

Where :: Shear distribution: depth

: Hilbert Transform

0)(2

2

0

Axx

AA

x

Ac

t

A

h

uc )(2 10

)(])12[(

)(4

102

20

ucn

uch

dx

xx

xAxA

'

)'(1))((

u

h

o Even if the well mixed layer extends to 4 km, the atmosphere is stably stratified above this level and the vertical radiation of wave energy there becomes a possibilty

o Atmosphere bore waves range of solutions for the evolution of solitary wave trains from a variety of initial disturbances, mostly in the form of long waves of elevation, including step like bores of infinite extent. The solution are based on integrations of the time-dependent forms of the BDO-equation and its frictional counterpart, the so-called BDO-Burgers equation

BDO – Burgers Equation

Where : = Amplitude of the leading soliton

= Eddy diffusivity coefficient

02

2

2

2

X

U

X

U

X

UU

T

U

)(1

0tcxh

X th

T2

),(),( txAh

TXU

U

o Fig shown an example of the amplitude evolution of a long wave of elevation of finite extent as governed by

BDO-Burgers equation for relatively smaal dissipation

Laboratory and Numerical Experiments

(Section 4)

o A number of laboratory experiments have been carried out with obvious relevance to the morning glory and related phenomena.

o Of particular importance is a series of experiments by Maxworthy (1980) which concerns the production of non linear internal solitary wave from the gravitational collapse of mixid regions of fluid into a stably stratified wave-guide.

o The basic configuration has features in common with the envisaged collapse of negatively buoyant air generated by the collision of the east and west coast sea breezes over Cape York Peninsula (as indicated in the numerical simulations of Noonan and smith (1986,1987).

o Maxworthy found that the collapse creates a sequence of amplitude ordered solitary waves in line with the theoretical predictions.

o Quite general and uncontrolled mixing events created solitary wave train and lead us suspect that they should be exited under many circumstances in natural system.

o Tepper (1950) argues that a cold front acceleration into a low-level stable layer would, in certain circumstances, lead to a propagating wave type disturbance on the layer which runs ahead of the front, eventually steepening to form a near discontinuity, a type of internal hydraulic jumps or bore.

o Baines(1984), along rectangular channel was filled through most of its depth with fresh water and then topped up with a much shallower layer of paraffin, forming a two layer system.

o Smith e al. (1982), describe an experiment of this type and snow a photograph of a wave like disturbance running ahead of the gravity current on the stable layer.

o A key feature of such flow is that the maximum phase speed Cw, for wave propagation on the stable layer is faster than the speed at which the gravity current advance, Cgr.

o However the supercritical case Cgr>Cw, is of interest also in relation to bore formation as demonstrated in laboratory experiments by wood and Simpson (1984).

o Conclude, undular bores can be generated, either in the subcritical regime as a disturbance moving ahead of a gravity current on stable layer, or supercritical regime as gravity current that has been modified by its interaction with the stable layer, or by the collapse of a mixed region of fluid into a table wave guide as occurs for example when two gravity current collide.

o In recent papers, Crook (1986, 1987) has considered the effects of ambient shear, continuous vertical stratification and moisture on the motion of atmospheric undular bores.

o The first of these paper shows that presence of the continuous stratification throughout the atmosphere significantly reduce the disturbance amplitudes at low levels by allowing wave energy to propagate upwards.

o The second paper, explores the relative importance of three mechanisms that may inhibit the leakage of energy from the bore wave into the upper atmosphere; these are opposing winds in the middle and upper troposphere; the presence of an opposing jet in the lower atmosphere.

Related Phenomena(Section 5)

• From laboratory experiments (Maxworthy) concluded that:

If a physical system is capable of supporting solitary wave motions then such motions will invariably arise from quite general excitations.

Frequent occurrences of Morning glories from varies directions in the southern gulf region of northern Australia and Nocturnal solitary wave disturbances in central Australia.

CONCUR

What is so special about Australia ?Do such disturbances occur frequently elsewhere?

While…. • The Gulf of Carpentaria region may

be exceptional for the variety of mechanisms that operate to produce undular-type bores.

• Schreffler and Binkowsky (1981) describe two pressure jump lines (PJL) that were observed on consecutive nights in the St. Louis area.

• PJL a line along which an atmospheric pressure wave produces a sudden increase of pressure that often results in storms.

o Haase and Smith (1984). Morning Glory was observed shortly after sunrise in central Oklahoma and appeared also to have been generated late on the previous evening by thunderstorms some 500 km away.

o In all these cases, the most plausible generation mechanism for the bore waves is that they were produced by thunderstorm outflows moving subcritically into the wave-guide provided by the nocturnal low-level stable layer underlying a much deeper well-mixed layer.

o Doviak and Ge (1984) investigated the characteristics of a nocturnal solitary-wave disturbance that was observed also in central Oklahoma.

From a synthesis of Doppler radar concluded that the wave was initiated by a thunderstorm outflow moving into an inversion layer formed by the passage of an earlier storm. The wave was followed by at least one weaker wave.

o A bore-like disturbance accompanied by two spectacular low roll-clouds, was apparently generated by the interaction of a sea-breeze front with a thunderstorm outflow near the northern coast of Western Australia (Smith, 1986).

Conclusion(Section 6)

Concluding Remarks (1)

o The morning glory is a line wind squall, accompanied by a pressure jump, and often by a long roll-cloud or series of such clouds.

o The morning glory frequently occurs in the early morning.

Concluding Remarks (2)

o Disturbances are sometimes accompanied by spectacular low-level roll cloud lines and frequently by low-level wind shears and up-and-down currents that are hazardous to low flying aircraft.

o Observations support the results of laboratory experiments which show that whenever a suitable wave-guide exists, solitary waves and bores evolve from quite general excitation mechanisms.

Concluding Remarks (3)

o Southerly morning glories are structurally similar to their northeasterly counterparts, but their mechanism of generation remains uncertain and there may be more than one mechanism.

o Laboratory and numerical simulations show that:

1. solitary waves and bores may be generated ahead of a gravity current on a stable layer.

2. The gravity current itself is modified in structure by the stable layer

3. in the aftermath of the collision of two gravity currents.

Morning Glory Roll Clouds (videos)

References

Clarke RH, Smith RK, Reid DG. 1981. The morning glory of the Gulf of Carpentaria: an atmospheric undular bore. Mon Wether Rev. 109:1726-1750

Christie DR. 1988. Long linear waves in the lower atmosphere. J Atm Sci.

Smith RK. 1988. Travelling waves and bores in the lower atmosphere: The ‘morning glory’ and related phenomena. Earth Sci Rev 25:267-290

Smith RK. 2002. Advanced lectures on dynamical meteorology. Munich.