The Self-Made Tapestry Phần 7 docx

Page 178 temperature). Assuming parameters close to those found experimentally for this transition, they found that convection was a mixture of these two processes. Sinking currents in the upper mantle generally did not penetrate the boundary at 660 km, but if two such currents were pushed together by one of the broad upwelling flows, together they might achieve a threshold size that would enable them to punch through the boundary and flush into the lower mantle. A similar picture of both layered and whole- mantle convection was painted by Paul Tackley of the California Institute of Technology and colleagues when they conducted the same kind of computer simulation, but with a somewhat more realistic model, in 1993. They found that again the flow pattern organized itself into hot rising plumes and cold sinking sheets. The plumes were able to punch their way from the base of the mantle straight through the 660-km boundary to the top; but the cold sinking sheets, the analogue of mantle slabs, generally stopped at this boundary, where the cold, dense fluid accumulated in spreading puddles. When these cold pools became large enough, they would suddenly flush through to the lower mantle in an avalanche, creating a broad sinking column that than spread in a vast pool at the core-mantle boundary (Plate 15). What limited direct evidence we have of the nature of mantle convection seems to support this picture: sometimes slabs of cool material borne downwards at subduction zones seem to be stopped or deflected at the 660-km boundary, but others appear to pass right through. Little by little, we are starting to piece together the mysteries of the Earth's bowels. Air, water, earth and fire There are ample examples of natural convection patterns to keep us diverted at the Earth's surface too. The canvas of the sky is streaked with their imprint. The towering piles of cumulus clouds are erected by convective updrafts as warm air, locally heated by the Sun, rises and bears water vapour with it (Fig. 7.20). As the air cools, the water vapour condenses out into tiny droplets that, by reflecting light, provide the cloud's white billows. Fig. 7.20 Clouds trace out the convection patterns of the atmosphere. towering cumulus stacks form around updrafts, where warm air rises. (Photo: Jackie Cohen.) The atmosphere loses its heat primarily by radiation from the uppermost layers, while it it warmed not only by direct sunlight but by heat radiated from the ground. So there is a perpetual imbalance set up between warmer, lower air masses and cooler air higher upwith the consequence that air is always on the move somewhere, bringing winds, storms and sometimes the violence of hurricanes. When this imbalance is suppressedwhen, for example, cold dense air gets trapped in a valleythe result is a temperature inversion, a stagnation of the atmosphere that can allow smog to accumulate. Convection in the atmosphere cannot be accurately described by Rayleigh's model, because many of the assumptions he madethat the fluid is incompressible, that the viscosity does not very significantly with temperaturejust aren't good ones for air. All the same, many of the general features of convection patterns still apply, and in particular convective motion can become organized into roll-like cells of more or less equal width. These can give rise to banded cloud formations called cloud streets or mare's tails (Fig. 7.21), which mark out the boundaries of the roll cells. These rolls are typically wider than they are deep, unlike the roughly square profile of Rayleigh-Bénard rolls. Approximately hexagonal cells can also be seen in satellite images of cloud convective patterns. On much larger scales, vast atmospheric convection cells are set up by the differences in temperature between the tropics and the polar regions. These cells don't have a simple, constant structure, and moreover they are distorted by the Earth's rotation; but nevertheless they do create characteristic circulation features, such as the tropical trade winds and the prevailing westerly winds of temperature latitudes. Edmund Halley first proposed in the seventeenth century that convection owing to tropical heating drives atmospheric circulation, and for some time after it was believed that a single convection cell in each hemisphere Page 179 Fig. 7.21 Convective roll cells in the atmosphere can create regular cloud streets, as water vapour condenses at the tops of the cells. (Photo: Wen-Chau Lee, NCAR, Boulder, Colorado.) carried warm air aloft in the tropics and bore it to the poles where it cooled and sank. We now know that this picture is too simplified, and that there are in fact three identifiable cells in the mean hemispheric circulation of the lower atmosphere: one (called the Hadley cell) that circulates between the equator and a latitude of about 30°, one (called the Ferrel cell) that rotates in the opposite direction at mid-latitudes, and one (called the polar cell) that rotates in the same sense at the pole (Fig. 7.22). The polar and Ferrel cells are both weaker than the Hadley cell and are not clearly defined throughout all the seasons. Where the northern Hadley and Ferrel cells meet, the effect of the Earth's rotation drives the strong westerly jet stream. Fig. 7.22 Large-scale convection in the Earth's atmosphere traces out three hemispheric convection cells: the Hadley cell between the equator and about 30° latitude, the Ferrel cell at mid-latitudes and the polar cell over the pole. The oceans too exhibit convection patterns over several size scales. Like the atmosphere, the oceans are warmed in the tropics and cooled in the polar regions, and so cool, dense water sinks around the poles. This helps to establish a vast conveyor-belt circulation from the tropics to high latitudes, and the warm water carried polewards at the top of the North Atlantic convection cell brings with it heat that keeps Northern Europe and the eastern North American seaboard temperate. This circulation pattern is modulated, however, by the fact that the density of sea water is also determined by the amount of dissolved salt it containsthe more saline the water, the denser it is. The salinity can be altered by evaporation, which removes water vapour and leaves behind saltier water. Freezing also affects salinity, since ice tends to leave salt behind and so the unfrozen water gets increasingly saline as ice develops. Thus the large scale pattern of ocean convection is influenced by evaporation in the tropics and freezing at the poles: together, these processes give rise to the so-called ocean thermo haline ('heat-salt') circulation. On smaller spatial scales, the interplay between salinity and thermal convection can create diverse circulation effects in the upper few metres of the oceans, such as oscillatory rising and falling of water parcels or finger-like protrusions of salty water into fresher water below, called salt fingers (Fig. 7.23). Fig. 7.23 Convection in the surface layer of the oceans due to differences in salinity (and therefore in density) produces forests of sinking 'salt fingers'. Here a laboratory model makes them visible. (From: Tritton 1988.) Once you start to spot convection patterns in the world around you, they crop up in the most unlikely places. You can find their polygonal imprint petrified Page 180 Fig. 7.24 The freezing and thawing of water in the solis of northern tundra sets up convective circulation owing to the unique density changes that water undergoes close to its freezing point. The imprint of this circulation can be seen as polygonal cells of stones at the ground surface. Shown here are stone polygons on the Broggerhalvoya peninsula in western Spitsbergen, Norway. (Photo: Bill Krantz, University of Colorado.) into stone and rock in some of the frozen wates of the world in Alaska and Norway (Fig. 7.24). Now here's a real puzzleit's natural enough to find these patterns in the fluid media of air and sea, and even in hot, sluggishly molten rock, but how do they find their way into frozen stony ground? Fig. 7.25 As water circulates in convection cells through the soil, the pattern is transferred to the 'thaw front', below which the ground remains frozen. Stones gather in the troughs of the thaw front, and are brought to the surface by frost heaving in the soil. The answer, according to William Krantz and colleagues at the University of Colorado at Boulder, is that convection takes place in the water-laden soild beneath these formations as the water undergoes seasonal cycle of freezing and thawing. The idea that these cases of 'patterned ground' are caused by convection in fact dates back to the Swedish geologist Otto Nordenskjold in 1907, but Krantz and his co-workers were the first to place this idea on a firm theoretical basis. In these cold northern regions, water in the soil spends much of its time frozen. But when the ground warms and the ice thaws, it does so from the surface downwards, so the liquid water gets cooler the deeper it is. For most liquids this would correspond to a situation in which the density increases with depth in similar fashion. This is a stable arrangement, for which no convection would take place. But water is not like other liquids; perversely, it is densest at 4°C above freezing. So when it is warmed by about this amount at the surface, the water closest to the surface is denser than the colder water below it, and convection will begin through the porous soil (Fig. 7.25). Where warmer water sinks, the ice at the top of the frozen zone (the so-called thaw front) will melt, while the rising of cold water in the ascending part of the convection cells will raise the thaw front. In this way, the pattern of convection becomes imprinted into the underground thaw front. But how does this find its surface expression in mounds of stones?? Krantz and colleagues proposed that sub-surface stones are concentrated in the troughs of the corrugated thaw front and then brought to the surface by subsoil processes that are known to shift stones around when soil freezes. This raising up of stones to the surface is known to farmers as 'frost heaving', and results in the littering of a field with stones when it freezes during a frost and then thaws. Polygonal patterns formed in this way can also be found on the beds of northern lakes when the water is shallow enough to freeze down into the lake bed (Plate 16). Krantz and Page 181 colleagues have developed a theoretical model of the convection patterns that can arise as water circulates through porous soils. They found that polygonal (particularly hexagonal) patterns are favoured on flat ground, but that the convection cells are roll-like on sloping ground, giving rise to striped formations at the surface (Fig. 7.26). Fig. 7.26 On sloping ground, the convection cells in freezing porous soils can become roll-like. The pattern traced out by stones at the surface is then a series of parallel stripes, seen here in the Rocky Mountains in Colorado. (Photo: Bill Krantz, University of Colorado.) Fig. 7.27 Solar granules are highly turbulent convection cells in the Sun's photosphere. (Photo: The Swedish Vacuum Telescope, La Palma Observatory, Canary Islands.) If you want to see convection on a grand scale, look to the Sun (though not literally, I hasten to add). The Sun's visible brightness comes from a 500-km thick layer of hydrogen gas close to its surface, called the photosphere, which is heated to a temperature of about 5500°C. This gas is heated from below and within, and radiates its heat outwards from the surface into spaceso that, although it is about a thousand times less dense than the air around us, it is a convecting fluid. The Rayleigh number of this fluid is so high that is should be utterly chaotic and unstructured. But photographs of the Sun's surface show that, on the contrary, the photosphere is pock-marked with bright regions called solar granules, surrounded by darker regions (Fig. 7.27). These granules are convection cells, whose bright centres are regions of upwelling and whose dark edges are regions of cooler, sinking fluid. Each granule is between 500 and 5000 km across, making the largest about half the diameter of the Earth. The pattern is constantly changing, each cell lasting only a few minutes. The very existence of these cells in such a turbulent fluid shows that we still have a lot to learn about convecting fluids and their patterns. Riverrun Let's now return to Jean Leray gazing into the Seine at the Pont Neuf. As the water flows around the columns of the bridge, swirling eddies disturb the surface in the wake downstream. Can we make sense of this flow pattern? [...]... flows The Reynolds number Page 183 (Re) is essentially the ratio of the forces driving the flow to the forces retarding it (the viscous drag) In its most general form it is given by the product of the velocity of the flow and the characteristic size of the system confining or deflecting the flow, divided by the viscosity For flow down a narrow channel, the 'size' is the width of the channel; for the. .. for the peaks In other words, the undulations of the wave are pushed outwardsthe wave becomes more pronounced (Fig 7. 30e) The same principle provides the lift under the wings of an aircraft, since the aerofoils are curved in the same mannerconvex on the upper side, concave below The undulations are eventually deformed into a train of vortices (Fig 7. 31), whose graceful regularity is fleeting: they... subsequently with the vortices that appear as a result of the latter (Fig 7. 31) But this is not so; the Kármán vortices have a different origin They are provided 'ready-made' from the flow field immediately behind the cylinder, where the sheared fluid layers acquire 'vorticity'a rotating tendencyas a consequence of the disturbance that the cylinder imposes on the flow The instability in the flow behind the cylinder... another (Fig 7. 40) Where they meet, something clearly has to give One possibility is that one flow bends to the right and one to the left; then the streams slip past one another in a shear flow But it turns out that another option is for both flows to splay in two, with the two streams diverging to left and right The streamlines in Page 190 each flow then follow trajectories in the shape of curves mathematically... that leave the wake looking like a swirling art nouveau design (Fig 7. 29d) This pattern is called a Kármán vortex street, after the Hungarian physicist Theodore von Kármán The vortices are carried along with the Page 184 flow, but more slowly than the average speed of the flow They slowly dissipate their energy through viscous drag and vanish further downstream Like the onset of convection or the appearance... this flow (Fig 7. 30d) This pushes together streamlines on the convex side of the disturbanceover the 'peaks' and pulls them apart on the concave side, in the dips What this means is that the fluid flows slightly faster (in opposite directions on each side) over the peaks and slower in the dips (Think of a similar squeezing-together of streamlines when a river flows through a narrow gorgethe flow gets... faster.) Now, the key to the instability is this: along any particular streamline in a flow, the pressure of the fluid decreases as its velocity increases This fact was demonstrated in 173 8 by the Swiss mathematician Daniel Bernoulli, and it is known as Bernoulli's law It means that the pressure of the fluid against the dips of the wavy interface increases (because the velocity decreases there), and... measure of the speed of the flow and the width of the cylinder At low Reynolds number, the streamlines simply bend around the obstacle (b) At higher Re, circulating vortices appear behind the cylinder (c) These grow with increasing Re, until they become highly elongated (d) happens to all the other parallel layers too This assumption is not perfect, and indeed we will find that the flow of the fluid... place behind the cylinder As the Reynolds number is increased, these eddies get bigger; by the time Re is about 40, they are highly elongated (Fig 7. 28d) But the wake downstream of the cylinder remains laminar: the deflected streamlines outside the eddies converge again until they resume their parallel paths Beyond a Reynolds number of about 40, something dramatic starts to happen to the wake It acquires... away from the disturbed region on alternating sides of the 'street' and are entrained in the wake So vortex creation takes place immediately behind the cylinder, not all along the shear flow as in the Kelvin-Helmholtz instability The vortex-shedding process is highly organized: at the same time as the vortex on one side is being shed, that on the other is in the process of reforming (Fig 7. 32) Such . that the pressure of the fluid against the dips of the wavy interface increases (because the velocity decreases there), and vice versa for the peaks. In other words, the undulations of the wave. through the porous soil (Fig. 7. 25). Where warmer water sinks, the ice at the top of the frozen zone (the so-called thaw front) will melt, while the rising of cold water in the ascending part of the. The flow pattern depends on the Reynolds number (Re), which is a measure of the speed of the flow and the width of the cylinder. At low Reynolds number, the streamlines simply bend around the