Strati cation and circulation produced by heating and evaporation on a shelf

Transcription

1 Journal of Marine Research, 56, , 1998 Strati cation and circulation produced by heating and evaporation on a shelf by J. S. Turner 1 ABSTRACT A series of exploratory laboratory experiments has been carried out to model an inverse estuary, in which density differences and out ows were generated by heating and evaporation on a shallow shelf. This shelf was connected to a deep, long region of uniform depth through a steep slope. The experimental tank was lled with homogeneous salt solution, and the shelf region heated with infrared lamps to produce temperature and salinity anomalies; fresh water was added at the far end of the tank to keep the depth (and the mean salinity) constant. The emphasis in these experimentswas on the in uence in a closed region of horizontal differences of T and S together; i.e., on the double-diffusiveeffects, which are quite different from those due to a simple source of buoyancy in the shallow region. The vertical density difference increased over time, and this and the internal circulations became quasi-steady after several days. Two distinct regions of circulation and types of layering were revealed by dye streaks and detailed pro le measurements. Near the surface there were strong salt ngers, driven by a hot saline layer spreading away from the shelf, with a counter ow of cooler, fresher water below. The warm salty water depositedby the ngers near the top of the slope formed a gravity current which owed to the bottom and extended away from the slope, building up a strati cation with salt and heat now distributed in the reversed diffusive sense. There was also evidence for a second mechanism of bottom water formation, the intermittent ow of hot very salty water off the shelf and down the slope. This latter process could be initiated more predictably by turning off the heater lamps. 1. Introduction The circulation in estuaries, and more generally in larger ocean basins, is determined, or at least strongly in uenced, by the local production of water in shallow regions which has a different temperature, salinity and density from the seawater at the mouth of the estuary or in the deeper ocean. In the most common case strati cation and horizontal circulations are set up when a river ows into the head of an estuary. Less usual, but in some regions very important, is the inverse estuary effect, in which property anomalies are produced by heating and evaporation to form warmer but denser water at the shallow end of an estuary or gulf which is surrounded by an arid region, with little runoff. A well-studied case is Spencer Gulf in South Australia, and on a larger scale the Mediterranean Sea owing out 1. Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia. 885

2 886 Journal of Marine Research [56, 4 into the Atlantic can be regarded as an inverse estuary. Similar effects can be observed on broader, wider shelves, and data from the Northwest Shelf off Western Australia will be presented later as an example of the application of the results of the present study. A series of laboratory experiments has been carried out to explore the physical processes which may be important in such geometries. Each experiment starts with a homogeneous salt solution contained in a long tank in which there is a shallow, gently sloping shelf at one end, falling off more steeply onto a slope leading to the main body of the tank, where the depth is uniform. The experiments are two-dimensional and non-rotating, implying that the scales considered are such that Coriolis effects are unimportant. There is no mechanical mixing on the shelf, (equivalent to that produced by tides and winds in a gulf or estuary, as described by Nunes and Lennon (1987)). The present experiments are part of a more general study of ows produced by double-diffusive sources in closed regions. The above rationale for the geometry adopted in fact came after the experiments were begun, and this con guration can perhaps more appropriately and generally be regarded as just a convenient way to introduce spatially non-uniform temperature and salinity anomalies into an experimental tank. There has been a considerable amount of theoretical and laboratory work on ows driven by simple sources of buoyancy in this geometry (see, for example, Phillips (1966), who considered the buoyancy-driven circulation in the Red Sea produced by a surface heat ux, and the recent review by Maxworthy (1997)). The emphasis in the experiments reported here, however, is on understanding the combined effects of temperature and salinity anomalies and in particular how these lead to double-diffusive processes, which can generate strati cation and circulations quite different from those produced by a single stratifying property. If denser water, produced by an increase in salinity, is added to an initially homogeneous region of lower salinity and the same temperature, the system will evolve to a strati ed state in which the range of densities always lies between those of the initial solutions, whatever mixing has taken place. This is not true when the temperature as well as the salinity of the input differs from that of the ambient uid. There are now many ocean observations of ne structure and microstructure in the ocean which can only be explained in terms of double-diffusive processes. Whenever there is a systematic association between temperature and salinity, such that they have opposing effects on the density, then it seems likely that the difference in molecular diffusivities can in uence the formation of relatively well-mixed layers and thus affect the vertical transports and the larger scale horizontal motions. Much of the detailed understanding of double-diffusive processes has come through laboratory experiments (see the reviews by Turner (1985, 1995) and Schmitt (1994)), but most of these studies have been onedimensional; i.e., they have concentrated on the vertical uxes across established sharp interfaces. There are still relatively few experiments which take into account horizontal differences of both properties, and most of these have used the sugar/salt analogue for salinity and temperature differences introduced by Stern and Turner (1969). Turner and Chen (1974)

3 1998] Turner: Model of inverse estuary 887 explored the effects of horizontal gradients of properties in various geometries, and Turner (1978) reported experiments on intrusions produced by localized sources of salt or sugar feeding into a salinity gradient. The behavior is very different without and with double diffusion in the latter case strong vertical convection occurs, with the spread of intrusions at many levels. A source of sugar solution, say, in a homogeneous salt solution of the same density also produces convection which leads to strati cation and associated horizontal motions. Another con guration which has received some attention is a vertical boundary or front with different diffusive properties across it. Ruddick and Turner (1979) used the sugar/salt system to study the formation of intrusions driven by horizontal property anomalies, with identical vertical density gradients on each side of a front. In the heat/salt case, there have been several studies of the layers formed by heating the side wall of a tank containing a solute gradient; the most recent of these, Chen and Chen (1997), summarizes the earlier work. Huppert and Turner (1980) reported an experimental study of iceblocks melting into a salinity gradient, which produced both temperature and salinity anomalies. These experiments, apart from some unpublished experiments and movies of my own, are the only studies known to me which have attempted to use a combination of horizontal temperature and salinity differences directly to model oceanic processes. Some of the same physical phenomena observed in the experiments outlined above are also important in the series of experiments reported here. Starting with homogeneous salt solution, heating and evaporation on the shelf produce out ows into the interior region and down ows along the slope, together with a strong vertical strati cation in the body of the tank. (Another aspect of this process is the lling box effect described by Baines and Turner (1969).) In the double-diffusive gradients so formed, horizontal circulations, intrusions and layering develop. All of these individual observations can be understood in terms of previously studied double-diffusive processes, but when they are considered in the context of the total experimental region they have some important and surprising implications for estuarine and larger scale ocean circulations. 2. Experimental method The experiments were all carried out in a perspex tank 1820 mm long, 80 mm wide and 250 mm deep. The experimental arrangement is shown schematically in Figure 1, and the conditions used for the experiments are set out in Table 1. Two forms of shelf and slope (made of foam plastic, weighted to stop it oating when the tank was lled) were inserted at one end of the tank for different runs. The rst, labeled A in Table 1, consisted of a 300 mm long shelf sloping down 10 mm over its length to a height above the bottom of 214 mm at the junction with the slope, which dropped off at 45 to the bottom of the tank. The second con guration (B in Table I) had a 500 mm long shelf with a slope of 1:30 and a gradual transition region (a curved section with radius 100 mm) leading to the slope which again had a 45 inclination. In later experiments, all those lmed in time-lapse, the top 200 mm of this shelf was blocked off to give an effective length of 300 mm (runs C in Table 1).

4 888 Journal of Marine Research [56, 4 Table 1. The experimental conditions. Run no. Shelf type S.G. of salt solution Depth over heated shelf (mm) Mean evap. rate (ml/min) Comments 2 A Prominent front on shelf 3 A Ditto 4 A (0.68) Lamp blew 5 B Photos, Fig. 2 6 B Photos, Fig. 5 7 C New lamps. Time lapse, runs C C C Deeper over shelf 11 C Lights lowered, larger heating rate Control B, C Mean of two long runs, no heating The tank was lled with salt solution in the range SG so that the minimum depth over the shelf was about 10 mm (with some variation, as recorded, between runs). Heating and evaporation were produced using two infrared lamps mounted above the slope. The placement and type of lamp was changed during the course of these experiments, so it cannot be assumed that the rate of heat input was constant between runs. Either a perspex or an aluminium plate painted black was let in ush with the upper surface of the foam over a section underneath the lamps, to protect it and absorb the heat penetrating to the solid surface. The total volume of water in the tank was kept constant by having a fresh water inlet, controlled by a constant head device, as shown in Figure 1. This was placed at the far end of the tank, 50 mm from the end wall and 30 mm below the surface, and there was some mixing between the input plume and the tank uid as the in owing fresh water rose to the surface and spread out. The precise geometry is not critical: in earlier preliminary runs the fresh water was added closer to the bottom of the tank, with more mixing, but the overall behavior of the ows near the shelf and slope was qualitatively little different. The fresh water was supplied to the constant head tank using a pump to circulate water from a larger reservoir. The level in this reservoir was allowed to fall before being topped up at convenient intervals, so providing a measure of the evaporation (and thus indirectly of the heating rate) over the intervening period. For comparison, we note that the evaporation rate measured over a long period with no heating was 0.26 ml/min. A section of the tank including all the slope and part of the shelf was illuminated from behind using tracing paper to diffuse the light from a projector, and the developing motions and strati cation were recorded at intervals on still and video pictures. Dye crystals were dropped in regularly by hand, or alternatively using an automatic dispenser in several long continuous time-lapse video runs. After the tank was lled with a homogeneous salt solution, the experiment was begun by switching on the heater lamps. The typical

5 1998] Turner: Model of inverse estuary 889 Figure 1. Schematic of the experimental tank, showing the shelf and slope at one end, and the fresh water supply at the other. The tank was 1820 mm long, 80 mm wide and 250 mm deep, with two alternative forms of foam plastic inserts (as described in the text) to model a gently sloping shelf and a steeper slope. evolution of the strati cation and ow, common to all the experiments, will now be described qualitatively, before proceeding to a more detailed presentation and analysis of the results. In less than 30 minutes after the heating was begun, steady counter- ows developed near the surface, with a surface out ow from the shelf about 15 mm thick, and a slightly thicker return ow below this. Dye streaks revealed that there was strong salt- nger convection between these layers, indicating that the out ow was less dense, but warmer and saltier, than the return layer. (Note immediately a striking difference from the case without double diffusion. This circulation in our experiments was in the opposite sense to that in Phillips (1966) Red Sea model, in which the surface water ows inwards, becomes denser due to surface cooling, and then sinks and ows out a greater depths.) After about two hours, further dye streaks showed that the nger convection was extending below the counter owing layers, right down to the slope and to the bottom of the region of constant depth. The warm salty (but denser) water deposited by the ngers near the top of the slope formed a gravity current which owed to the bottom and extended away from the slope, so building up a strati cation through the lling box mechanism, (with salt and heat now distributed in the reversed diffusive sense). Fluid deposited further down the slope was successively more diluted, so that it owed a shorter distance along the slope before spreading out (at its level of neutral buoyancy) at successively higher levels. In this way a succession of extending layers and counter ows was formed in the main body of the tank having constant depth.

6 890 Journal of Marine Research [56, 4 A second mechanism for the production of bottom water also became apparent later. As the temperature and salinity of the uid on the shallow shelf increased and reached a more nearly steady state, an inclined front developed on the shelf, sloping upward from the bottom toward the shallow end. There was a ow toward this front along the solid bottom from both directions, an up ow along the front, and an out ow at the surface. The hottest, saltiest water produced by the heating and evaporation was con ned behind the front, the position of which moved back and forth irregularly. At intervals this layer broke out past the front and owed over the edge of the shelf and down the slope, to produce a thin hot, salty gravity current directly. At the same time, there was a near-surface in ow onto the shelf to replace the volume removed. The spontaneous ow off the slope seemed to occur more readily with the shelf/slope con gurationa. This process could also be initiated more predictably by turning off the heater lamps; it was then observed that an upslope counter- ow developed above the down ow, driven by heat transfer through the doublediffusive interface at its upper surface. This up ow in turn spread out into the interior to produce further layers at various levels. Thus the apparently straightforward process of heating a homogeneous salt solution over a shelf, which is connected to a slope and a deeper basin, can produce a stable density gradient, with a strati cation in the nger sense near the surface, and in the diffusive sense near the bottom. The redistribution of the heat and salt also sets up strong shear ows and unsteady intrusions, driven by the horizontal and vertical property gradients. 3. Case histories of representative experiments Eleven runs have been carried out to date, using various conditions of shelf geometry, salinity and heating, with photographic or time-lapse video recording. In the rst run, a leak of fresh water from behind the slope was detected, and the results were therefore discarded without detailed analysis. This problem was corrected by lling this space with foam, and the conditions for each of the other experiments are set out in Table 1. In Run 4, one of the heater lamps blew overnight, so that the period and rate of heating is not known, but this run is nevertheless included in the table. More detailed data on the progress of several experiments are presented below. Photographs and density and temperature pro les measured at various times are used to illustrate the major points described in the preceding section. The description and interpretation of these observations, made over limited time intervals, have been reinforced by further insight gained from the later time-lapse runs carried out under similar conditions. a. Run 5. Deductions from the advection of dye This run is recorded in the series of photographs reproduced as Figure 2. The rst dye streak was injected after 46 min from the start of the experiment at 80 cm from the end of

7 1998] Turner: Model of inverse estuary 891 the tank, just off the end of the slope, (the position marked by the black arrow at the top). Figure 2a, taken 2 min after dropping in the dye crystals, shows that a strong shear ow had by that time been established at the surface, with an out ow from the shelf near the surface (A) and a counter ow of cooler fresher water below this (B). Between these layers vigorous salt ngers were apparent, and these extended deeper into the nearly stagnant uid below (C). Also seen in this photograph,at D, is the upward transport of dye above the dyed layer deposited on the bottom, driven by convection above a warm, salty layer. The mechanism of deposition of this bottom layer is made clearer in Figure 2b, which was taken 3 min after a dye streak was injected at 1 hr 2 min, this time at 70 cm from the end of the tank, near the center of the slope. In addition to showing the surface counter ows again, this photo shows the ow down the slope and out along the bottom. Note also the clear region (E) on the slope below the dyed down ow, which shows that even denser salt solution has been deposited by ngers higher up along the slope and has owed under the marked part of the down ow. Continuation of this down ow process gradually produced a strati cation in the tank. Figure 2c, taken 1 min after two dye streaks were deposited 60 cm and 70 cm from the end of the tank at 1 hr 53 min, shows that dye from the upper source had reached the bottom of the tank, while that from the source at 70 cm was owing out 25 mm above this, at F. Another photo (not shown) taken two minutes later revealed a clear layer spreading away from the slope between these two levels, evidently fed by undyed ngers reaching the slope between the two dye streaks. At later times the strati cation and the associated shear ows intensi ed. Figure 2d taken 1 min 40 sec after the injection of a dye streak at 3 hr 20 min shows two deeper layers in the body of the tank (G and H), below the surface shear layers, in which shears had been set up by the combination of horizontal and vertical property gradients set up by the injection of heat and salt near the slope. Note the interface (I) between these, inclined downwards to the right, which is revealed by dye in the lower layer which has been convected up from the bottom. Dye streaks inserted about an hour later at various horizontal positions revealed extra features of the ow. Figure 2e shows that ngers extended through both the deeper sheared layers G and H (a deduction which is supported by the density pro les discussed below). In this frame we can also see a clearly de ned surface layer (J) owing from the far end of the tank where the fresh water input is located, above the previously identi ed counter owing layers with ngers between them. (A thinner layer from this source can be identi ed in earlier photographs.) The strati cation at the bottom of the tank, below the sharp dyed interface, was clearly in the diffusive sense. Figure 2f shows that there was an up ow (K, marked by dye in this picture) above an undyed bottom current. This up ow was evidently driven by the transfer of heat through the diffusive interface above the down owing layer, and it was feeding warm salty water into the interior higher up the slope. This experiment was monitored intermittently for a total of 48 hr, during which a general

8 892 Journal of Marine Research [56, 4 Figure 2. Sequence of photographs taken during Run 5, showing the development of the ow and layering due to heating and evaporation on a shelf. (The added letters refer to speci c features of the ow, which are described in the text.) rise of the interfaces was observed; the bottom current owing down the slope nally did not reach the bottom but fed out above a stagnant layer. There are clearer photographs of the later stages of other runs, in which other physical phenomena were also observed. We will now proceed to describe the development of the vertical density structure in Run 5.

9 1998] Turner: Model of inverse estuary 893 Figure 2. (Continued) b. Run 5. The measurement of density pro les At intervals during the experiment, samples were withdrawn from standard depths at xed horizontal positions, and their density measured directly using an Anton Paar densitometer. The values obtained at the carefully maintained constant temperature in the instrument are therefore a measure of the salinity, not in situ density. Preliminary attempts have been made to measure temperature pro les, (and one such pro le will be reproduced

10 894 Journal of Marine Research [56, 4 below), but the precision attained was not sufficient to give consistently reliable readings, and further work will be required. However some deductions about the temperature gradient can be made from the reversal of salinity gradient over certain depth ranges (which would be hydrostatically unstable without a compensating temperature gradient). Since the timescale of the ows greatly exceeds the buoyancy period N 2 1, there is a hydrostatic balance at each horizontal position, while the shear ows observed imply that there will be a dynamic balance in the horizontal momentum equations. Figure 3 plots the density pro les measured at four times during the experiment. At each time, close to 3 hr, 6 hr, 24 hr and 48 hr into the experiment, samples were withdrawn at 80 cm from the shelf end of the tank; at 24 hr only, another pro le was measured near the far end of the tank, at 160 cm, but this is not shown here. Over the period documented in the photographs of Figure 2, up to 6 hr into the experiment, the main changes are twofold. First, the water near the surface became fresher than the original tank uid. (The readings right at the surface, corresponding to the observed thin surface layer, marked J in Figure 2e, are off scale on this plot, though they still indicate that there was substantial mixing of the in ow with the tank uid.) Second, at the bottom of the tank the salinity was increasing above the original value. Over most of the depth, however, the gradients were weak, with several barely detectable reversals which imply compensating temperature gradients, and are consistent with the observation of ngers. At 24 hr there was a further substantial decrease in salinity down to 10 cm from the surface (12 cm above the bottom), with a larger change at 160 cm, nearer the fresh input, than at 80 cm. The salinity increased at the bottom, with the value right at the boundary being marginally higher near the slope. At 48 hr there was a further decrease of salinity at 80 cm over the range 12 to 18 cm above the bottom, with a smaller change near the surface, while the salinity increased between the bottom and 6 cm. There was a slight decrease in salinity right at the bottom between 24 hr and 48 hr, consistent with the downslope ow feeding out at higher levels over this interval, and diffusion reducing the salinity attained earlier. c. Run 2. Density and temperature pro les In this run only, a satisfactory temperature pro le was obtained using a calibrated thermistor, in addition to the density obtained from withdrawn samples. In Figure 4 are plotted both this temperature pro le and the corresponding density pro le (which is a measure of salinity) obtained shortly after the temperature measurements were completed. There is a strong temperature maximum at the level of the out ow of warm salty water off the shelf, with above it a thin cooler, fresher in ow, and below it a 10 cm deep layer having a nearly uniform salinity and a stabilizing temperature gradient. Salt ngers were observed in this latter region. Below this again the salinity increases continuously to a maximum at the bottom, and there is a barely detectable second temperature maximum some distance above the bottom, evidently due to the out ow of warm salty water off the slope.

11 1998] Turner: Model of inverse estuary 895 Figure 3. Density pro les due to salinity variations, measured in Run 5 at four times after the beginning of the heating. Samples were withdrawn at 30 cm from the top of the slope, and the densities measured at constant temperature. Figure 4. Temperature and density pro les (due to salinity, at constant temperature) for Run 2, measured 28 hours after the start of the experiment at 30 cm from the top of the slope.

12 896 Journal of Marine Research [56, 4 Figure 5. Sequence of photographstaken during Run 6, after the heater lamps were turned off. These document the down ow of hot salty water directly off the shelf, the resulting down- and up ows along the slope and the intrusions into the interior. (See text for a detailed description of the speci c features marked by the added letters.)

13 1998] Turner: Model of inverse estuary 897 Figure 5. (Continued) It is also worth reporting spot measurements made on the shelf itself in this experiment a more thorough study of this region is planned. In the middle of the shelf the temperature (averaged over the depth) was 61.5 C and the S.G. of a sample here was ; both of these are much higher than the values characteristic of the interior of the tank, due to mixing. The temperature measured at the out ow end of the shelf was 46.0 C at this time, but no density measurement was made there. d. Run 6. Flow of dense water down and away from slope Run 6 was monitored longer than the previous run, and the general features of the ow reported above were con rmed, with a further freshening at the top and increasing salinity at the bottom of the tank. This run also provided a clearer picture of the nature of the ow down the slope, coming directly off the shelf, and the ow on the shelf itself. The series of photographs reproduced in Figure 5 shows the development of the down ow after the heater lamps had been turned off at 23 hr 30 min into the experiment.at the same time, dye streaks were dropped in at 50 cm (on the shelf) and 80 cm from the end of the tank. (We will concentrate on the new phenomena; the description of features

14 898 Journal of Marine Research [56, 4 identi ed on Figure 2 will not be repeated here.) Figure 5a shows the distortion of these dye streaks after 40 sec, and other features revealed by previously injected dye (and documented in earlier photos in this run, not reproduced here). There is a dye layer along the slope, formed by a down ow with a counter ow above it, and two layers (A and B) spreading away from the slope near the top (these features originated from a dye streak dropped in 60 cm from the end of the tank over the slope at 23 hr 10 min). At a height of 8 cm above the bottom is a thin dye layer (C) which has spread right across the frame and beyond, above a thicker more slowly intruding nose (D). These layers resulted from a down ow which did not reach the bottom, together with an upslope counter ow, both of which were marked by dye injected much earlier, (also at 60 cm), at 18 hr 50 min. Figure 5b shows the effect of the ow of dense, hot salty water off the shelf and down the slope, resulting from the removal of active heating. There is a clear down owing layer (E) against the slope at mid depth, and above it a counter ow (F), driven by double-diffusive heating through the interface above the bottom current and marked by dye from the pre-existing layers. Figure 5c shows the development of this up ow (F) as it goes unstable (G) and mixes with uid above and below it. Also visible is a more rapid extension of the existing thick dyed intrusion (D) owing off the slope, which is also indicated by the distortion of the dye streak beyond its nose. Figure 5d documents the further extension of this layer, and also of the thinner intrusion above it at H, just above the level of one of the earlier out ows of dye. Finally, Figure 5e records a later stage of these out ows from the bottom current, and also reveals that the counter ow along the slope has risen to its level of neutral buoyancy and produced a warm, salty out ow (I) higher up, below which salt ngers have developed. e. Run 7. Time lapse record of the thickening of the bottom layer The overall effect of the downslope ow on the density structure in the body of the tank was monitored by measuring the height of the top of a dyed bottom layer, such as that marked I in Figures 2d to 2f. This was followed over many hours, using a time-lapse video recording. Figure 6 plots the height of this dyed layer as a function of time. The observed behavior, a rapid increase in depth at rst, and a gradually decreasing rate at later times, is characteristic of the turbulent lling box process (Baines and Turner, 1969), which results from the deposition of uid below the front and a continual entrainment, or in ow of uid toward the slope. It is not consistent with the alternative laminar lling box mechanism, described by Worster and Leitch (1985). f. Comparison of experiments with different initial salinities Finally, we will compare the density pro les produced after one day in three different experiments. Each of these used the same heating rate and depth over the heated section of the shelf, but the initial homogeneous salinity in the tank was different. Run 5 started with salt solution of S.G , Run 6 with S.G , and both of these used the full 50 cm

15 1998] Turner: Model of inverse estuary 899 Figure 6. The thickening of the bottom layer over time in Run 7, as a result of the ow of dense water down the slope and the lling box process. length of the second version of the shelf. Run 8 started with S.G , and the shortened 30 cm long shelf. The three density pro les at the same horizontal distance (30 cm) from the beginning of the slope are shown in Figure 7, plotted as differences from the original values in the tank. The maximum concentration changes near the bottom are little different in the three runs, suggesting that the changes of salinity on the shelf due to evaporation are insensitive to the salinity itself, (although one would expect changes in salinity due to evaporation to be proportional to the salinity and to the amount of fresh water removed). The pro les at mid-depth are rather different, but these too do not vary systematically with salinity or evaporation rate (see Table 1). The mixing on the slope and the pattern of out owing intrusions seem to be sensitive to the detailed geometry of the shelf and the density of the down ows, not just to the heating rate. Clearly, there are many more measurements which can and should be made before these ows can be fully understood. The details of the ow on the shelf, the temperature and salinity distributions there, and the buildup and release of the hottest, saltiest water are the most important of these. The rate of evaporation over various intervals was measured in all the experiments described, so that we have an overall estimate of the salt ux at the shelf; but in the absence of a good measure of the simultaneous heat ux and its spatial distribution, this is of limited value.

16 900 Journal of Marine Research [56, 4 Figure 7. Comparison of the density pro les (due to salinity, at constant temperature) in three runs started with different initial salinities and the same heating rate. One day after the beginning of the heating the increase in salinity at the bottom is almost the same, though the pro les at mid-depth are evidently sensitive to the detailed geometry and evaporation rate. 4. Comparison with ocean observations There are no eld observations known to me which have been obtained with the express purpose of investigating the combined effects of heating and the increase in salinity due to evaporation on a shelf. However, CTD data obtained on the Australian Northwest Shelf in the course of a study of the generation of internal tides, brought to my attention by P.E. Holloway (personal communication, 1997), do exhibit features comparable to those observed in the laboratory. The processes on this Shelf are undoubtedly more complex than those modeled in the laboratory experiments. There could have been considerable mechanical mixing due to the tidal ows and winds over the shelf, which would add to the mixing due to convection alone. Nevertheless, the double-diffusivenature of the ows off the Shelf seems very clear in the data. A detailed CTD survey of the NW Shelf area was conducted in January 1995 during the deployment of moorings to measure currents. At each of 13 locations in a section across the shelf and slope, repeated CTD pro les were measured over a 13 hr period (in order to cover one complete cycle of the semi-diurnal tide). The temperature gradient was in each case strongly stable, with the highest temperature at the surface and superimposed small uctuations and reversals of gradient (associated with saline intrusions). The salinity pro les give the most graphic indication of the processes of interest, and only these will be reproduced here. The time series at each station show strong variability due to vertical and intrusive motions, but the overall difference between stations is adequately demonstrated using the rst cast at each position.

17 1998] Turner: Model of inverse estuary 901 Figure 8. Salinity pro les obtained on the Australian NW Shelf, in January 1995, at the stations recorded in Table 2. The shaded areas show the extent of the high salinity intrusion as it moves off the slope. (Unpublished data, courtesy of Dr P. E. Holloway, Australian Defence Force Academy.) In Figure 8 are plotted the salinity pro les at ve stations, starting from the edge of the shelf and extending down the slope, at the distances from the rst station (C1 in 65 m of water) shown in Table 2; the corresponding depths are also given. The rst three pro les extend to the bottom, but the last two in deeper water are plotted only to 500 m. The salinity range in each case is to parts per thousand. These pro les have been chosen for illustration because they were all obtained within a period of three days. Other upshelf or intermediate pro les obtained about a week earlier are rather different from these, showing that the structure changed considerably on this timescale. The pro les plotted certainly do not constitute a synoptic cross-shelf section, but they are the best measures available of the properties of the water column and their spatial variations. There is a clear well-mixed saline (and hot) surface layer in each of the pro les, extending away from the shelf and across the slope. At C8 there is also a maximum in salinity just above the bottom, lower than the surface value and consistent with the deposition of salt by the action of salt ngers. At C9 there are many intruding saline layers extending over the whole depth, as well as a decrease in surface salinity and a (transient?) decrease in the depth of the surface mixed layer. At section C10, a thicker intrusion has developed, leaving the slope some distance above the bottom. Since the salinity of this is greater than the surface value here, or even at C8, it must have been formed by more saline water formed by evaporation higher up the shelf pouring down the slope and separating at its level of neutral buoyancy. The pro le at C12 shows a thickening of this out owing Table 2. The stations on the NW Shelf where the salinity pro les plotted in Figure 8 were recorded. Station C8 C9 C10 C12 C13 Distance from C1 (km) Water depth (m)

18 902 Journal of Marine Research [56, 4 layer, with a further increase in salinity of the intrusion at greater depths, and more thinner layers below. Finally C13, in 1382 m of water, shows the further extension of the thick intrusion away from the slope at about 200 m. 5. Discussion The results of the experiments presented above have demonstrated that even in this simple geometry consisting of shelf, slope and a deeper tank, the heating of an initially homogeneous salt solution in a shallow region can produce large scale horizontal motions and strong strati cation. The effects demonstrated are essentially double-diffusive: they depend on the changes in both temperature and salinity produced by the heating and evaporation, and could not occur if dense uid produced by only one stratifying property had been supplied to the shelf. Near the surface there are strongly sheared salt ngers, driven directly by the out ow of hot salty water off the shelf. At greater depths, the relative contributionsof heat and salt to the strati cation are reversed to the diffusive sense, due to two types of down ow along the slope. First, the ux through the near-surface ngers supplies warm, salty water to the slope, and second there is a direct, intermittent down ow of hot, very salty water directly off the shelf. The strati cation produced achieves a quasi-steady state after several days; superimposed on this are unsteady ows in the form of intrusions moving away from the shelf and slope, and the compensating counter ows away from the fresh water in ow. (It seems possible that the nal, long term steady state in the experiments could be one in which the water right at the surface becomes fresh over the whole length of the tank, with evaporation occurring only from this layer, and little motion below. None of the runs was monitored nearly long enough to test this conjecture.) The details of the very dynamic phenomena observed depend on the initial conditions, and on the boundary geometry and heating rates. However all the available, mainly qualitative, evidence suggests that the signi cant mechanisms producing the observed effects have been identi ed, and that the overall conclusions are robust. The connection with the estuarine and oceanic ows which have provided one motivation for this study is so far tenuous, though the data shown in Figure 8 have demonstrated the existence of double diffusive intrusions on the Australian NW Shelf. The striking similarity to the observations presented here suggests that the processes documented in the laboratory can be effective on the larger scale, but the relative importance of various mixing processes on the shelf has not been properly assessed. I hope that the ideas explored in this paper might prompt coastal oceanographers to consider suitable regions where they could make measurements speci cally designed to resolve these questions. It is premature to propose a quantitative scaling between the laboratory and the ocean, but an important general point is worth emphasizing in conclusion. Whatever differences there are in geometry, scale and the rate of heating and evaporation, the existence of saline intrusions, with a compensating increase in temperature which causes them to spread at

19 1998] Turner: Model of inverse estuary 903 their level of neutral buoyancy, guarantees that in both cases double-diffusive processes will be signi cant. Double-diffusive convection is strongest when the density anomaly ratio of the two properties is close to unity, and this is always true near intrusions. Previous well-documented examples of such double-diffusive activity are the layers under the Mediterranean out ow (Tait and Howe, 1971), and the intrusions which drive the mixing of a Mediterranean salt lens with its surroundings (Ruddick, 1992). Regardless of any immediate application to the ocean, this geometry has certainly proved to be a convenient way to introduce horizontal temperature and salinity anomalies into an experimental tank. In comparison with studies of vertical transports through interfaces, double-diffusive process in two-dimensional geometries have not received the attention that their importance in the ocean deserves. The present study, and complementary experiments using the salt-sugar analogue of heat and salt (Turner, 1998), represent two attempts to redress the balance. Acknowledgments. I am grateful to Tony Beasley for his assistance with the experiments, to Ross Wylde-Browne for the preparation of the photographs and diagrams, and to Peter Holloway for drawing my attention to his observations on the North West Shelf and for his permission to publish the pro les shown in Figure 8. Ross Griffiths and Ross Kerr kindly read an earlier draft of the manuscript and provided helpful comments. Criticisms and suggestions from the editor and two anonymous referees have greatly improved the clarity of the presentation. REFERENCES Baines, W. D. and J. S. Turner Turbulent buoyant convection from a source in a con ned region. J. Fluid Mech., 37, Chen, C. F. and F. Chen Salt- nger convection generated by lateral heating of a solute gradient. J. Fluid Mech., 352, Huppert, H. E. and J. S. Turner Ice blocks melting into a salinity gradient. J. Fluid Mech., 100, Maxworthy, T Convection into domains with open boundaries. Ann. Rev. Fluid Mech., 29, Nunes, R. A. and G. W. Lennon Episodic strati cation and gravity currents in a marine environment of modulated turbulence. J. Geophys. Res., 92, Phillips, O. M On turbulent convection currents and the circulation in the Red Sea. Deep-Sea Res., 13, Ruddick, B. R Intrusive mixing in a Mediterranean salt lens intrusion slopes and dynamical mechanisms. J. Phys. Oceanogr., 22, Ruddick, B. R. and J. S. Turner The vertical length scale of double-diffusive intrusions. Deep-Sea Res., 26, Schmitt, R. W Double diffusion in oceanography.ann. Rev. Fluid Mech., 26, Stern, M. E. and J. S. Turner Salt ngers and convecting layers. Deep-Sea Res., 16, Tait, R. I. and M. R. Howe Thermohaline staircase. Nature, 231, Turner, J. S Double-diffusive intrusions into a density gradient. J. Geophys. Res., 83, Multicomponent convection.ann. Rev. Fluid Mech., 17,

20 904 Journal of Marine Research [56, Laboratory models of double-diffusiveprocesses in Proceedingsof Chapman Conference on Double-Diffusive Convection, Scottsdale, AZ, American Geophysical Union, Geophysical Monograph 94, Strati cation and circulation produced by double-diffusive sources in closed regions. (Manuscript in preparation) Turner, J. S. and C. F. Chen Two-dimensional effects in double-diffusive convection. J. Fluid Mech., 63, Worster, M. G. and A. M. Leitch Laminar free convection in con ned regions. J. Fluid Mech., 156, Received: 6 January, 1998; revised: 7 May, 1998.