CONVECTION AT A.MODEL ICE EDGE

Transcription

1 JACK CALMAN CONVECTION AT A.MODEL ICE EDGE The flow pattern near the edge of a melting ie blok is modeled by heating a metal edge in a saltstratified fluid. An unexpetedly strong, horizontal boundary urrent was found moving out from under the ie. Convetive layers along the vertial wall were also observed. INTRODUCTION The presene of vast quantities of ie is one of the dominant harateristis of the polar seas. Physial proesses affeted by the ie inlude those on the largest limati sales to those on the smallest mirosales. Reently, the effets on the water irulation in the immediate viinity of melting ie have reeived attention in the literature. I - 6 Laboratory investigations have been onduted to study the flow along vertial and horizontal ie boundaries in water of various temperatures and of different strengths of salt stratifiation. All the studies are onerned with flow along an infinite boundary of either vertial or horizontal orientation; none investigates the flowfield near the ie edge (Fig. 1). Sine sharp boundaries our on ie of many types and sizes (glaiers, iebergs, et.), the peuliar nature of the flow near the edges will influene both the life yle of the ie and the nearby oean urrent and density struture at ertain length and time sales. The soure of the water flowing upward along a vertial ie wall must be the interior fluid (i.e., the fluid away from the wall). However, if there is a horizontal bottom (Fig. 1), the soure of water an be either under the ie or the interior fluid. Hene a different flowfield ould result. Under an infinite horizontal ie surfae, there is no asymmetry to ause the fluid to move preferentially to the left or right. However, near the edge of a horizontal ie slab, a large horizontal density gradient between the region under the ie and the open oean an exist and may ause a strong urrent. The purpose of the preliminary investigation is to show that unique flow features result near an ie edge. An understanding of the flow at an infinite vertial or horizontal boundary alone is insuffiient for understanding the geophysial ase. THE EXPERIMENTS Previous results 2 have shown that many essential features of flow along a vertial ie wall in a saltstratified fluid an be modeled by heating or ooling a metal wall for ambient temperatures well above the freezing point. Melting ie produes old fresh water; warmer, saltier water is often underneath the ie. Although old water is heavier, the effets of salinity an dominate, so the possible net effet is that the melt- Buoyant meltwater Stratified oean Figure 1-Sketh of the physial problem: onvetion at an ie edge in stratified water. water is buoyant; it is this buoyany that an be modeled by heating a metal wall. Although this method of modeling eliminates the atual addition of water (and therefore some phenomena that would result), the results ited above showed that flowfields near melting ie and outside a metal wall an be similar in the parameter range of interest. Sine aurate experiments with ie are muh more diffiult than with heated metal walls, the latter approah was adopted for the preliminary experiments. First, the ie orner was modeled by flow outside a metal orner that was plaed inside a 70-gallon aquarium filled with a salt-stratified fluid (Fig. 2). Inside the metal ontainer, a reservoir of hot water was maintained at a onstant temperature to drive the flow. The metal ontainer was sealed so no water was exhanged between the hot-water reservoir and the salt-stratified region. Measurements of density were made with a profiling ondutivity probe, and shadowgraphs were obtained from the flowfield. The proedure was as follows: The ondutivity probe was alibrated in solutions of known salinity. The salt-stratified solution was made by filling the tank with small layers of onstant salinity and waiting overnight for the density gradient to smooth by diffusion. After measuring the density gradient with the ondutivity probe, the hot water reservoir was quikly (in a few minutes) filled with preheated water. The tem- 211

2 J. Caiman - Convetion at a Model Ie Edge I 48 em 4= tial wall, and the displaed dye line was photographed to determine the veloity profile. In the first two experiments, an impervious insulated partition was plaed so as to extend the vertial wall of the metal ontainer all the way to the bottom of the 70-gallon aquarium to eliminate the effets of the horizontal boundary and, therefore, to repeat previous results as a hekout. In the subsequent three experiments, the partition was removed, giving a heightwidth aspet ratio of about 1 :2. RESULTS Five experiments were run. The temperature of the hot water reservoir, T R, varied from 30 to 60 C, while the ambient stratified fluid was isothermal at the onstant laboratory temperature, Too - 24 C. A onventional measure of the strength of stratifiation, apl az, is the buoyany period, t B, whih is the time during whih a fluid partile would osillate about its initial position if given a small vertial displaement. It is defined by - \12 tb = 27r _ ~ ap, ( ) p az Figure 2-Experimental apparatus: (top) shemati, (bottom) photograph. where g is the aeleration due to gravity and p is the fluid density. As the stratifiation gets stronger, fluid partiles osillate more quikly and the buoyany period dereases. The buoyany period, due only to salinity stratifiation, varied from 3 to 12 seonds. The maximum salinity, Soo, varied from 20 to The driving temperature differene, tlt = TR - T oo, varied from 5 to 28 C. Parameters for the experiments (some of whih are defined in the next setion) are listed in Table 1. Beause of nonuniformities in the denperature in the reservoir was maintained by a thermostatially ontrolled heater I stirrer. Shadowgraphs were taken as the flow developed. Oasionally, potassium perman~anate rystals were dropped near the ver- Table 1-Experi ment parameters. Experiment Too t::.t tb S oo h L h/l Ra No. ( C) ( C) (se) (ref. 7) (m) (m) V (m/se) Vo (em /se) VIVo x x x x x x x X X x X x x X X 10 2 Legend: Too Ambient temperature h/l Nondimensional layer thikness t::.t Temperature differene aross wall Ra Rayleigh number t8 Buoyany period V Horizontal veloity Soo Maximum salinity Vo Veloity sale h Layer thikness VIVo Nondimensional horizontal veloity L Length sale 212 fohns Hopkins APL Tehnial Diges, Volume 6, Number 3

3 J. Caiman - Convetion at a Mode! Ie Edge sity gradient, there were two distint regions of flow in experiments 2 and 3. The flowfield in the viinity of the orner was measured both by shadowgraph and by photographing dye-line displaements. A typial shadowgraph result is shown in Fig. 3, whih is a view looking into the side of the tank. The small (about 1 entimeter) onvetive layers along the vertial wall develop as they have in other experiments. 3,4 However, at the orner, a very strong, thik urrent moves out horizontally into the open water. Veloities in the large horizontal urrent were an order of magnitude larger than they were in the small onvetive layers. Similar horizontal flows appeared in photos of the experiments by Gebhart et ai., I but no quantitative results were presented by them. Shadowgraphs of the five experiments are shown in Fig. 4. The partition at the bottom of the vertial wall an be seen in Figs. 4a and 4b. Layers are formed along the vertial wall, but no strong horizontal urrent is developed. (The bright horizontal line in Fig. 4a, where the partition joins the heated vertial wall, is the result of a nonuniformity in the initial density gradient.) The three experiments with a horizontal boundary (Figs. 4, 4d, and 4e) all developed strong horizontal boundary urrents in addition to the onvetive layers along the vertial wall. (Figure 4e is the same as Fig. 3. It is inluded to make omparison easy.) The quantitative harateristis of these flow features are examined in the next setion. Figure 3-Shadowgraph of the flow near the edge (experiment 5) showing the strong horizontal boundary urrent going out from the edge and the onvetive layers along the vertial wall (time is 7 minutes after hot water had started to fill the reservior). ANALYSIS The simplest possible dimensional analysis onsiders the following six variables: the vertial density gradient due to the mean salinity stratifiation, ap l az; the density differene due to the imposed temperature differene, t::.p; gravitational aeleration, g; and the diffusivities of momentum, temperature, and salt, v, KT, and KS, respetively. These variables give three nondimensional parameters and three sales. The parameters are the Prandtl number (Pr), the Shmidt number (S), and the Rayleigh number (Ra), defined by 1. Pr == V/KT (::::; 7) is the square of the ratio of lengths to whih momentum and temperature diffuse in a given time; also the ratio of time of temperature or momentum diffusion to a given length. 2. S == V/KS (::::; 7 X 10 2 ) is the same as Pr, but for momentum and salt; 3.Ra == t::.pgl 3 /pktv(::::; ) is the square of the ratio of time sales for a fluid partile to move a distane L by buoyany fores or by mean temperature-momentum diffusion. The three sales are for length, time, and density. These are defined by 1. L == t::.p/(apl az) (::::; 10-2 meter) is the distane a fluid partile of density perturbation t::.p would move vertially to find its new equilibrium position in the stratified fluid; Johns Hopkins APL Tehnial Digesr, Volume 6, Number 3 2. to == L 2 / K (minutes to hours) is the time it takes for the imposed temperature differene to diffuse aross the length sale L. 3. Po == t::.p (::::; 10) kilograms per ubi meter is the magnitude of the imposed density perturbation. In the present experiments, this is the result of temperature differenes. The first item to onsider is whether the thikness of the onvetive layers along the wall is affeted by the horizontal boundary. The thikness, h, of the layers was measured from the shadowgraphs of Fig. 4, saled by the length, L, given above, and plotted as a funtion of the Rayleigh number in Fig. 5. (The experiments shown in Figs. 4b and 4 had rionuniform density gradients. Two data points were obtained for eah of these experiments, one for the upper and one for the lower group of layers. In eah ase, the loal length sale L was used.) The sizes of the layers in the present experiment, as seen in Fig. 5, are essentially the same as those found by Huppert and Turner 3 and Huppert and Joseberger. 4 The onlusion is that flow along the vertial wall is unaffeted by the horizontal boundary, exept in the region that is only one or two layers thik above the orner. The displaement of dye lines reated by the rystals of potassium permanganate dropped in the fluid near the heated vertial wall was used to measure the veloity in the horizontal boundary urrent. A veloity sale, Vo, was formed from the length sale, L, 213

4 J. CaIman - Convetion at a Model Ie Edge Figure 4-Shadowgraphs (a) through (e) (at times 10 to 15 minutes after start) for the parameters listed in Table 1 are for experiments 1 through 5, respetively. ~ 1.2 ~ ~- Q) 1.0..::,t,.~.f Q)! >- 0.6 ~ ~ ~,.. 'I 1 ~ ro 0 ' Vi 0.4 Q) E 0.2 "0 C 0 Z Rayleigh number Figure 5-Layer thikness (normalized by length sale, L, as a funtion of Rayleigh number. Cirled points are from the present experiments (edge flow); others are from Huppert and Turner 2,3 (vertial wall). and the time sale, to, given above. Although only three data points were obtained (Figs. 4, 4d, and 4e) 214 for only one aspet ratio (height/length z 0.5), the results (Fig. 6) suggest a power law dependene of where d z Y2 and z DISCUSSION Sine the experiments were designed only to demonstrate the effet of the edge on the flow, many important questions about the variability, strength, extent, and time sales remain unanswered. Although the effet of ie melting on upwelling has been disussed before,2,6 the magnitude and details of the upwelling remain to be measured. The present experiment implies that for a horizontally finite blok of free ie, upwelling would be enhaned by the strong horizontal urrent at the edge. The important dependenies of the boundary urrent on distane from the edge and the details of the return flow (via upwelling or other-

5 J. Caiman - Convetion at a Mode/ Ie Edge 103~------~ ~------~ ~ 100~------~ ~------~ ~ Rayleigh number Figure 6-Speed of the horizontal boundary urrent (normalized by Lito) as a funtion of the Rayleigh number. wise) were beyond the sope of the present experiments. The fat that the orner flow eliminated the first one or two layers along the vertial wall ould be important in the geophysial ase if the layer thikness is similar to the ie thikness. Huppert and Turner 3 estimated onvetive layers of fluid to be at least 1 meter thik in the Arti. If that estimate is orret, the present results imply that horizontal urrent below the ie will dominate the flow for ie thikness less than about 2 meters. The horizontal urrent at the edge will ertainly affet the melt rate of the ie and ould be an important omponent of the heat budget of the ie and of the upper oean below the ie. I The question of threedimensional effets (instabilities and interations with urrents and waves along the ie edge) has not been addressed in these experiments. Several useful steps logially follow the present study: to repeat the experiments using real ie, to study the boundary layer flow numerially and theoretially, and to obtain some detailed measurements in the field near all types of ie edges. REFERENCES and NOTE I B. Gebhart, B. Sammakia, and T. Audunson, "Melting Charateristis of Horizontal Ie Surfaes in Cold Saline Water," J. Geophys. Res. 88, (1983). 2H. E. Huppert and J. S. Turner, "On Melting Iebergs, " Nature 271,46-48 (1978). 3H. E. Huppert and J. S. Turner, "Ie Bloks Melting into a Salinity Gradient," J. Fluid Meh. 100, (1980). 4H. E. Huppert and E. G. Jqseberger, "The Melting of Ie in Cold Stratified Water," J. Phys. Oeanogr. to, (1980). 5S. Martin and P. Kauffman, "An Experimental and Theoretial Study of Turbulent and Laminar Convetion Generated Under a Horizontal Ie Sheet Floating on Warm Salty Water," J. Phys. Oeanogr. 7, (1977). 6S. Neshyba, "Upwelling by Iebergs," Nature 267, (1977). 7This nondimensional new standard salinity sale, alled "pratial," is numerially equivalent to the old 0 / 00 unit. ACKNOWLEDGMENTS-The support of the Applied Physis Laboratory's Independent Researh and Development Fund is gratefully aknowledged. I had useful disussions with C. E. Shemm during the ourse of the work, and J. E. Hopkins provided exellent laboratory support. THE AUTHOR JACK CALMAN has been on the staff of the Submarine Tehnology Department sine joining APL in He was born in New York City in 1947 and attended City College of New York (B.S. physis, 1969) and Harvard University (S.M., 1970; Ph.D., applied physis (oeanography), 1975). His areer has inluded positions at MIT and the Weizmann Institute of Siene, Environmental Researh and Tehnology, In., and NASA's Goddard Spae Flight Center. The subjets of his previous work were instabilities of oean irulation, the fluid dynamis of solar ponds, theoretial methods of interpreting oean urrent spetra, pollution problems of oil spills and jet airraft exhaust, and limate studies of sea-surfae temperature. After joining APL, Dr. Caiman worked on small-sale oean turbulene for several years and on drag redution briefly. He is now interested in appliation of satellite altimetry to studies of oean irulation. He has published extensively and is a member of the Amerian Geophysial Union, the New York Aademy of Sienes, the Amerian Physial Soiety, and the Committee for International Freedom of Sientists. 215