Columbia University in the City of New York LAMONT GEOLOGICAL OBSERVATORY * PALISADES, NEW YORK FIXING AND RESIDENCE TIME ON THE GREAT BAHAMA BANK Report prepared by: J. Michael Costin Technical Report No. CU-17-65 to the Atomic Energy Commission Contract AT (30~1) 2663 January, 1965 LA MONT GEOLOGICAL OBSERVATORY (Columbia University) Palisades, New York MIXING AND RESIDENCE TIME ON THE GREAT BAHAMA BANK Report prepared by: J. Michael Costin Technical Report No. CU-17-65 to the Atomic Energy Commission Contract AT (30-1) 2663 January, 1965 This publication is for technical information only and does not represent recommendations or conclusions of the sponsoring agency. Reproduction of this document in whole or in part is permitted for any purpose of the U.S. Government. In citing this manuscript in a bibliography, the reference should state that it is unpublished. Digitized by the Internet Archive in 2020 with funding from Columbia University Libraries https://archive.org/details/mixingresidencetOOcost ABSTRACT Tany studies cf regular and random motions have been made in the shallow waters of the Great Bahama Banks. Dye tracer experiments have been made near the edge of the shoal water-deep water boundary and at positions 20 and 50 miles in from the edge on the western banks in the lee of Andros Island. These studies are discussed with regard to circulatory patterns and flushing times. Estimates are made of the magnitude of horizontal shearing stresses during the ebb and flood periods under conditions of wind and current moving in the same and opposing directions. A tv/o-dimensional model is proposed which gives the time in days for a particle to move from the experimental areas to the edge of the bank during the summer season. The computed values are in close agreement with the experimental results. INTRODUCTION Many studies of regular and random motions have been made in the shallow waters of the Great Bahama Banks. It is felt that, before any further work is initiated, a summary of the work to date would be useful. Dye diffusion experiments (Costin, 1963) have shown that the level of turbulent energy on the western Great Bahama Banks is relatively low. Computed values of "the most probable diffusion velocity", after the method of Joseph and Sender, are on the order of 0.4 cm/sec in the area north of Russell Beacon (referred to as Bahama Banks North, BBN) and 0,2 cm/sec in an area some 50 km, to the south (BBS, see Fig. 1). Values of the flushing time, t were obtained by estimating the time in days it would take for a dyed water mass to leave the banks. Measurements of the insitu C*4/ C^ ratio (Broecker and Takahashi, January, 1965) have given estimates of a residence time, 7 r , The authors point out that since 1954 there has been an 14 irregular but continuous increase in atmospheric C due to nuclear testing. The C^4 falling on the open sea is mixed rapidly to an average depth of at least 100 meters, and therefore, the concentration of atmospheric carbon in the adjacent open ocean surface water is considerably depleted before this water moves onto the banks. The shallow water (2.5 fm) on the banks inhibits loss of C14 due to vertical mixing, and thus the corrected 3 ' o rO o 00 o ro o CO r- I o G) N- OJ Location of dye dumps on the Greot Bahama Bonk - August, t962 depth in fathoms 1 14 increase in C will be a measure of residence time, q , defined as the mean time since the water parcel in a given sample entered the banks from the adjacent open ocean. The longer a 14 sample remains on the banks, the higher the C concentration. Although, by definition, there are differences in the physi¬ cal meanings of t ^ and q q» it was observed that their respec¬ tive values tend to increase by the same order of magnitude in the direction of decreasing diffusion velocities. This general trend has prompted a re-examination of these data in the light of more recent studies in an attempt to discover recurrent relationships of circulation and mixing on the banks. GENERAL CIRCULATION The advective motions of the two dye patches, represented in outline form in Figures 2 and 3, are in close agreement with the general circulatory pattern discussed by Smith (1940). This pattern consists of tidal oscillations with major axes nearly per¬ pendicular to the 100 fathom line near the edge of the bank and trending NW-SE on the central portion in the lee of Andros Island. These tidal oscillations are superimposed on a residual drift dependent on wind variation resulting in a northerly drift in summer, and a southerly drift in winter. Note: Dye patch out¬ line #5 (Fig. 2, BBN) may be as much as 30% too large due to temporary difficulties in both the dye-sampling and navigational ■ . ! > . I ribllRE. 2 I ! ♦ * Point of high con centrotion Contour No. Mrs a 11 « r dump High Concentration(ppb) 1 4.58 -120 2 6.46 *120 3 24.40 113 ' \h i n d -y 0° 4 28.59 67 1 1 1 J 5 30.5 9 60 0 0.1 0.25 0.5 IX) 6 48.8 0 49 7 50.9 0 44 Scale in miles FIGURE 3 -3- systems, but has been included to show the northernmost position of the dye patch. In such shallow water as encountered on the Bahama Banks, the direction of tidal current flow may be described as being nearly normal to the cotidal lines. Due to the rotation of the earth, the water particles move in elliptic orbits, but because of frictional stresses over the shallow bottom, the ratio of the major to minor axes of the tidal ellipse is greater than in the case of an unlimited ocean. The narrow elliptical trajectories of the dye patches are due both to the earth's deflecting force and the interference of tidal streams crossing the banks from north to south and west to east. Smith also indicates that during most of the summer season, there is a high salinity wedge with an axis lying along 25®N which is being pinched off by an invasion of less saline water on both sides (Fig. 4) . The salinity gradient is consistently sharper on the northern side of the high salinity wedge which indicates that there may be a net flow in that direction. Figure 4A was con¬ structed from measurements made during September 15th to 18th, 1938 when the average wind was about 4 knots from ENE. The isohalines are displaced somewhat to the south of those in Fig, 4B April 18th to 22nd, 1939> when the average wind was from the east at over 7 knots, illustrating the local dependence of drift on the wind direction. The dye survey was conducted during a period of generally . f ■ Distribution of Isohalines after Smith (1940) FIGURE 4 -4- light southeasterly winds, and, as expected, the dye patches showed a net drift toward the north with average residual velocities of 0.07 knots for BBN, and 0.03 knots for BES0 EXPERIMENTAL RESULTS (1): Residence times from dye studies and C14 measurements Estimates of the time it would take for the dye patches to leave the northern edge of the bank were made by projecting the respective motions of the leading edges of the dye patches through time. It is seen that if the southeasterly winds were to prevail for a given length of time, the dye patch at BBN would have reached the 100 fathom line in 6 to 8 days, and that of BBS in 40 to 50 days. However, the winds are constantly shifting and in the southern area where the tidal currents are quite weak, the above figures could be in error by as much as 20 or 25 days. If the experiments had been made under conditions of steady northerly winds, the above values of t pj would be considerably different. Figure 5 (after Broecker and Takahashi, 1964) illustrates values of Tq made from measurements of insitu during June, 1962 (open circles) and June, 1963 (closed circles). These charted values indicate that water north of Andros (about 25° 10' N) had been in residence for a period of less than 20 days and that of the BBS area between 50 and 100 days. The reference states that the absolute residence times could be in error by as much as a factor of two, and that the ratios of residence tixnes for various ' • ; : .. i it 79°30 CM C MbUfiL 5 in c oo 78°30' 78° Values of Residence Times'^ after Broeker BTakahashi (1964} ~5~ samples should be good to ± 20%. 14 The results of the C study also indicate that increased values of 7 q will generally be found in areas of higher salinity, although salinities of June, 1962 were lower than average because of heavy rains during that period. EXPERIMENT RESULTS (2): Circulation near the shoal water-deep water boundary It has long been felt that, due to density considerations in the area, water leaving the banks on the ebb current generally sinks as it moves out into deeper water. In the Tongue of the Ocean basin (TOTO) to the east of Andros, v/ater having the same density as the shoal water is found to depths of about 200 meters (Busby and Dick, 1964). In April, 1964, a small-scale experiment was conducted in TOTO in an attempt to observe circulatory patterns near the boundary of the shoal water.