Harrison, Wyman

Virginia Institute of Marine Science

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College of William & Mary: W&M Publish

W&M ScholarWorks Reports 1963 Diffusion in a low-velocity, inshore tidal current off Virginia Beach, Virginia Wyman Harrison Virginia Institute of Marine Science Follow this and additional works at: https://scholarworks.wm.edu/reports  Part of the Hydrology Commons, and the Marine Biology Commons Recommended Citation Harrison, W., & Virginia Institute of Marine Science. (1963) Diffusion in a low-velocity, inshore tidal current off Virginia Beach, Virginia. Special scientific report (Virginia Institute of Marine Science); no. 40. Virginia Institute of Marine Science, College of William and Mary. https://doi.org/10.21220/V51C74 This Report is brought to you for free and open access by W&M ScholarWorks. It has been accepted for inclusion in Reports by an authorized administrator of W&M ScholarWorks. For more information, please contact scholarworks@wm.edu. VIRGINIA INSTITUTE OF MARINE SCII-liCE GLOUCESTER POINT, VIRGINIA ·DIFFUSION IN A LOW-VELOCITY, INSHORE TIDAL CURRENTOFF VIRGINIA BEACH, VIRGINIA Wyman Harrison SPECIAL SCIENTIFIC REPORT NO. ,40January 1963 VIRGINIA INSTITUTE OF MARINE SCIENCE GLOUCESTER POINT, VIRGINIA DIFFUSION IN A LOW-VELOCITY, INSHORE TIDAL CURRENT OFF VIRGINIA BEACH, VIRGINIA Wyman Harrison SPECIAL SCIENTIFIC REPORT 40 This report contains results of work carried out for the Hampton Roads Sanitation District Commission. It does not constitute final publica·tion. w. J. Hargis, Jr.DirectorJanuary 1963 DIFFUSION IN A LOW-VELOCITY, INSHORE TIDAL CURRENT OFF VIRGINIA BEACH, VIRGINIA Studies of turbulent diffusion in estuarine and inshore waters have given recent impetus to the development of a superior technique for tagging water masses and detecting the decrease in concentration of the tag through time. Independent research by scientists of the Japanese Governmen-tal Agencies (1958) and the Chesapeake Bay Institute (Pritchard and Carpenter, 1960) led to the selection of rhodamine-B dye, an organic pigment, as a tagging agent, and to t he development of fluorescence analysis as a detecting technique. The fluorescence spectrum of rhodami.ne-B has a maximum at 575 millimicrons and use of a Turner Model III fluorometer per­mits detection to 0.02 - 0.004 ppb. A review of the technique and its limitations was presented by Pritchard and Carpenter (1960). Studies by the Virginia Institute of Marine Science have utilized their experimental techniques. Recent attempts to develop usable theoretical relation­ships for horizontal diffusion in oceanic waters have been made by Joseph and Sendner (1958, 1962), Ozmidov (1958), and Schonfeld (1959, 1962). The results of dye studies offer experimental verification of certain features of the theoretical equations (Pritchard and Carpenter, 1960; Okubo, 1962). Okubo (1962) has made - 2 -a comprehensive analysis of the recent theoretical treatments of diffusion in the sea and of the results of exper:Lmen-tal studies. He proposes a solution to the diffusion equations (1962, p. 56) that involves an··'i•energy-dissipation" parameter having the dimensions 2/3 cm /sec. On August 1, 1962, between 0800 and 1400 hours, personnel of the Virginia Institute of Marine Science and the U. s. Coast and Geodetic Survey initiated, maintained, and monitored a continuous release of dye from a point approximately 800 meters off Cape Henry, Virginia {Fig. 1). The rate of release of rhodamine-B dye was 0.7 g/sec and the vehicle solution was adjusted to the density and temperature of the surrounding water (1.01 g/cc and 2s 0c, respec-tively). Release was from a point source at approximately 4 meters depth. In addition, a small number of surface and bottom drifters were introduced at the point of dye release (Fig. 1) to gain a crude measure of neighbor diffusion, in the event that the dye study should fail in some respect. Wind, current, and wave data for portions of the release period are shown in Figure 1. The average current velocity, U, integrated along the axis of the dye plume, was 0.30 m/sec (0.58 kn) during the period of monitoring (1130 - 1230 hours) upon which the results below are based. Neighbor diffusivity, F Ci), was calculated from returns - 3 -of neutrally-buoyed drift bottles. F (2-) had a oinimum value of 316 2/s d th �r-· • t 3 . (n) 4/3 cm ec an e coel.l.l.Cl.en e , in F �- = el , had theminimum value 0.062. This last value was calculated using Stommel's (1949) expression F�l :p� I_I _ _f = �1 -R�f2T for the reduction of the experimental observations, where .£0 is initial neighbor separation (cm), L1 is S?paration after time T(sec), and the bars denote averages. The minimum value of e3 falls (Table 1) within a range of values (0.006 - a.OB) that have been determined for other oceanic areas subject to ·tidal currents of variable strength. A calculation that allows for the turning of the drifters as they enter the longshore-current system shows that a maximum value for e3 would not exceed 0.075. Additional diffusion values were calculated from measure-ments of dye concentration along the axis of the steady ... state plume (Fig. 1). A log-log plot (Fig. 2) of a ';concentration ratio," -1c•M �n versus x, for values of x between 800 and 3800 meters, fitsan x-1 relationship where c equals peak dye concentration, M equals- -rate of dye discharge (g/sec), .Il equals layer depth (meters) and � equals distance in meters along the axis of the plume. Thus, there was a decrease in dye concentration downstream from the discharge point proportional to the minus one power of the distance. - 4 -Table l Comparison of Neighbor Diffusivities Observed at Various Places (Compiled from Pearson, 1956, table 10) Ocean conditions Place of Observation Depth (meters) . .L .-.. 2 Loch Long, Scotland1Loch Long, Scotland ,--2Virginia Beach, Virginia 4-6(this repo2t) Vineyard Sound ,-· .. 25Near Woods Hole ... --...25 Near Woods Hole /'-25 Vineyard Sound, I off Falmouth Beach2 4-10Vineyard Sound, off Falmouth Beach2 4-10Near Cata�act Hill, �·'·,_ 2 ,oooBermuda Near Cata2act Hill, ./'-. 2,000 Bermuda NOTES: ! Richardson and Stammel (1948) 3 Stammel (1949) Wind - current Wind slight Wind slight Wind 3-6 kn Current 0.6 kn Strong tidal current Strong tidal current Strong tidal current Very strona tidal C:: '"' current.., Very strona current5.., tidal Observed moveraent of Parsnips Parsnips Drift Bottles Dye patches Dye patches Single dye spot Mimeo paper Mimeo paper Mimeo paper ¥rimeo paperComputed from data supplied to Pearson (1956) 4 Computed by Pearson (1956) from ordinary diffusivity, k 5 Scour of bottom visible from air Initial neighbor separation }!.� ' in cm 187.7 26.7 150 cm 9,000 l,800 290 dia 430 77 795 103F �) e3incm 2 /sec F<i_ )=e �4/384.3 0.0799 6.4 0.0800 316-336 0.062 to2, 4004 0.075 4 0.013241204 0.0056 50 0.0259 I 92 0.0284 l0o4 0110318 337 0.0457 36 0.0751 - .s -Calculation of the so-called "diffusion velocity" yielded -3a value of 2 X 10 m/sec. This value was computed from a relation-ship proposed by Schonfeld (1959) and expressed by Okubo (1962) as:S(x,y)= m/UiT w x/U �2 (-;/U) 2 + y2 where S(x,y) equals the mean concentration at some poj.nt (x,y) in the plume,� being in the direction along the axis of the plume and y the direction perpendicular to the axis of the plume,.!!! equals the number of particles released per unit time,� equals the mean flow, and�equals the 11diffusion velocity'! vJhen solv:ing for W, S (x) is expressed as the concentration ratio (mentioned above), in order to correct for depth-dependent variations in dye concen-tration along the axis of the plume. The approximate value for -3diffusion velocity (2 X 10 m/sec) found in this study has beenfound also by Pritchard and Carpenter (1960) in some of their ex-periments with continuous dye releases in waters influenced bycurrents. Finally, a semi-log plot (Fig. 3) of the lateral dis­tribution of dye concentration is presented for a transect (Fig. 1) across the plume, 1,695 meters downstream from the release point. A drop of one order of magnitude of dye concentration in 150 meters distance perpendicular to the plume was found. - 6 -REFERENCES Japanese Governmental Agencies. 1958. Oceanographic research on waste disposal, p. 404-409. In Proc. 2d Intern. Conf. Peaceful Uses of Atomic Energy in Geneva, v. 18, P/ 1355. Joseph, J. and H. 8endneJ:-. 1958. Ober die horizontal.e Diffusion in Meere. Deut. Hydrogr. z. ll:49. 1962. On the spectrum of mean diffusion ---ve-i�o-c_i_t_i-es in the ocean. J. Geophys e Res. 67:3201-3205. Okubo, A. 1962. A review of theoretical models of turbulent diffusion in the sea. Chesapeake Bay Inst:. Tech. Rept. 30, 105 p. Ozmidov, R. V. 1958. (On the calculation of horizont:al turbulent diffusion of the pollutant patches in the sea.) Doklady Akad. Nauk SSSR 120:761. Pearson, E. A. 1956. An investigation of the e:fficac:y of sub­marine outfall disposal of sewage and sludge. Calif. State Water Pollution Control Board ?ubl. no. 14, 154 p. Pritchard, D. W. and J. H. Carpenter. 1960. Measurements of turbulent diffusion in estuarine and inshore waters. Bull. Intern. Assoc. Sci. Hydrol. no. 20: 1-14. Richardson, L. Po and H. Stammel. 1948. Notes on eddy diffusion in the sea. J. Meteorol. 5:238-240. Stomme1� H. 1949. Horizontal diffusion due to oceanic turbulence J. Mar. Res. 8:199-225 ••• Schonfeld, J. c. 1959. Diffusion by homogenous isotropic tur-bulence. Rept. FA-1959-1, Rijkswaterstaat, Netherlands. 1962. Integral diffusivity. J. Geophys. Res. 67:3187-3199. 

Diffusion in a low-velocity, inshore tidal current off Virginia Beach, Virginia

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Diffusion in a low-velocity, inshore tidal current off Virginia Beach, Virginia

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