JOURNAL OFGEOPHYSICAL RESEARCH, VOL.96,NO.C2, PAGES 2561-2575, FEBRUARY 15,1991 Transient Eddy Formation AroundHeadlands RICHARD P. SIGNELL1 AND W. ROCKWELL GEYER Woods' ttole Oceanographic Institution, Woods Hole, Massachusetts Eddies with length scales of 1-10 km are commonly observed in coastal waters and playan important role in thedispersion of water-borne materials. Thegeneration and evolution ofthese eddies byoscillatory tidalflow around coastal headlands is investigated withanalytical and nu- merical models. Using shallow water depth-averaged vorticity dynamics, eddies are shown to form when flow separation occurs near thetip oftheheadland, causing intense vorticity generated along theheadland to beinjected into theinterior. An analytic boundary layer model demonstrates that flow separation occurs when the pressure gradient along the boundary switches from favoring (ac- celerating) to adverse (decelerating), and itsoccurrence depends principally onthree parameters: theaspect ratio [b/a], where b and a are characteristic width and length scales of theheadland; [H/CDa], where H isthe water depth, CDisthe depth-averaged drag coefficient; and [Uo/aa], where Uo and a are the magnitude and frequency of the far-field tidal flow. Simulations with a depth-averaged numerical model show a wide range of responses to changes in these parameters, including cases where noseparation occurs, cases where only one eddy exists at a given time, and cases wherebottom friction is weakenough that eddies produced duringsuccessive tidal cycles coexist, interacting strongly with each other. These simulations also demonstrate thatin unsteady flow, a strong start-up vortex forms after theflow separates, leading to a much more intense patch of vorticity andstronger recirculation than found in steady flow. 1. INTRODUCTION The generation of eddies behind islands and headlands has been observed in a variety of coastal environments [Pin- gree, 1978; Wolanski el al., 1984; Black andGay, 1987; Pal- liaralchiel al., 1987; Geyer and Signell, 1990]. They are commonly associated with oscillatory tidal currents, form- ing on alternate sides of the island or headland with the reversal of the tide. The strongly nonlinear flow associated with the development of these eddies hassubstantial influ- ence on fluid and sedimenttransport processes, including the trapping of sediment in the cores of the eddies [Wolan- ski el al., 1984; Pingtee, 1978], andthe enhanced dispersion of fluid by thestraining motions of the eddies [Awaji el al., 1980; Signell andGeyer, 1990; Signell, 1989]. This studyfocuses on the formation and evolution of transient eddies in stronglynonlinear flow around head- lands. This is in contrast with most research on nonlin- ear tidal flow, which has concentrated on the generation of tide-induced residual circulation, or tidally rectified flow [Hulhnance, 1973; Loder, 1980; Zimmerman, 1978; Pingtee and Maddock, 1980b; Robinson, 1981]. When the scale of the tide-induced residual is large compared to the tidal ex- cursion, the residual can be an importantcontributor to the long-term transport of water-borne material [Robinson, 1981]. When the scale of the tide-induced residual flow is comparable to or smaller than the tidal excursion, how- ever, the residual displacements of water parcels bear no resemblance to the tide-inducedresidualflow, and the tide- induced residual flowhaslittle significance [Imasalo, 1983]. This occurswhen the scale of coastline or topographic vari- ation is itselfcomparable to the tidal excursion (1.4-14 km for M2 tidal currents of 0.1-1.0 m s -• amplitude). Under theseconditions, the net displacement of a particle over a tidal cycle depends on its interaction with fundamentally transient flow featuresthat form during both phases of the tide[Awaji el al.,1980; Signell and Geyer, 1990]. Much of the framework that has been developed for study- ingtide-induced residual flow can beused for studying time- dependent processes of eddy formation andevolution. Both problems involve vorticity dynamics in shallow water, and both owe their existence to the nonlinearity of the momen- tum equation. Manyinvestigators [e.g.Pingtee, 1978; Zim- merman, 1978] have shown how the generation of residual features canbe explained by considering the production, dis- sipation, and nonlinear transfer of the depth-averaged ver- tical component of vorticity. Thisapproach was exemplified by Robinson [1981], who employed ananalytic model oftide- induced residualcirculationin which vorticity was produced by the tide in a specified source region, advected by the tidal flow,and dissipated by bottom friction.In this study the vorticitystrongly modifies the tidal flowfield, and the production, transport anddissipation of vorticity is studied with a numerical model. Another aspect that distinguishes small-scale eddy for- mation from the study of large-scale tide-induced residual flow is the degree to which the vorticityis concentrated; around headlandsthe rotational flow is pronouncedenough that it stands out against the flow that generated it. The common element of most flows in which this intense vorticity formsis the occurrence of flow separation, wherestreamlines break away from the coast, carrying high vorticity fluidfrom the lateral boundary into the interior of the flow. Because of the critical role of flow separation, the understanding of 1Now at U.S. Geological Survey, Woods Hole, Massachusetts. eddyformation in coastal waters requires an understand- Copyright 1991 by the American Geophysical Union. ing of the flow separation process. Once the flow has sep- arated, providing a pathway of highvorticity fluid into the Paper number 90JC02029. interior, theproblem becomes one of nonlinear interaction 0148-0227/91/90JC-02029505.00 between the energetic rotational flow and the larger scale, 2561