Vorticity and Divergence of Surface Velocities Near Shore

Jerome A. Smith Scripps Institution of Oceanography, La Jolla, California

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Abstract

The nearshore environment is complex, with many competing dynamical elements. Surface waves and edge waves (a form of surface wave trapped to the shore) can generally be separated from other forms of motion because of their fast propagation speeds. However, other motions such as internal waves, shear waves, density flows, and isolated vortex pairs can move at comparable speeds. A tool to help separate these dynamical elements is decomposition of the surface 2D flow into two parts, one nondivergent and the other irrotational (solenoidal and potential flows, respectively). Here, an efficient algorithm for this separation is developed and applied, and two examples are examined from data taken at Duck, North Carolina, in 1997 as part of the SandyDuck experiment. The first example is a fresher-water density flow propagating downcoast (probably from the Chesapeake Bay). It is seen that 1) the wave-driven alongshore flow leads the flow, generating a “surge” of offshore surface flow in its wake; 2) the isolation of the irrotational (2D divergent) part of the flow permits estimates of some dynamical characteristics of the flow; and 3) the nondivergent part of the flow indicates a meander in the alongshore flow that moves downcoast with the surge. The second example is a hypothesized form of isolated vortical structure, such as might be generated by a pulsed rip current that detaches from the shore and bottom and coasts offshore some distance before dissipating. A kinematically self-consistent structure is formulated that would have both divergence and vorticity fields associated with it. However, the observations inspiring the hypothesis are inconclusive, so the existence of such a structure has not been verified.

Corresponding author address: Jerome A. Smith, Mail Code 0213, Scripps Institution of Oceanography, UCSD, La Jolla, CA 92093-0213. Email: jasmith@ucsd.edu

Abstract

The nearshore environment is complex, with many competing dynamical elements. Surface waves and edge waves (a form of surface wave trapped to the shore) can generally be separated from other forms of motion because of their fast propagation speeds. However, other motions such as internal waves, shear waves, density flows, and isolated vortex pairs can move at comparable speeds. A tool to help separate these dynamical elements is decomposition of the surface 2D flow into two parts, one nondivergent and the other irrotational (solenoidal and potential flows, respectively). Here, an efficient algorithm for this separation is developed and applied, and two examples are examined from data taken at Duck, North Carolina, in 1997 as part of the SandyDuck experiment. The first example is a fresher-water density flow propagating downcoast (probably from the Chesapeake Bay). It is seen that 1) the wave-driven alongshore flow leads the flow, generating a “surge” of offshore surface flow in its wake; 2) the isolation of the irrotational (2D divergent) part of the flow permits estimates of some dynamical characteristics of the flow; and 3) the nondivergent part of the flow indicates a meander in the alongshore flow that moves downcoast with the surge. The second example is a hypothesized form of isolated vortical structure, such as might be generated by a pulsed rip current that detaches from the shore and bottom and coasts offshore some distance before dissipating. A kinematically self-consistent structure is formulated that would have both divergence and vorticity fields associated with it. However, the observations inspiring the hypothesis are inconclusive, so the existence of such a structure has not been verified.

Corresponding author address: Jerome A. Smith, Mail Code 0213, Scripps Institution of Oceanography, UCSD, La Jolla, CA 92093-0213. Email: jasmith@ucsd.edu

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  • Batchelor, G. K., 1967: An Introduction to Fluid Dynamics. Cambridge University Press, 615 pp.

  • Bowen, A. J., and R. A. Holman, 1989: Shear instabilities of the mean longshore current. 1. Theory. J. Geophys. Res., 94 , 1802318030.

    • Search Google Scholar
    • Export Citation
  • Castelle, B., P. Bonneton, N. Senechal, H. Dupuis, R. Butel, and D. Michel, 2006: Dynamics of wave-induced currents over an alongshore non-uniform multiple-barred sandy beach on the Aquitanian Coast, France. Cont. Shelf Res., 26 , 113131.

    • Search Google Scholar
    • Export Citation
  • Cooley, J. W., and J. W. Tukey, 1965: An algorithm for machine calculation of complex Fourier series. Math. Comput. Amer. Math. Soc., 19 , 297301.

    • Search Google Scholar
    • Export Citation
  • Crawford, C. B., and D. M. Farmer, 1987: On the spatial distribution of ocean bubbles. J. Geophys. Res., 92 , 82318243.

  • Dorr, F. W., 1970: Direct solution of discrete poisson equation on a rectangle. SIAM Rev., 12 , 248.

  • Fox-Kemper, B., R. Ferrari, and J. Pedlosky, 2003: On the indeterminacy of rotational and divergent eddy fluxes. J. Phys. Oceanogr., 33 , 478483.

    • Search Google Scholar
    • Export Citation
  • Hockney, R. W., 1965: A fast direct solution of Poissons equation using Fourier analysis. J. Assoc. Comput. Mach., 12 , 95.

  • Johnson, D., and C. Pattiaratchi, 2004: Transient rip currents and nearshore circulation on a swell-dominated beach. J. Geophys. Res., 109 .C02026, doi:10.1029/2003JC001798.

    • Search Google Scholar
    • Export Citation
  • Lentz, S. J., and K. R. Helfrich, 2002: Buoyant gravity currents along a sloping bottom in a rotating fluid. J. Fluid Mech., 464 , 251278.

    • Search Google Scholar
    • Export Citation
  • Lentz, S. J., S. Elgar, and R. T. Guza, 2003: Observations of the flow field near the nose of a buoyant coastal current. J. Phys. Oceanogr., 33 , 933943.

    • Search Google Scholar
    • Export Citation
  • Li, Z. J., Y. Chao, and J. C. McWilliams, 2006: Computation of the streamfunction and velocity potential for limited and irregular domains. Mon. Wea. Rev., 134 , 33843394.

    • Search Google Scholar
    • Export Citation
  • Marmorino, G. O., T. F. Donato, M. A. Sletten, and C. L. Trump, 2000: Observations of an inshore front associated with the Chesapeake Bay outflow plume. Cont. Shelf Res., 20 , 665684.

    • Search Google Scholar
    • Export Citation
  • Marshall, J., and G. Shutts, 1981: A note on rotational and divergent eddy fluxes. J. Phys. Oceanogr., 11 , 16771680.

  • Pickering, W. M., 1977: Some comments on solution of Poissons equation using Bickleys formula and Fast Fourier Transforms. J. Inst. Math. Appl., 19 , 337338.

    • Search Google Scholar
    • Export Citation
  • Pinkel, R., and J. A. Smith, 1992: Repeat-sequence coding for improved precision of Doppler sonar and sodar. J. Atmos. Oceanic Technol., 9 , 149163.

    • Search Google Scholar
    • Export Citation
  • Rennie, S. E., J. L. Largier, and S. J. Lentz, 1999: Observations of a pulsed buoyancy current downstream of Chesapeake Bay. J. Geophys. Res., 104 , 1822718240.

    • Search Google Scholar
    • Export Citation
  • Sangster, W. E., 1960: A method of representing the horizontal pressure force without reduction of station pressures to sea level. J. Meteor., 17 , 166176.

    • Search Google Scholar
    • Export Citation
  • Schmidt, W. E., R. T. Guza, and D. N. Slinn, 2005: Surf zone currents over irregular bathymetry: Drifter observations and numerical simulations. J. Geophys. Res., 110 .C12015, doi:10.1029/2004JC002421.

    • Search Google Scholar
    • Export Citation
  • Shepard, F. P., and D. L. Inman, 1950: Nearshore water circulation related to bottom topography and wave refraction. Trans. Amer. Geophys. Union, 31 , 196212.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., 2002a: The use of phased-array Doppler sonars near shore. J. Atmos. Oceanic Technol., 19 , 725737.

  • Smith, J. A., 2002b: Continuous time–space sampling of near-surface velocities using sound. J. Atmos. Oceanic Technol., 19 , 18601872.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., and J. L. Largier, 1995: Observations of nearshore circulation: Rip currents. J. Geophys. Res., 100 , 1096710975.

  • Thornton, E. B., and R. T. Guza, 1986: Surf zone longshore currents and random waves: Field data and models. J. Phys. Oceanogr., 16 , 11651178.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1986: Bubble clouds: A review of their detection by sonar, of related models, and of how. Kv may be determined. Oceanic Whitecaps and Their Role in Air-Sea Exchange Processes, E. C. Monahan and G. M. Noicaill, Eds., D. Reidel, 57–68.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., and L. R. Centurioni, 2000: On the use of the method of images to investigate nearshore dynamical processes. J. Mar. Res., 58 , 779788.

    • Search Google Scholar
    • Export Citation
  • Turner, J. S., 1973: Buoyancy Effects in Fluids. Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, 367 pp.

    • Search Google Scholar
    • Export Citation
  • Watterson, I. G., 2001: Decomposition of global ocean currents using a simple iterative method. J. Atmos. Oceanic Technol., 18 , 691703.

    • Search Google Scholar
    • Export Citation
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