Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-24T23:49:07.376Z Has data issue: false hasContentIssue false
  • English
  • Français

Coastal outflow currents into a buoyant layer of arbitrary depth

Published online by Cambridge University Press:  08 November 2018

S. Jamshidi Open the ORCID record for S. Jamshidi [Opens in a new window]  and
E. R. Johnson Open the ORCID record for E. R. Johnson [Opens in a new window]
S. Jamshidi*
Affiliation:
University College London, Department of Mathematics, 25 Gordon Street, London WC1H 0AY, UK
E. R. Johnson
Affiliation:
University College London, Department of Mathematics, 25 Gordon Street, London WC1H 0AY, UK
*
†Email address for correspondence: sean.jamshidi.16@ucl.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

The long-wave, reduced-gravity, shallow-water equations (the semi-geostrophic equations) are used to study the outflow of a river into the ocean. While previous models have studied dynamics driven by gradients in density, the focus here is on the effects of potential vorticity anomaly (PVa). The river water is taken to have the same density as a finite-depth upper layer of oceanic fluid, but the two fluids have different, uniform, potential vorticities. Under these assumptions, the governing equations reduce to two first-order, nonlinear partial differential equations which are integrated numerically for a prescribed efflux of river water and PVa. Results are found to depend strongly on the sign of the PVa, with all fluid turning downstream (in the direction of Kelvin-wave propagation) when the river water has positive PVa and anticyclonic flow upstream of the river mouth when the PVa is negative. In all cases, a nonlinear Kelvin wave propagates at finite speed ahead of the river water. Away from the river mouth, the uniformity of one set of Riemann invariants allows for similarity solutions that describe the shape of the outflow, as well as a theory that predicts properties of the Kelvin wave. A range of behaviours is observed, including flows that develop shocks and flows that continue to expand offshore. The qualitative behaviour of the outflow is strongly correlated with the value of a single dimensionless parameter that expresses the ratio of the speed of the flow driven by the Kelvin wave to that driven by image vorticity.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Shallow water flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , pp. 656 - 688
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Avicola, G. & Huq, P. 2003 The characteristics of the recirculating bulge region in coastal buoyant outflows. J. Mar. Res. 61 (4), 435–463.Google Scholar
Benjamin, T. B. & Lighthill, M. J. 1954 On cnoidal waves and bores. Proc. R. Soc. Lond. A 224 (1159), 448–460.Google Scholar
Cannon, G. A.1978 Circulation in the Strait of Juan de Fuca: some recent oceanographic observations. Tech. Rep. Environmental Research Laboratories (US).Google Scholar
Chant, R. J. 2011 2.11. Interactions between estuaries and coasts: river plumes – their formation, transport, and dispersal. In Treatise on Estuarine and Coastal Science (ed. Wolanski, E. & McLusky, D.), pp. 213–235. Academic Press.Google Scholar
Clarke, S. R. & Johnson, E. R. 1999 Finite-amplitude topographic Rossby waves in a channel. Phys. Fluids 11 (1), 107–120.Google Scholar
Curran, C. A., Konrad, C. P., Dinehart, R. L. & Moran, E. H.2008 Bank topography, bathymetry, and current velocity of the lower Elwha river, Clallam county, Washington, May 2006. Tech. Rep. Geological Survey (US).Google Scholar
El, G. A. 2005 Resolution of a shock in hyperbolic systems modified by weak dispersion. Chaos 15 (3), 037103.Google Scholar
Engquist, B., Lötstedt, P. & Sjögreen, B. 1989 Nonlinear filters for efficient shock computation. Math. Comput. 52 (186), 509–537.Google Scholar
Fedorov, A. V. & Melville, W. K. 1996 Hydraulic jumps at boundaries in rotating fluids. J. Fluid Mech. 324, 55–82.Google Scholar
Garvine, R. W. 1995 A dynamical system for classifying buoyant coastal discharges. Cont. Shelf Res. 15 (13), 1585–1596.Google Scholar
Gill, A. E. 1977 The hydraulics of rotating-channel flow. J. Fluid Mech. 80 (04), 641–671.Google Scholar
Gregorio, S. O., Haidvogel, D. B., Thomas, P. J., Taskinoglu, E. S. & Skeen, A. J. 2011 Laboratory and numerical simulations of gravity-driven coastal currents: departures from geostrophic theory. Dyn. Atmos. Oceans 52 (1), 20–50.Google Scholar
Helfrich, K. R. 2006 Nonlinear adjustment of a localized layer of buoyant, uniform potential vorticity fluid against a vertical wall. Dyn. Atmos. Oceans 41 (3), 149–171.Google Scholar
Helfrich, K. R., Kuo, A. C. & Pratt, L. J. 1999 Nonlinear Rossby adjustment in a channel. J. Fluid Mech. 390, 187–222.Google Scholar
Holbrook, J. R. & Halpern, D. 1982 Winter-time near-surface currents in the strait of Juan de Fuca. Atmos.-Ocean 20 (4), 327–339.Google Scholar
Holbrook, J. R., Muench, R. D., Kachel, D. G., Wright, C., Klutznick, P. M., Frank, R. A. & Hess, W. N.1980 Circulation in the Strait of Juan de Fuca: recent oceanographic observations in the eastern basin. Tech. Rep. Environmental Research Laboratories (US).Google Scholar
Horner-Devine, A. R., Fong, D. A., Monismith, S. G. & Maxworthy, T. 2006 Laboratory experiments simulating a coastal river inflow. J. Fluid Mech. 555, 203–232.Google Scholar
Isobe, A. 2005 Ballooning of river-plume bulge and its stabilization by tidal currents. J. Phys. Oceanogr. 35 (12), 2337–2351.Google Scholar
Johnson, E. R. & McDonald, N. R. 2006 Vortical source-sink flow against a wall: the initial value problem and exact steady states. Phys. Fluids 18 (7), 076601.Google Scholar
Johnson, E. R., Southwick, O. R. & McDonald, N. R. 2017 The long-wave vorticity dynamics of rotating buoyant outflows. J. Fluid Mech. 822, 418–443.Google Scholar
Kubokawa, A. 1991 On the behaviour of outflows with low potential vorticity from a sea strait. Tellus A 43 (2), 168–176.Google Scholar
Kubokawa, A. & Hanawa, K. 1984a A theory of semigeostrophic gravity waves and its application to the intrusion of a density current along a coast. J. Oceanogr. Soc. Japan 40 (4), 247–259.Google Scholar
Kubokawa, A. & Hanawa, K. 1984b A theory of semigeostrophic gravity waves and its application to the intrusion of a density current along a coast. Part 2. Intrusion of a density current along a coast in a rotating fluid. J. Oceanogr. Soc. Japan 40, 260–270.Google Scholar
Martin, J. R., Smeed, D. A. & Lane-Serff, G. F. 2005 Rotating gravity currents. Part 2. Potential vorticity theory. J. Fluid Mech. 522, 63–89.Google Scholar
McCreary, J. P., Zhang, S. & Shetye, S. R. 1997 Coastal circulations driven by river outflow in a variable-density 11/2-layer model. J. Geophys. Res. 102 (C7), 15535–15554.Google Scholar
Münchow, A. & Garvine, R. W. 1993 Buoyancy and wind forcing of a coastal current. J. Mar. Res. 51 (2), 293–322.Google Scholar
Pichevin, T. & Nof, D. 1997 The momentum imbalance paradox. Tellus A 49 (2), 298–319.Google Scholar
Sher, D. & Woods, A. W. 2017 Mixing in continuous gravity currents. J. Fluid Mech. 818, R4.Google Scholar
Shetye, S. R., Gouveia, A. D., Shenoi, S. S. C., Sundar, D., Michael, G. S. & Nampoothiri, G. 1993 The western boundary current of the seasonal subtropical gyre in the Bay of Bengal. J. Geophys. Res. 98 (C1), 945–954.Google Scholar
Simpson, J. H. & Hill, A. E. 1986 The Scottish coastal current. In The Role of Freshwater Outflow in Coastal Marine Ecosystems, pp. 295–308. Springer.Google Scholar
Southwick, O. R., Johnson, E. R. & McDonald, N. R. 2017 Potential vorticity dynamics of coastal outflows. J. Phys. Oceanogr. 47 (5), 1021–1041.Google Scholar
Stern, M. E. 1980 Geostrophic fronts, bores, breaking and blocking waves. J. Fluid Mech. 99 (4), 687–703.Google Scholar
Stern, M. E. & Helfrich, K. R. 2002 Propagation of a finite-amplitude potential vorticity front along the wall of a stratified fluid. J. Fluid Mech. 468, 179–204.Google Scholar
Stern, M. E., Whitehead, J. A. & Hua, B. L. 1982 The intrusion of a density current along the coast of a rotating fluid. J. Fluid Mech. 123, 237–265.Google Scholar
Thomas, P. J. & Linden, P. F. 2007 Rotating gravity currents: small-scale and large-scale laboratory experiments and a geostrophic model. J. Fluid Mech. 578, 35–65.Google Scholar
Wensu, W. 1988 Yangtze brackish water plume: circulation and diffusion. Prog. Oceanogr. 21 (3–4), 373–385.Google Scholar
Whitehead, J. A. & Salzig, J. 2001 Rotating channel flow: control and upstream currents. Geophys. Astrophys. Fluid Dyn. 95 (3–4), 185–226.Google Scholar
Yankovsky, A. E. & Chapman, D. C. 1997 A simple theory for the fate of buoyant coastal discharges. J. Phys. Oceanogr. 27 (7), 1386–1401.Google Scholar