Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T00:54:19.542Z Has data issue: false hasContentIssue false

A three-dimensional numerical model of the response of the Australian North West Shelf to tropical cyclones

Published online by Cambridge University Press:  17 February 2009

Songping Zhu
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, NSW 2500, Australia
Jörg Imberger
Affiliation:
Centre for Water Research, The University of Western Australia, Nedlands, WA 6009, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A three-dimensional barotropic and baroclinic model is developed to simulate currents and temperature changes induced by tropical cyclones traversing the continental shelf and slope region of the Australian North West Shelf. The model is based on a layered, explicit, finite difference formulation using the nonlinear primitive equations with an embedded entrainment scheme; a mixed-surface-layer interface is defined, which is allowed to shift from one interface to another, depending on the strength of a storm. The model has been tested by simulating the currents and temperature changes induced by tropical cyclones Orson and Ian. The modelled currents and temperatures agreed well with the available measured records except near the seabed. It has been found that the pre-storm currents have very little influence on the peak of the storm-induced currents and the currents in the wake of a tropical cyclone. The model contained no coefficients which must be calibrated for a particular application and clearly illustrated the importance of the baroclinic effects on the storm-induced response over the North West Shelf of Australia.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Arakawa, A. and Lamb, V. R., “Computational design of the basic dynamical processes of the UCLA general circulation model”, Methods in Comp. Phys. 17 (1977) 173265.Google Scholar
[2]Chang, S. W., “Deep ocean response to hurricanes as revealed by an ocean model with free surface”, J. Phys. Oceanogr. 15 (1985) 18471858.2.0.CO;2>CrossRefGoogle Scholar
[3]Chang, S. W. and Anthes, R. A., “Numerical simulations of the ocean's nonlinear, baroclinic response to translating hurricanes”, J. Phys. Oceanogr. 8 (1978) 468480.2.0.CO;2>CrossRefGoogle Scholar
[4]Chapman, D. C., “Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model”, J. Phys. Oceanogr. 15 (1985) 10601075.2.0.CO;2>CrossRefGoogle Scholar
[5]Church, J. A., Joyce, T. M. and Price, J. F., “Current and density observation across the wake of Hurricane Gay”, J. Phys. Oceanogr. 19 (1989) 259265.2.0.CO;2>CrossRefGoogle Scholar
[6]Cooper, C. and Pearce, B., “Numerical simulations of hurricane-generated currents”, J. Phys. Oceanogr. 12 (1982) 10711091.2.0.CO;2>CrossRefGoogle Scholar
[7]Cooper, C. and Thompson, J. D., “Hurricane-generated currents on the outer continental shelf. Part 1”, J. Geophy. Research 94 (1989) 1251312539.CrossRefGoogle Scholar
[8]Cooper, C. and Thompson, J. D., “Hurricane-generated currents on the outer continental shelf. Part 2”, J. Geophy. Research 94 (1989) 1254012554.CrossRefGoogle Scholar
[9]Elsberry, R. T., Fraim, T. and Trapnell, R. Jr, “A mixed layer model of the oceanic thermal response to hurricane”, J. Geophy. Research 81 (1976) 11531162.CrossRefGoogle Scholar
[10]Forristall, G. Z., “A two-layer model for hurricane-driven currents on an irregular grid”, J. Phys. Oceanogr. 10 (1980) 14171438.2.0.CO;2>CrossRefGoogle Scholar
[11]Garratt, J. R., “Review of drag coefficients over oceans and continents”, Mon. Weather Rev. 105 (1977) 915929.2.0.CO;2>CrossRefGoogle Scholar
[12]Geisler, J. E., “Linear theory of the response of a two layer ocean to a moving hurricane”, Geo. Phys. Fluid Dyn. 2 (1970) 249272.CrossRefGoogle Scholar
[13]Greatbatch, R. J., “On the response of the ocean to a moving storm: the nonlinear dynamics”, J. Phys. Oceanogr. 13 (1983) 357367.2.0.CO;2>CrossRefGoogle Scholar
[14]Greatbatch, R. J., “On the response of the ocean to a moving storm: parameters and scales”, J. Phys. Oceanogr. 14 (1984) 5978.2.0.CO;2>CrossRefGoogle Scholar
[15]Heaps, N. S., “Development of storm-surge models at Bidston”, Report No. 53, Institute of Ocean-ographic Sciences, Bidston Observatory (UK), 1977.Google Scholar
[16]Hearn, C. J. and Holloway, P. E., “A three-dimensional barotropic model of the response of the Australian north west shelf to tropical cyclones”, J. Phys. Oceanogr. 20 (1990) 6080.2.0.CO;2>CrossRefGoogle Scholar
[17]Hearn, C. J. and Hunter, J. R., “Modelling wind-driven flow in shallow systems on the southwest australian coast”, Numerical Modelling: Application to Marine Systems (1987) 4757.Google Scholar
[18]Holland, G. J., “An analytic model of the wind and pressure profiles in hurricanes”, Mon. Weather Rev. 108 (1980) 12121218.2.0.CO;2>CrossRefGoogle Scholar
[19]Holloway, P. E., “Internal tides on the Australian north west shelf: A preliminary investigation”, J. Phys. Oceanogr. 13 (1983) 13571370.2.0.CO;2>CrossRefGoogle Scholar
[20]Holloway, P. E., “Tides on the Australian north west shelf”, Aust. J. Mar. Fresh. Res. 34 (1983) 213230.CrossRefGoogle Scholar
[21]Holloway, P. E., “On the semi-diumal internal tide at a shelf-break region on the Australia north west shelf”, J. Phys. Oceanogr. 14 (1984) 17871799.2.0.CO;2>CrossRefGoogle Scholar
[22]Holloway, P. E., “Internal hydraulic jumps and solitons at a shelf break region on the Australian north west shelf”, J. Geophy. Research 92 (1987) 54055416.Google Scholar
[23]Holloway, P. E., Barnes, I., Webster, I. and Imberger, J., “Dynamics of the north west shelf. Report prepared for Woodside Offshore Petroleum”, Centre for Water Research Environmental Dynamics Report ED-81–008, University of Western Australia, 1981.Google Scholar
[24]Holloway, P. E. and Nye, H. C., “Observed response of the north-west shelf waters to tropical cyclones: 1979 to 1984”, Centre for Water Research Environmental Dynamics Report ED-84–092, University of Western Australia, 1984.Google Scholar
[25]Imberger, J. and Holloway, P. E., “Dynamics of the north west shelf. Progress report and proposal for future studies”, Centre for Water Research Environmental Dynamics Report ED-81–006, University of Western Australia, 1981.Google Scholar
[26]Jordan, C. L., “On the influence of tropical cyclones on the sea surface temperature field”, Proc. Symp. on Tropical Meteorology, N. Z. (1963) 614622.Google Scholar
[27]Kajiura, K., “A forced wave caused by atmospheric disturbances in deep water”, Technical report 133–1, Dept. of Oceanography and Meteorology, Texas A&M University, 1956.Google Scholar
[28]Kato, H. and Phillips, O. M., “On the penetration of turbulent layer into stratified fluid”, J. Fluid Mech. 37 (1969) 643655.CrossRefGoogle Scholar
[29]Kuo, H.-H. and Ichiye, T., “A numerical study of the response of barotropic ocean to a moving hurricane”, Tellus 29 (1977) 561571.CrossRefGoogle Scholar
[30]Lovell, K. F., Harper, B. A. and Chandler, B. D., “Calibration of an analytic model of the wind and pressure profiles in hurricanes”, Report to Woodside Offshore Petroleum, 1990.Google Scholar
[31]Madala, R. V. and Piacsek, S. A., “A semi-implicit numerical model for baroclinic oceans”, J. Comp. Phys. 23 (1977) 167178.CrossRefGoogle Scholar
[32]Martin, P. J., “Mixed-layer simulation of buoy observations taken during hurricane Eloise”, J. Geophysic. Res. 87 (1982) 409427.CrossRefGoogle Scholar
[33]Munk, W. H. and Anderson, E. R., “Notes on a theory of the thermocline”, J. Mar. Res. 7 (1948) 276295.Google Scholar
[34]Noye, J., “Finite difference methods for solving the 1-D transport equation”, in Numerical Modelling: Application to Marine Systems (ed. Noye, J.), (1987), 231256.CrossRefGoogle Scholar
[35]O'Brien, J. J., “The non-linear response of a two-layer, baroclinic ocean to a stationary, axially-symmetric hurricane: Part II. Upwelling and mixing induced by momentum transfer”, J. Atmos. Sci. 24 (1967) 208215.2.0.CO;2>CrossRefGoogle Scholar
[36]O'Brien, J. J. and Reid, R. O., “The non-linear response of a two-layer, baroclinic ocean to a stationary, axially-symmetric hurricane: Part I. Upwelling induced by momentum transfer”, J. Atmos. Sci. 24 (1967) 197207.2.0.CO;2>CrossRefGoogle Scholar
[37]Pedlosky, J., Geophysical fluid dynamics (Springer-Verlag, New York, 1979).CrossRefGoogle Scholar
[38]Peyret, R. and Taylor, T. D., Computational methods for fluid flow (Springer-Verlag, New York, 1982).Google Scholar
[39]Pollard, R.T., Rhines, P. B. and Thompson, R. O. R. Y., “The deepening of the wind-mixed layer”, Geophys. Fluid Dyn. 3 (1973) 381404.CrossRefGoogle Scholar
[40]Price, J. F., “On the scaling of stress-driven entrainment experiments”, J. Fluid Mech. 90 (1979) 509529.CrossRefGoogle Scholar
[41]Price, J. F., “Upper ocean response to a hurricane”, J. Phys. Oceanogr. 11 (1981) 153175.2.0.CO;2>CrossRefGoogle Scholar
[42]Shay, L. K., Chang, S. W. and Elsberry, R. L., “Free surface effects on the near-inertial ocean current response to a hurricane”, J. Phys. Oceanogr. 20 (1990) 14051424.2.0.CO;2>CrossRefGoogle Scholar
[43]Simons, T. J., “Circulation models of lakes and inland seas”, Can. Bull. Fish. Aquat. SCI. 203 (1980) 25.Google Scholar
[44]Smith, G. D., Numerical solution of partial differential equations, 2nd ed. (Clarendon Press, 1978).Google Scholar
[45]Spigel, R.H, Imberger, J. and Rayner, K. N., “Modeling the diurnal mixed layer”, Limnol. Oceanogr. 32 (1986) 533556.CrossRefGoogle Scholar
[46]Suginohara, N., “Response of a two-layer ocean to typhoon passage in the western boundary region”, J. Oceanogr. Soc. in Japan 29 (1973) 1023.CrossRefGoogle Scholar
[47]Tennekes, H., “Turbulent entrainment in stratified fluids”, Memoires Societe Royale des Sciences de Liege 6 (1973) 131139.Google Scholar
[48]Webster, I., “Frictional continental shelf waves and the circulation response of a continental shelf to wind forcing”, J. Phys. Oceanogr. 15 (1985) 855864.2.0.CO;2>CrossRefGoogle Scholar
[49]Webster, I., “Wind-driven circulation on the North West Shelf of Australia”, J. Phys. Oceanogr. 15 (1985) 13571368.2.0.CO;2>CrossRefGoogle Scholar
[50]Withee, G. W. and Johnson, A., “Buoy observation during hurricane Eloise (September 19 to October 11, 1975)”, Data report, U. S. Department of Commerce, NOAA, NSTL Station, Mississippi, 1976.Google Scholar
[51]Wu, J., “Wind-stress coefficients over sea surface near neutral conditions: A revisit”, J. Phys. Oceanogr. 10 (1980) 727740.2.0.CO;2>CrossRefGoogle Scholar
[52]Zelt, J. A., “A three-dimensional model of currents and mixing induced by a tropical cyclone on a shelf”, Centre for Water Research Environmental Dynamics Report ED-88–267, University of Western Australia, 1988.Google Scholar