Abstract
A non-linear two-dimensional vertically stratified cross-sectional model of a constant depth basin without rotation is used to investigate the influence of vertical and horizontal diffusion upon the wind-driven circulation in the basin and the associated temperature field. The influence of horizontal grid resolution, in particular the application of an irregular grid with high resolution in the coastal boundary layer is examined. The calculations show that the initial response to a wind impulse is downwelling at the downwind end of the basin with upwelling and convective mixing at the opposite end. Results from a two-layer analytical model show that the initial response is the excitation of an infinite number of internal seiche modes in order to represent the initial response which is confined to a narrow near coastal region. As time progresses, at the downwind end of the basin a density front propagates away from the boundary, with the intensity of its horizontal gradient and associated vertical velocity determined by both horizontal and vertical viscosity values. Calculations demonstrate the importance of high horizontal grid resolution in resolving this density gradient together with an accurate density advection scheme. The application of an irregular grid in the horizontal with high grid resolution in the nearshore region enables the initial response to be accurately reproduced although physically unrealistic short waves appear as the frontal region propagates onto the coarser grid. Parameterization of horizontal viscosity using a Smagorinsky-type formulation acts as a selective grid size-dependent filter, and removes the short-wave problem although enhanced smoothing can occur if the scaling coefficient in the formulation is too large. Calculations clearly show the advantages of using an irregular grid but also the importance of using a grid size-dependent filter to avoid numerical problems.
Similar content being viewed by others
References
Blumberg AF, Mellor GL (1987) A description of a three-dimensional coastal ocean circulation model. In: Heaps NS (eds) Three-dimensional coastal ocean models. Coastal and Estuarine Sciences, vol 4. American Geophysical Union, Washington, pp 1–16
Bolding K, Burchard H, Pohlmann T, Stipps A (2002) Turbulent mixing in the northern North Sea: a numerical model study. Cont Shelf Res 22:2707–2724
Csanady GT (1972) Response of large stratified lakes to wind. J Phys Oceanogr 2:3–13
Csanady GT (1973) Transverse internal seiches in large oblong lakes and marginal seas. J Phys Oceanogr 3:339–447
Csanady GT (1996) Circulation in the Coastal Ocean. D. Reidel Publishing Company, Boston, p 236
Davies AM (1980) Three dimensional hydrodynamic numerical models. Part 1. A homogeneous ocean-shelf model. Part 2. A stratified model of the Northern North Sea. In: Saetre R, Mork M (eds) The Norwegian Coastal Current. Bergen University, Bergen, pp 370–426
Davies AM, Xing J (2003) Processes influencing wind induced current profiles in near coastal stratified regions. Cont Shelf Res 23:1379–1400
Davies AM, Xing J (2004) Modelling processes influencing wind-induced internal wave generation and propagation. Cont Shelf Res 24:2245–2271
Goudsmit G-H, Burchard H, Peeters F, Wuest A (2002) Application of k-ε turbulence models to enclosed basins: The role of internal seiches. J Geophys Res 107:3230, doi:10.1029/2001JC000954
Heaps NS (1980) Density currents in a two-layered coastal system, with application to the Norwegian Coastal Current. Geophys J R Astron Soc 63:298–310
Heaps NS, Ramsbottom AE (1966) Wind effects on the water in a narrow two-layered lake. Philos Trans R Soc Lond 259:391–430
James ID (1996) Advection schemes for shelf sea models. J Mar Syst 8:237–254
Luettich RA, Westerink JJ (1995) Continental shelf scale convergence studies with a barotropic tidal model. In: Lynch DR, Davies AM (eds) Quantitative skill assessment for coastal ocean models. American Geophysical Union, pp 349–372
Luyten PJ, Deleersnijder E, Ozer J, Ruddick KG (1996) Presentation of a family of turbulence closure models for stratified shallow water flows and preliminary application to the Rhine outflow region. Cont Shelf Res 16:101–130
Luyten PJ, Carniel S, Umgiesser G (2002) Validation of turbulence closure parameterisations for stably stratified flows using the PROVESS turbulence measurements in the North Sea. J Sea Res 47:239–267
Lynch DR, Naimie CE (1993) The M2 tide and its residual on the outer banks of the Gulf of Maine. J Phys Oceanogr 23:2222–2253
Mellor GL (2001) One-dimensional, ocean surface layer modeling: a problem and a solution. J Phys Oceanogr 31:790–809
Platzman GW (1963) The dynamic prediction of wind tides on Lake Erie. Meteorol Monogr 4(26):44
Smagorinsky J (1963) General circulation experiments with the primitive equations I. The basic experiment. Mon Weather Rev 91:99–164
Werner FE (1995) A field test case for tidally forced flows: a review of the tidal flow forum. In: Lynch DR, Davies AM (eds) Quantitative skill assessment for coastal ocean models. American Geophysical Union, pp 269–284
Winant CD (2004) Three-dimensional wind-driven flow in an elongated, rotating basin. J Phys Oceanogr 34:462–476
Xing J, Davies AM (1998) A three-dimensional model of internal tides on the Malin-Hebrides shelf and shelf edge. J Geophys Res 103:27821–27847
Xing J, Davies AM (2001a) A three-dimensional baroclinic model of the Irish Sea : formation of thermal fronts and associated circulation. J Phys Oceanogr 31:94–114
Xing J, Davies AM (2001b) Non-linear effects of internal tides on the generation of the tidal mean flow at the Hebrides shelf edge. Geophys Res Lett 28:3939–3942
Xing J, Davies AM (2004) On the influence of a surface coastal front on near inertial wind induced internal wave propagation. J Geophys Res 109(C1):1023, doi:10.1029/2003JC001794.
Xing J, Davies AM (2005) Influence of a cold water bottom dome on internal wave trapping. Geophys Res Lett 32:L03601, doi:10.1029/2004GLO21833
Xing J, Chen F, Proctor R (1999) A two-dimensional slice model of the shelf edge region off the west coast of Scotland: model response to realistic seasonal forcing and the role of the M2 tide. Cont Shelf Res 19:1353–1386
Acknowledgements
The authors are indebted to Mrs L. Parry for typing the paper and Mr R.A. Smith for help in figure preparation.
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible Editor: Phil Dyke
Rights and permissions
About this article
Cite this article
Hall, P., Davies, A.M. Effect of coastal boundary resolution and mixing upon internal wave generation and propagation in coastal regions. Ocean Dynamics 55, 248–271 (2005). https://doi.org/10.1007/s10236-005-0014-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10236-005-0014-5