Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 1
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    de Boer, Wiebe P. Roos, Pieter C. Hulscher, Suzanne J.M.H. and Stolk, Ad 2011. Impact of mega-scale sand extraction on tidal dynamics in semi-enclosed basins. Coastal Engineering, Vol. 58, Issue. 8, p. 678.

  • Journal of Fluid Mechanics, Volume 640
  • December 2009, pp. 421-439

Horizontally viscous effects in a tidal basin: extending Taylor's problem

  • P. C. ROOS (a1) and H. M. SCHUTTELAARS (a2)
  • DOI:
  • Published online: 27 October 2009

The classical problem of Taylor (Proc. Lond. Math. Soc., vol. 20, 1921, pp. 148–181) of Kelvin wave reflection in a semi-enclosed rectangular basin of uniform depth is extended to account for horizontally viscous effects. To this end, we add horizontally viscous terms to the hydrodynamic model (linearized depth-averaged shallow-water equations on a rotating plane, including bottom friction) and introduce a no-slip condition at the closed boundaries.

In a straight channel of infinite length, we obtain three types of wave solutions (normal modes). The first two wave types are viscous Kelvin and Poincaré modes. Compared to their inviscid counterparts, they display longitudinal boundary layers and a slight decrease in the characteristic length scales (wavelength or along-channel decay distance). For each viscous Poincaré mode, we additionally find a new mode with a nearly similar lateral structure. This third type, entirely due to viscous effects, represents evanescent waves with an along-channel decay distance bounded by the boundary-layer thickness.

The solution to the viscous Taylor problem is then written as a superposition of these normal modes: an incoming Kelvin wave and a truncated sum of reflected modes. To satisfy no slip at the lateral boundary, we apply a Galerkin method. The solution displays boundary layers, the lateral one at the basin's closed end being created by the (new) modes of the third type. Amphidromic points, in the inviscid and frictionless case located on the centreline of the basin, are now found on a line making a small angle to the longitudinal direction. Using parameter values representative for the Southern Bight of the North Sea, we finally compare the modelled and observed tide propagation in this basin.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

T. Brown 1987 Kelvin wave reflection at an oscillating boundary with applications to the North Sea. Cont. Shelf Res. 7 (4), 351365.

T. Brown 1989 On the general problem of Kelvin wave reflection at an oscillating boundary. Cont. Shelf Res. 9 (10), 931937.

S. C. Cai , X. Long , H. Liub & S. Wanga 2006 Tide model evaluation under different conditions. Cont. Shelf. Res. 26 (1), 104112.

N. Carbajal 1997 Two applications of Taylor's problem solution for finite rectangular semi-enclosed basins. Cont. Shelf Res. 17 (7), 803817.

M. K. Davey , W. W. Hsieh & R. C. Wajsowicz 1983 The free Kelvin wave with lateral and vertical viscosity. J. Phys. Oceanogr. 13, 21822191.

A. M. Davies & J. E. Jones 1995 The influence of bottom and internal friction upon tidal currents: Taylor's problem in three dimensions. Cont. Shelf Res. 15 (10), 12511285.

A. M. Davies & J. E. Jones 1996 The influence of wind and wind wave turbulence upon tidal currents: Taylor's problem in three dimensions with wind forcing. Cont. Shelf Res. 16 (1), 2599.

K. R. Dyer & D. A. Huntley 1999 The origin, classification and modelling of sand banks and ridges. Cont. Shelf Res. 19 (10), 12851330.

G. Fang , Y.-K. Kwok , K Yu & Y. Zhu 1999 Numerical simulation of principal tidal constituents in the South China Sea, Gulf of Tonkin and Gulf of Thailand. Cont. Shelf Res. 19 (7), 845869.

P. H. LeBlond & L. A. Mysak 1978 Waves in the Ocean. Elsevier.

P. Ripa & J. Zavala-Garay 1999 Ocean channel modes. J. Geophys. Res. 104 (C7), 15 47915 494.

S. Rizal 2002 Taylor's problem – influences on the spatial distribution of real and virtual amphidromes. Cont. Shelf Res. 22 (15), 21472158.

B. Sinha & R. D. Pingree 1997 The principal lunar semidiurnal tide and its harmonics: baseline solutions for M2 and M4 constituents in the North-West European Continental Shelf. Cont. Shelf Res. 17 (11), 13211365.

C. D. Winant 2007 Three-dimensional tidal flow in an elongated, rotating basin. J. Phys. Oceanogr. 37, 23452362.

J. T. F. Zimmerman 1982 On the Lorentz linearization of a quadratically damped forced oscillator. Phys. Lett. A 89, 123124.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *