Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 15
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ngo-Cong, D. Mohammed, F.J. Strunin, D.V. Skvortsov, A.T. Mai-Duy, N. and Tran-Cong, T. 2015. Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution. Journal of Hydrology, Vol. 525, p. 87.

    Mohammed, F.J. Ngo-Cong, D. Strunin, D.V. Mai-Duy, N. and Tran-Cong, T. 2014. Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method. Applied Mathematical Modelling, Vol. 38, Issue. 14, p. 3672.

    Patrachari, Anirudh R. and Johannes, Arland H. 2012. A conceptual framework to model interfacial contamination in multiproduct petroleum pipelines. International Journal of Heat and Mass Transfer, Vol. 55, Issue. 17-18, p. 4613.

    Nepf, Heidi and Ghisalberti, Marco 2008. Flow and transport in channels with submerged vegetation. Acta Geophysica, Vol. 56, Issue. 3,

    Murphy, E. Ghisalberti, M. and Nepf, H. 2007. Model and laboratory study of dispersion in flows with submerged vegetation. Water Resources Research, Vol. 43, Issue. 5, p. n/a.

    Nepf, H. Ghisalberti, M. White, B. and Murphy, E. 2007. Retention time and dispersion associated with submerged aquatic canopies. Water Resources Research, Vol. 43, Issue. 4, p. n/a.

    Andradóttir, Hrund Ó. and Nepf, Heidi M. 2000. Thermal mediation by littoral wetlands and impact on lake intrusion depth. Water Resources Research, Vol. 36, Issue. 3, p. 725.

    Watt, S. D. and Roberts, A. J. 1996. The construction of zonal models of dispersion in channels via matched centre manifolds. The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, Vol. 38, Issue. 01, p. 101.

    Watt, Simon D. and Roberts, Anthony J. 1995. The Accurate Dynamic Modelling of Contaminant Dispersion in Channels. SIAM Journal on Applied Mathematics, Vol. 55, Issue. 4, p. 1016.

    Van den Broeck, C. 1990. Taylor dispersion revisited. Physica A: Statistical Mechanics and its Applications, Vol. 168, Issue. 2, p. 677.

    Roberts, A. J. 1989. The Utility of an Invariant Manifold Description of the Evolution of a Dynamical System. SIAM Journal on Mathematical Analysis, Vol. 20, Issue. 6, p. 1447.

    Smith, Ronald 1987. Shear dispersion looked at from a new angle. Journal of Fluid Mechanics, Vol. 182, Issue. -1, p. 447.

    Smith, Ronald 1987. Diffusion in shear flows made easy: the Taylor limit. Journal of Fluid Mechanics, Vol. 175, Issue. -1, p. 201.

    Chikwendu, S.C. 1986. Application of a slow-zone model to contaminant dispersion in laminar shear flows. International Journal of Engineering Science, Vol. 24, Issue. 6, p. 1031.

    Chikwendu, S. C. 1986. Calculation of longitudinal shear dispersivity using an N-zone model as N [rightward arrow] [infty infinity]. Journal of Fluid Mechanics, Vol. 167, Issue. -1, p. 19.

  • Journal of Fluid Mechanics, Volume 152
  • March 1985, pp. 15-38

Slow-zone model for longitudinal dispersion in two-dimensional shear flows

  • S. C. Chikwendu (a1) and G. U. Ojiakor (a2)
  • DOI:
  • Published online: 01 April 2006

A two-zone model is proposed for the longitudinal dispersion of contaminants in two-dimensional turbulent flow in open channels – a fast zone in the upper region of the flow, and a slow zone nearer to the bottom. The usual one-dimensional dispersion approach (Elder 1959) is used in each zone, but with different flow speeds U1 and U2 and dispersion coefficients D1 and D2 in the fast and slow zones respectively. However, turbulent vertical mixing is allowed at the interface between the two zones, with a small vertical diffusivity ε. This leads to a pair of coupled, linear, one-dimensional dispersion equations, which are solved by Fourier transformation. The Fourier-inversion integrals are analysed using two different methods.

In the first method asymptotically valid expressions are found using the saddle-point method. The resulting cross-sectional average concentration consists of a leading Gaussian distribution followed by a trailing Gaussian distribution. The trailing Gaussian cloud disperses (longitudinally) faster than the leading one, and this gives the long tail observed in most dispersion experiments. Significantly the peak value of the average concentration is found to decay exponentially with time at a rate which is close to the rate observed by Sullivan (1971) in the early stage of the dispersion process. The solution is useful for fairly small times, and both the calculated value of D1 and the predicted bulk concentration distribution are in meaningful agreement with the experimental and simulation data of Sullivan (1971).

In the second method an exact solution is found in the form of a convolution integral for the case D1 = D2 = D0. Explicit expressions which are valid for small times and for large times from the release of contaminant are found. For small times this exact solution confirms the basic results obtained by the saddle-point method. For large times the exact solution gives a contaminant concentration which approaches a Gaussian distribution travelling with the bulk speed as predicted by the Taylor model. The overall longitudinal dispersion coefficient at large times, D(∞), consists of the diffusivity D0 plus a contribution D[ell ](∞) which depends entirely on the vertical mixing. D(∞) is in good agreement with Chatwin's (1971) interpretation of Fischer's (1966) experimental data.

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? *