### Abstract

In wide streams the variations in the water quality parameters are fundamentally affected by transverse mixing, prohibiting in general the use of one-dimensional water quality models. A two-dimensional mixing mode applying to steady conditions is presented, which serves as the basis for developing two-dimensional water quality models. The mixing model is formulated in a curvilinear coordinate system following the curvature conditions of the stream and contains depth integrated (average) values. The numerical solution based on the equations of the mass flux constant line, along which normal transport is zero, presents a visual geometric picture of the process. The difference scheme obtained is second order transversally, first order longitudinally and explicit. Stability criteria of the solution are given and the numerical solution is verified by checks against the possible analytical solutions. An attempt has been made to make the model suited to the study of several hundred km length, relying only on existing data, i.e. without the need for special observations, further to examination under different streamflow rates. In such applications the stream must also be 'simulated' for which a one-dimensional hydraulic model is used. Practical applications of the model are illustrated by three numerical examples for the Danube. In the first the results of tracer observations are compared with those obtained analytically. The second applies to a 12 km long reach of the river. Actually observed NH^{+}_{4} values are compared to those obtained with the model (at the time of observations t ~ 6°C; thus the component considered underwent virtually no change). The pollution effect of a tributary stream is examined finally over a reach of 59.4 km length. A fair agreement between the values observed and computed demonstrates the validity of the model developed.

Original language | English |
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Pages (from-to) | 97 |

Number of pages | 1 |

Journal | Progress in Water Technology |

Volume | 10 |

Issue number | 5 |

Publication status | Published - 1978 |

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### ASJC Scopus subject areas

- Medicine(all)

### Cite this

**Mixing model for large streams.** / Somlyódy, L.

Research output: Contribution to journal › Article

*Progress in Water Technology*, vol. 10, no. 5, pp. 97.

}

TY - JOUR

T1 - Mixing model for large streams

AU - Somlyódy, L.

PY - 1978

Y1 - 1978

N2 - In wide streams the variations in the water quality parameters are fundamentally affected by transverse mixing, prohibiting in general the use of one-dimensional water quality models. A two-dimensional mixing mode applying to steady conditions is presented, which serves as the basis for developing two-dimensional water quality models. The mixing model is formulated in a curvilinear coordinate system following the curvature conditions of the stream and contains depth integrated (average) values. The numerical solution based on the equations of the mass flux constant line, along which normal transport is zero, presents a visual geometric picture of the process. The difference scheme obtained is second order transversally, first order longitudinally and explicit. Stability criteria of the solution are given and the numerical solution is verified by checks against the possible analytical solutions. An attempt has been made to make the model suited to the study of several hundred km length, relying only on existing data, i.e. without the need for special observations, further to examination under different streamflow rates. In such applications the stream must also be 'simulated' for which a one-dimensional hydraulic model is used. Practical applications of the model are illustrated by three numerical examples for the Danube. In the first the results of tracer observations are compared with those obtained analytically. The second applies to a 12 km long reach of the river. Actually observed NH+4 values are compared to those obtained with the model (at the time of observations t ~ 6°C; thus the component considered underwent virtually no change). The pollution effect of a tributary stream is examined finally over a reach of 59.4 km length. A fair agreement between the values observed and computed demonstrates the validity of the model developed.

AB - In wide streams the variations in the water quality parameters are fundamentally affected by transverse mixing, prohibiting in general the use of one-dimensional water quality models. A two-dimensional mixing mode applying to steady conditions is presented, which serves as the basis for developing two-dimensional water quality models. The mixing model is formulated in a curvilinear coordinate system following the curvature conditions of the stream and contains depth integrated (average) values. The numerical solution based on the equations of the mass flux constant line, along which normal transport is zero, presents a visual geometric picture of the process. The difference scheme obtained is second order transversally, first order longitudinally and explicit. Stability criteria of the solution are given and the numerical solution is verified by checks against the possible analytical solutions. An attempt has been made to make the model suited to the study of several hundred km length, relying only on existing data, i.e. without the need for special observations, further to examination under different streamflow rates. In such applications the stream must also be 'simulated' for which a one-dimensional hydraulic model is used. Practical applications of the model are illustrated by three numerical examples for the Danube. In the first the results of tracer observations are compared with those obtained analytically. The second applies to a 12 km long reach of the river. Actually observed NH+4 values are compared to those obtained with the model (at the time of observations t ~ 6°C; thus the component considered underwent virtually no change). The pollution effect of a tributary stream is examined finally over a reach of 59.4 km length. A fair agreement between the values observed and computed demonstrates the validity of the model developed.

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M3 - Article

VL - 10

SP - 97

JO - Water Science and Technology

JF - Water Science and Technology

SN - 0273-1223

IS - 5

ER -