#### Date of Award

Spring 1976

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mechanical & Aerospace Engineering

#### Program/Concentration

Engineering Mechanics

#### Committee Director

Chin Kuo

#### Committee Member

Chester Grosch

#### Committee Member

Ronald E. Johnson

#### Committee Member

Bruce Neilson

#### Abstract

The project began with the design and construction of a hydraulic Froude model of the Lafayette River, a small well mixed estuary in Norfolk, Virginia. Horizontal scale is 1/540, vertical scale 1/12 yielding a vertical distortion of 45. Adjustment by roughness strips and screens produced close agreement of model-prototype tide heights, currents, and salinities in the deep reaches comprising 80% of the estuary volume. Some scale effect in velocity and tide height could not be eliminated in the shallow upper branches of the estuary, probably because of the high geometric distortion and the narrowness of the channel at kilometer 6.7. Similar slug releases of Rhodamine WT dye tracer in model and prototype produced concentration fields which were monitored over eight tidal cycles. The normalized concentration fields

were in close agreement in the lower reaches. In the shallow upper branches, model concentrations increased to about double those in the prototype as depth decreased. Using an analytic solution to the one-dimensional advection-diffusion equation, values of low-and high-water slack dispersion coefficients were computed for model and prototype. Their mean was taken as an approximation of the real-time coefficient. By running the model with fresh water as well as with fresh/ salt mixed, it was possible to separate the dispersion coefficients into components dependent upon oscillatory turbulent velocity shear and upon density gradients.

The model-to-prototype ratio of turbulent velocity shear components must be of order 10^{-4} for similitude of dispersion. If the Taylor-Elder equations for dispersion coefficient apply, the actual ratio will be of order 10^{-1}; if on the other hand the "four-thirds law" applies, the actual ratio will be of order 10^{-4} as required for similitude. Data from the Lafayette River model agreed closely with the latter. Model-prototype comparisons of dispersion in several other models at varying scales and distortions have also been reported to demonstrate similitude, as would be predicted by the four-thirds law. It appears that this is the governing relationship for dispersion coefficients in at least nine models; consequently, similitude of mixing is attainable in at least these and possibly other estuaries. No particular restriction on the relationship between horizontal and vertical scales is necessary. An analysis of the derivation of the one-dimensional longitudinal dispersion equation shows that the coefficient is in fact the sum of two terms, one related to the Taylor-Elder concept (mixing due to velocity shear and small-scale eddies) and the other to the four-thirds law (mixing due to large-scale eddies). More research is needed to determine, for any given estuary, the relative magnitude of the two components.

#### DOI

10.25777/j695-fe38

#### Recommended Citation

Blair, Carvel H..
"Similitude of Mass Transfer Processes in Distorted Froude Model of an Estuary"
(1976). Doctor of Philosophy (PhD), dissertation, Mechanical & Aerospace Engineering, Old Dominion University, DOI: 10.25777/j695-fe38

https://digitalcommons.odu.edu/mae_etds/217