Steady Open Channel Flow Research Articles

Normal Stress Effects in the Creep of Ice

AbstractMost non-linear fluids for which the appropriate measurements have been made exhibit non-zero and unequal normal stress differences in shearing flows. Power-law models such as Glen’s law cannot represent this phenomenon. The simplest constitutive equation that does embody normal stress effects defines the second-order fluid. An exact analytical solution for biaxial creep of such a fluid is fit to data from four tests on polycrystalline ice. The model gives an excellent representation of both primary and secondary creep. The fits provide values for the three material constants. These coefficients indicate positive first and second normal stress differences. One consequence is the prediction that a steady open-channel flow will exhibit a longitudinal free-surface depression of up to several meters for sufficiently thick ice on steep slopes. In addition, the compressive principal stress at the channel margin is decreased and the tensile principal stress is increased in magnitude over those predicted by models without normal stresses. The normal stresses thus favor the formation of crevasses. Furthermore, the angle these crevasses form with the channel margin is decreased.

Normal Stress Effects in the Creep of Ice

AbstractMost non-linear fluids for which the appropriate measurements have been made exhibit non-zero and unequal normal stress differences in shearing flows. Power-law models such as Glen’s law cannot represent this phenomenon. The simplest constitutive equation that does embody normal stress effects defines the second-order fluid. An exact analytical solution for biaxial creep of such a fluid is fit to data from four tests on polycrystalline ice. The model gives an excellent representation of both primary and secondary creep. The fits provide values for the three material constants. These coefficients indicate positive first and second normal stress differences. One consequence is the prediction that a steady open-channel flow will exhibit a longitudinal free-surface depression of up to several meters for sufficiently thick ice on steep slopes. In addition, the compressive principal stress at the channel margin is decreased and the tensile principal stress is increased in magnitude over those predicted by models without normal stresses. The normal stresses thus favor the formation of crevasses. Furthermore, the angle these crevasses form with the channel margin is decreased.

MEASUREMENT OF BED FRICTION IN TIDAL INLETS

The flow characteristics and the stability of a tidal inlet are governed, among other factors, by the channel bed friction. In order to determine the bed shear stress regime and the frictional characteristics, near-bed velocity profiles were obtained at the throat sections of two inlets, John's Pass and Blind Pass, on the Gulf Coast of Florida. A specially designed steel cage with five current meters in a vertical array was used to obtain the profiles in the bottom one meter of the flow. The profiles were found to be logarithmic but it is noted that, especially near the times of slack water, the effect of inertia becomes significant. However, during the major part of the flood or ebb flow period, frictional effects are dominant. In the fully rough regime of flow, the bed-shear stress - velocity relationship is found to follow the square law, with a constant, characteristic friction factor and Manning's n for each inlet. This friction factor is used in hydraulic formulas, based on uniform, steady open channel flow relationships, to obtain the tidal prism - throat cross-sectional area ratio, which is then compared with that obtained from flow discharge measurements. Agreements and discrepancies in the comparison are discussed. The relationship between the bed shear stress at incipient motion and the grain size at the bed is reviewed, and it is noted that the observed relationship at the two inlets does not agree with the well-known correlation of Shields for uniform sandy beds.

Free Surface Slopes at Controls in Channel Flow

It is commonly held that the slope of a free water surface in steady open channel flow is indeterminate at a control section. It is shown that the surface slope is finite and, subject to certain approximations, determinate. Expressions are derived for the surface slopes of critical flows over a smooth weir and through a smooth contraction. Experiments confirmed the validity of these expressions up to the surface slopes of tan - ¹0.3 for weirs and tan - ¹0.8 for contractions. It is shown that the same expressions could have been obtained using the one-dimensional energy equation, even though the assumption of hydrostatic pressure is not valid. The expression derived for the water surface slope yields a well-conditioned equation for numerical calculation of water surface profiles through a control. The possibility of using surface slope at a control section as a rating parameter is mentioned.