Geoscience Reference
In-Depth Information
Estimation of River Banks Influence
on Tachoida Shape at the Meridian
Zygmunt Meyer
1
Introduction
The concept of the so-called modified tachoida was presented in the author's
previous paper (Meyer
2009a
). The concept focuses on the problem of avoiding
simplifications that were taken by Prandtl (
1956
) in formulating the so-called
logarithmic tachoida. The proposed modified logarithmic tachoida makes it possi-
ble to define hydrodynamic equilibrium state for the flowing stream by introducing
eddy viscosity coefficient of water at the bottom layer. The method also allows for
the approximation of the model parameters, based upon data coming from measure-
ments. The verification made for a set of data taken from the literature (Stone and
Hotchkiss
2007
) indicates that the tachoida measured at the meridian of the river
differs from the one proposed by the author in the previous papers (Meyer
2009b
).
The reason is the assumption of a two-dimensional (2D), vertically plane model,
taken for consideration. This suggests that three-dimensional (3D) model should be
used to include the influence of river banks on the tachoida measured at the
meridian of the river.
In the chapter, the mathematical description of the 3D approach is given and an
example of the verification based upon experimental data is presented.
2 Mathematical Description of Phenomenon
Mathematical description of the water flow phenomenon when no tangential stres-
ses are applied at the free water surface (no wind, no ice) was achieved under the
following assumptions (Meyer
2009a
):
z
H
t
xz
ð
z
Þ¼t
b
1
(1)
