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Introduction

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Book cover Non-Hydrostatic Free Surface Flows

Abstract

An introduction to Boussinesq theory for depth-averaged non-hydrostatic open-channel flows is given. A historical note is used to depict the development of this theory, starting with Boussinesq (1877) treatise, pursued and expanded by the developments of Fawer (1937), Serre (1953), Matthew (1963) and Peregrine (1966). The importance of non-hydrostatic depth-averaged free surface flow modeling is then discussed in the context of environmental fluid mechanics, including the problems of flows in control structures, seepage flows, flows in alluvial rivers, and water waves in coastal engineering, among others.

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Abbreviations

D :

Still water depth (m)

E :

Specific energy head (m)

F :

Flux vector (m2/s, m3/s2)

g :

Gravity acceleration (m/s2)

h :

Flow depth measured vertically (m)

H :

Energy head (m)

K :

Parameter in curvature law (–)

N :

Flow depth measured on normal to channel bottom (m)

p :

Pressure (N/m2)

p b :

Bottom pressure (N/m2)

q :

Unit discharge (m2/s)

r :

Radius of bottom curvature (m)

r z :

Radius of streamline curvature at elevation z (m)

R :

Radius of free surface curvature (m)

S :

Momentum function (m2/s)

S o :

Bottom slope (–)

S f :

Friction slope (–)

S :

Source term vector (m/s, m2/s2)

t :

Time (s) also flow depth measured as vertical projection of equipotential curve (m)

u :

Velocity in x-direction (m/s)

U :

Mean flow velocity (m/s) = q/h

U :

Vector of conserved variables (m, m2/s)

w :

Velocity in z-direction (m/s)

x :

Streamwise coordinate (m)

z :

Vertical elevation (m)

z b :

Elevation of channel bottom (m)

β :

Boussinesq velocity correction coefficient (–)

γ :

Specific weight (N/m3)

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Authors and Affiliations

  1. University of Cordoba, Cordoba, Spain

    Oscar Castro-Orgaz

  2. ETH Zurich, Zürich, Switzerland

    Willi H. Hager

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  1. Oscar Castro-Orgaz
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  2. Willi H. Hager
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Correspondence to Oscar Castro-Orgaz .

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Castro-Orgaz, O., Hager, W.H. (2017). Introduction. In: Non-Hydrostatic Free Surface Flows. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-47971-2_1

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