Civil Engineering Reference
In-Depth Information
8
Improved Numerical
Modeling for Perturbations
in Homogeneous and
Stratified Flows
contents
8.1 Introduction ....................................................................................................................144
8.2 Materials and Methods ...................................................................................................144
8.3 Results and Discussion ...................................................................................................147
8.3.1 Velocity Phase of the Harmonic Wave ...............................................................147
8.4 Conclusion .....................................................................................................................147
Keywords .................................................................................................................................150
References ................................................................................................................................150
nomenclAtures
v
F
= speed of long waves
(
)
m
s
λ
= wavelength
σ
= surface tension
h
= free surface of the liquid
h
= liquid level is above the bottom of the channel
ξ
= difference of free surface of the liquid and the liquid level is above the bottom of
the channel(a deviation from the level of the liquid free surface)
u
= fluid velocity
(
)
m
s
τ
= time period
a
= distance of the order of the amplitude
f
= wavelength
k
= wave number
Φ = a function of frequency and wave vector
( )
= phase velocity or the velocity of phase fluctuations
(
)
v
Ô
k
m
s
( )
λ
= wavelength
( )
ω
= damping the oscillations in time
ω
= waves with stationary in time but varying in length amplitudes
k
= waves with a uniform length, but a time-varying amplitude.
k
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