Hydraulics Prof. B.S.

Thandaveswara

37.3 Classification of waves

Translatory, longitudinal shallow water waves can be classified based on different

criteria as shown in table below. (Ref. unsteady flow in open channels edited by

Mahmood K and Yevjevich V. Vol 1, 1975).

Table: Criteria for classification of wave

Criteria Classification

Surges (Moving hydraulic jugs - hydraulic bore)

(1) Rate of
variation Intermediate waves

Long waves

capillary wave

gl
Gravity C 2 =
2π
(2) Controlling
force
(
gL 2πσ
)
2πy
C2 = ___ + ____ tanh ____ (for shallow water waves)
2π ρL ρL
Capillary wave

(
gL 2πσ
C2 = ___ + ____
2π ρL ) (for deep wave)

Gravity and friction

3a
η = 2a S ec h 2 ( x − ct )
Simple solitary 2 y3
(Single form of gravity wave )
Undisturbed water flow
a
η
(3) Frequency of
occurrence

The Solitary Wave

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Hydraulics Prof. B.S. Thandaveswara

Mutiple

Wave train
cg

Wave Groups
Downstream
Relative to channel bed slope
Upstream

Vw Vw Vw
y V2 V2 y V2 y V2 y
2 V1 y1 y1 V1 2 y1 V1 2 y V1 2
1

Type A - Advancing Type B - Advancing Type B - Advancing Type B - Advancing

downstream upstream upstream upstream
(positive surge) (positive surge) (positive surge) (positive surge)

Vw = c + V1 Vw = c - V1 Vw = c + V1 Vw = c - V1
(4) Direction of
movement

V - Vw+V2 Vw - V2 +V
y w V2 Vw - V1 V +V y Vw - V1 y y Vw 2 Vw+V1
2 y1 y w 1 2 y1 2 2 y1
1

Type A Type B Type C Type D

Four Types of rapidly varied uniformly progressive flow. (Top)

Unsteady flows; (bottom) the corresponding flows that appear steady to
an observer following the wavefront.

Downstream
Relative to underlying flow
Upstream

(5) Wave
surface
elevation

Indian Institute of Technology Madras

Hydraulics Prof. B.S. Thandaveswara

Positive(higher) uniformly
progressive wave (sluice gate)
Relative to level of underlying flow Surge
Negative(lower) Type C (Sluice gate)
and D is operated Demand Surge
Positive-negative (when Sluice is operated these these appear in pairs)

Occur Tidal in rivers

Type A, B occur in Tidal rivers
Rejected Surge

(6) Form Single-faced (Monoclinical progressive rising wave)

Symmetrical
Two-faced
Asymmetrical

FLOOD
WAVE
Q

Time

Mean Water Level L

η a
(7) Periodic or
oscillatory wave
A Periodic y

Definition Sketch for Oscillatory Wave Motion

Particles constantly progressing the wave movement (Example: Sea waves)

(8) Translatory
Orbital

Circular particle Orbits in Deep Water

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Hydraulics Prof. B.S. Thandaveswara

(9) Transverse
wave
Longitudinal
wave

L
Mean water level
(10) Deep water
wave
Stokesian wave
Cnoidal wave y
Shallow water y'
wave

Elliptical Particle Orbits in Shallow Water

Mean water level

Typical Cnoidal Wave Profile

(11) Mechanical
Oscillation Finite amplitude due to initial disturbance
(pulsating flows) Mechanical oscillation
Kinematic wave Surface instability
Eg: Roll wave (progressive wave train)
Diffusive wave Steep slopes F > 2.0
Dynamic wave

(12)Rapidly
varying Progressing Surges, bores, depression
unsteady flow
Gradually Floods in reservoirs and in channels / rivers
varying
unsteady flow

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