3.12 Lee Waves and the Froude Number
53
3.11.5 Additional Exercise for the Reader
Repeat this exercise with ρ 1 = 1,027.5 kg/m
3 and ρ 2 = 1,028.5 kg/m
3 , which
halves the density contrast between the layers. Equation (3.61) suggests that the
thickness of the initial mixing regime will double in this situation. The reader is
encouraged to verify this.
Fig. 3.26 Exercise 6. Vertical
profiles of 1/Ri after (left
panel) 25 min and (left panel)
100 min of simulation.
Vertical profiles are computed
from horizontal averages of
density and lateral flow
speed. The value 1/Ri = 4
indicates the theoretical
transition between laminar
and turbulent flow
3.12 Lee Waves and the Froude Number
3.12.1 The Hydraulic Jump
Lee waves are created by flow past a topographic irregularity such as a mountain in
the atmosphere or a sill in the ocean. Resultant disturbances of density interfaces in
the lee of topographic obstacles are internal waves of a certain phase speed. Whether
disturbances can locally grow to great amplitudes depends on the phase speed of
internal waves in relation to the carrier speed of the ambient flow.
The ratio between speed of the incident flow and the phase speed of long gravity
waves is called the Froude number, introduced by William Froude (1874). For a
Froude number less than unity, wave disturbances can travel upstream against the
ambient flow, a situation referred to as subcritical. For a Froude number is excess of
unity, on the other hand, wave disturbances are carried downstream by the ambient
flow. This situation is referred to as supercritical.
The transition between these two regimes is called the hydraulic jump, which
implies a Froude number of unity. In this situation, wave disturbances remain
trapped and can amplify. Hydraulic jumps occur when a flow of water at high,
supercritical velocity discharges into a zone of lower, subcritical velocity. Lee waves
of large amplitudes are the traces of such hydraulic jumps.
53
3.11.5 Additional Exercise for the Reader
Repeat this exercise with ρ 1 = 1,027.5 kg/m
3 and ρ 2 = 1,028.5 kg/m
3 , which
halves the density contrast between the layers. Equation (3.61) suggests that the
thickness of the initial mixing regime will double in this situation. The reader is
encouraged to verify this.
Fig. 3.26 Exercise 6. Vertical
profiles of 1/Ri after (left
panel) 25 min and (left panel)
100 min of simulation.
Vertical profiles are computed
from horizontal averages of
density and lateral flow
speed. The value 1/Ri = 4
indicates the theoretical
transition between laminar
and turbulent flow
3.12 Lee Waves and the Froude Number
3.12.1 The Hydraulic Jump
Lee waves are created by flow past a topographic irregularity such as a mountain in
the atmosphere or a sill in the ocean. Resultant disturbances of density interfaces in
the lee of topographic obstacles are internal waves of a certain phase speed. Whether
disturbances can locally grow to great amplitudes depends on the phase speed of
internal waves in relation to the carrier speed of the ambient flow.
The ratio between speed of the incident flow and the phase speed of long gravity
waves is called the Froude number, introduced by William Froude (1874). For a
Froude number less than unity, wave disturbances can travel upstream against the
ambient flow, a situation referred to as subcritical. For a Froude number is excess of
unity, on the other hand, wave disturbances are carried downstream by the ambient
flow. This situation is referred to as supercritical.
The transition between these two regimes is called the hydraulic jump, which
implies a Froude number of unity. In this situation, wave disturbances remain
trapped and can amplify. Hydraulic jumps occur when a flow of water at high,
supercritical velocity discharges into a zone of lower, subcritical velocity. Lee waves
of large amplitudes are the traces of such hydraulic jumps.