maintain the ocean stratification via turbulence exchange, i.e. to govern the 25,000
times larger potential energy input by the sun.
Sea floor topography is important in both the generation (e.g., [5–7]) and the
breaking of internal waves (e.g., [8, 9]). Not only the topography around ocean basin’s
edges act as source/sink of internal waves but especially also the topography found in
ridges, mountain ranges and seamounts distributed over the ocean floor. There is more
underwater topography than on land. The main mechanical source interacting with the
topography is the tidal motion, which carries about 70% of the internal wave energy on
average [3]. Another prominent source is related with the rotation of the Earth and the
geostrophic response to sudden changes, e.g., by the passage of atmospheric disturbances or by the collapse of fronts: Inertial motions [1, 10]. Although the general
aspect ratio of large-scale vertical:horizontal ocean current components is 1:1000, or
perhaps 1:100, an encounter with topography forces a relatively large vertical motion
that sets the, initially flat and horizontal, layers of constant density into oscillatory
movements. The thus generated internal waves can propagate in full three-dimensions
3D spatially. After interactions with waves at other frequencies, or currents, or
topography, the dominant process still being unknown, the initially linear waves
become nonlinear and break whereby dissipating their energy. The associated turbulence not only affects the ocean stratification but also the marine geology and
chemistry, by resuspending sediment and redistributing suspended material, and
marine biology by the redistribution of nutrients and oxygen.
As internal waves can propagate freely when their frequencies are between the
inertial frequency f, of horizontal oscillatory motion with short vertical scale thus an
important shear ‘source’, and the buoyancy frequency N, the natural frequency of
vertical oscillatory motion governed by the stratification, they are rather slow waves
compared to surface waves. Internal wave periods vary between about a day and
hours (in the deep ocean) to minutes (in generally stronger stratified waters of
shallow seas and near the ocean surface). Such a slow motion is associated with
linear waves that go up and down regularly. Faster motions are found beyond the
buoyancy scales where the transitions to turbulence are found. When turbulence is
mainly induced by wave-breaking, fronts of deformed internal waves pass instrumentation fixed in space within minutes.
The wave-breaking is a complex process in which the two main mechanisms to
stratified turbulence co-exist. Vertical current shear across thin interfaces leads to
overturning of Kelvin Helmholtz billows or instabilities KHI (e.g., [11]). The
wave-overturning leads to ‘free’ buoyancy driven convection turbulence of
Rayleigh-Taylor instabilities of a collapse of unstable (‘cold’) fluid overlying less
dense (‘warm’) water [12]. Both mechanisms relate in a complex manner, e.g., a
convection column [13] leads to shear instabilities along its fringes [14] and
shear-induced overturning leads to convection in its core [15]. In the ocean these
processes are most developed above sloping bottom topography.
Although some topography-internal wave interaction processes are well
described, such as internal hydraulic jumps or lee-wave formation over seamounts
and ridges [16, 17] and frequent overturning from internal wave breaking over
slopes steeper ‘supercritical’ than the internal tide slope (e.g., [18, 19], Sarkar 2016,
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H. van Haren
times larger potential energy input by the sun.
Sea floor topography is important in both the generation (e.g., [5–7]) and the
breaking of internal waves (e.g., [8, 9]). Not only the topography around ocean basin’s
edges act as source/sink of internal waves but especially also the topography found in
ridges, mountain ranges and seamounts distributed over the ocean floor. There is more
underwater topography than on land. The main mechanical source interacting with the
topography is the tidal motion, which carries about 70% of the internal wave energy on
average [3]. Another prominent source is related with the rotation of the Earth and the
geostrophic response to sudden changes, e.g., by the passage of atmospheric disturbances or by the collapse of fronts: Inertial motions [1, 10]. Although the general
aspect ratio of large-scale vertical:horizontal ocean current components is 1:1000, or
perhaps 1:100, an encounter with topography forces a relatively large vertical motion
that sets the, initially flat and horizontal, layers of constant density into oscillatory
movements. The thus generated internal waves can propagate in full three-dimensions
3D spatially. After interactions with waves at other frequencies, or currents, or
topography, the dominant process still being unknown, the initially linear waves
become nonlinear and break whereby dissipating their energy. The associated turbulence not only affects the ocean stratification but also the marine geology and
chemistry, by resuspending sediment and redistributing suspended material, and
marine biology by the redistribution of nutrients and oxygen.
As internal waves can propagate freely when their frequencies are between the
inertial frequency f, of horizontal oscillatory motion with short vertical scale thus an
important shear ‘source’, and the buoyancy frequency N, the natural frequency of
vertical oscillatory motion governed by the stratification, they are rather slow waves
compared to surface waves. Internal wave periods vary between about a day and
hours (in the deep ocean) to minutes (in generally stronger stratified waters of
shallow seas and near the ocean surface). Such a slow motion is associated with
linear waves that go up and down regularly. Faster motions are found beyond the
buoyancy scales where the transitions to turbulence are found. When turbulence is
mainly induced by wave-breaking, fronts of deformed internal waves pass instrumentation fixed in space within minutes.
The wave-breaking is a complex process in which the two main mechanisms to
stratified turbulence co-exist. Vertical current shear across thin interfaces leads to
overturning of Kelvin Helmholtz billows or instabilities KHI (e.g., [11]). The
wave-overturning leads to ‘free’ buoyancy driven convection turbulence of
Rayleigh-Taylor instabilities of a collapse of unstable (‘cold’) fluid overlying less
dense (‘warm’) water [12]. Both mechanisms relate in a complex manner, e.g., a
convection column [13] leads to shear instabilities along its fringes [14] and
shear-induced overturning leads to convection in its core [15]. In the ocean these
processes are most developed above sloping bottom topography.
Although some topography-internal wave interaction processes are well
described, such as internal hydraulic jumps or lee-wave formation over seamounts
and ridges [16, 17] and frequent overturning from internal wave breaking over
slopes steeper ‘supercritical’ than the internal tide slope (e.g., [18, 19], Sarkar 2016,
128
H. van Haren