Internal ocean waves can have amplitudes of 50–100 meters, far larger than typical surface waves, yet they travel much more slowly. What is the underlying physical reason for both of these properties?
AInternal waves carry far more total energy than surface waves, and high-energy waves always travel slowly
BInternal waves are generated by stronger tidal forces than surface waves, producing larger displacements
CThe density contrast at internal interfaces is a tiny fraction of a percent, making the restoring force weak — for a given energy, weak restoring forces produce large displacements and slow propagation
DInternal waves are confined to the thermocline depth range, where pressure gradients are too small to accelerate them quickly
Both properties — large amplitude and slow speed — stem from the same root cause: the tiny density contrast at internal interfaces. Surface waves feel a restoring force from the enormous air-water density difference (~800:1). Internal waves feel a restoring force from a density difference of perhaps 0.1–1% between adjacent water layers. A weak restoring force means the medium resists displacement less, so the same energy input produces larger displacement. It also means wave energy propagates slowly — wave speed scales with the square root of the restoring-force-per-unit-displacement. This is the central paradox of internal waves: they are the ocean's 'hidden giants.'
Question 2 Multiple Choice
Internal tides generated at a submarine ridge in the Pacific are observed to cause turbulent mixing at a location 2,500 km away. What does this imply about how vertical mixing is distributed in the ocean?
AMixing is concentrated at the generation site and decays exponentially with distance
BThe ocean must have multiple submarine ridges that together produce uniform background mixing
CInternal wave energy propagates horizontally over great distances, so mixing at one location can be driven by tidal forcing at a distant topographic feature
DDiapycnal mixing requires local wind forcing at the ocean surface and cannot be driven by deep-ocean processes
Internal waves are not local phenomena — they propagate thousands of kilometers from their generation sites before breaking. This non-local character is critical for ocean circulation models: you cannot predict mixing intensity at a given location simply by looking at local wind or tidal forcing. A seamount in the mid-Pacific generates internal tides that dissipate and mix water far from their source. This means the global distribution of diapycnal mixing — which drives deep-ocean ventilation and nutrient cycling — depends on the geography of submarine ridges and seamounts, not just on local conditions.
Question 3 True / False
Internal waves travel more slowly than surface waves because the density contrast between adjacent water layers is far smaller than the density contrast between water and air.
TTrue
FFalse
Answer: True
True. Wave propagation speed depends on the restoring force per unit displacement of the interface. For surface waves, the restoring force comes from the ~1000 kg/m³ vs. ~1.2 kg/m³ density contrast between water and air — an enormous difference. For internal waves, the restoring force comes from density differences between water layers that may be less than 1 kg/m³ apart — roughly 0.1% of the surface wave contrast. The much weaker restoring force produces much slower propagation. Internal wave speeds are typically measured in cm/s to a few m/s, compared to m/s to tens of m/s for surface waves.
Question 4 True / False
Because internal waves have large amplitudes (50–100 m), they carry far more energy per wave than surface waves and are the dominant source of energy input to the upper ocean.
TTrue
FFalse
Answer: False
False. Large amplitude does not mean large energy when the restoring force is weak. The energy density of a wave scales with the restoring force times the square of amplitude. For internal waves, the tiny density contrast severely limits energy density despite the large displacements. Surface waves, powered by wind over vast fetch areas, dominate upper-ocean energy input. Internal waves are important not because they carry more total energy, but because they are one of the primary mechanisms for mixing energy across density interfaces in the deep ocean — transporting heat, nutrients, and dissolved gases to regions inaccessible to wind-driven mixing.
Question 5 Short Answer
Why does strong stratification (a sharp pycnocline) simultaneously support internal waves and resist the very mixing that internal waves ultimately cause?
Think about your answer, then reveal below.
Model answer: Strong stratification creates a sharp density interface that acts as an elastic 'membrane,' providing the restoring force that sustains internal wave oscillations — steeper density gradients support higher-frequency, larger-amplitude internal waves. But stratification also suppresses vertical mixing by requiring energy to move denser water upward; the stronger the stratification, the more energy needed to mix across it. Internal waves thread this contradiction: they propagate along the stratification and carry energy horizontally until they steepen and break, at which point their kinetic energy is converted into turbulence that mixes across the density gradient. Without stratification, there are no internal waves; without wave breaking, stratification prevents the mixing that eventually erodes it.
This tension is central to ocean thermodynamics. The seasonal thermocline is strong enough to support large internal waves from wind-driven near-inertial oscillations, yet shallow enough to be mixed by them. The deep pycnocline requires the enormous energy of internal tides from major topographic features to generate enough breaking to achieve slow but geologically important diapycnal exchange between the deep and intermediate ocean.