Internal wave dynamics

Layered fluids can carry waves inside themselves.

An internal wave is a wave that travels within a stably stratified fluid rather than on its outer surface. In the ocean, these waves move through varying density gradients created by temperature and salinity, carrying energy and momentum through water that can look still from above.

The basic idea

Stratification creates a restoring force.

When a fluid is layered by density, a displaced parcel tends to move back toward the level where its density fits. That restoring motion can oscillate. When the oscillation organizes in space, the result is an internal wave.

Surface waves use the air-water interface as their visible boundary. Internal waves use density gradients inside the fluid. The interface may be sharp, like a two-layer tank, or smoothly distributed, like much of the ocean below the near-surface mixed layer.

The important quantity is the buoyancy frequency, often written N. It describes how quickly a displaced fluid parcel would oscillate vertically in a stable density gradient. Internal waves generally exist at frequencies below N, and their direction, speed, and energy pathways depend on the stratification around them.

Composite showing free surface waves, Kaena Ridge tidal flow, and internal waves in temperature data
Internal waves can be thought of as the hidden cousin of surface waves. This proposal figure connects visible ripples to waves generated by tidal flow over Kaena Ridge. Underlying ocean examples were adapted from Zilberman et al., 2011 and Carter et al., 2006.
Sketch comparing free-surface waves, interfacial waves, and internal waves over topography
Lab-created schematic separating three related ideas: waves on a free surface, waves on a density interface, and internal waves moving through a stratified fluid.

What controls the motion

Internal waves are geometry, frequency, and energy budget all at once.

Schematic showing six controls on internal waves: stratification N of z, forcing frequency omega, beam angle theta, topography h of x, interaction energy spectrum E of k, and mixing consequences.
Six connected controls shape the internal-wave story: stratification, forcing frequency, beam angle, topography, wave interactions, and mixing consequences.
N(z)

Stratification

The density profile sets the buoyancy frequency. When stratification changes with height, waves can bend, slow, reflect, decay, or pass through a turning depth into a new region.

ω

Frequency

The forcing frequency determines whether a wave can propagate in a given layer. If the local conditions do not support propagation, the response may become evanescent.

θ

Beam Angle

Internal wave energy often travels in beams at angles tied to wave frequency and stratification. That geometry makes laboratory visualization especially powerful.

h(x)

Topography

Ridges, slopes, and rough seafloor-like features can convert oscillating flow into internal waves as fluid is pushed up and around them. Small shape details can change how much energy leaves the source.

E(k)

Interactions

Wave beams can collide, generate harmonics, and move energy across scales. Those interactions help explain why simple wave fields become complex.

mixing

Consequences

Internal waves can contribute to ocean mixing and transport. Understanding when they propagate, break, or transfer energy matters for larger-scale fluid systems.

A mental picture

Think of the fluid as a stack of springy layers.

Push one region up or down, and buoyancy tries to restore it. The disturbance can travel away from the source as a wave, but the path is constrained by the density structure and by the frequency of the forcing.

Color visualization of high-frequency internal wave interactions
In the lab, density-gradient motion becomes visible through optical measurements and image processing. Related work: Casaday and Crockett, 2012.
Schematic showing tidal flow over topography generating internal wave beams
Tides set the forcing frequency, while topography and stratification help set the amplitude and wavelength of the internal waves that radiate away. Source: 2023 NSF proposal figure.

Why topography matters

Tidal energy can be converted into internal-wave energy.

As barotropic tidal flow moves over ridges and rough bathymetry, it can lift and lower density layers. That motion converts some tidal energy into internal waves, which can propagate away, interact with other waves or boundaries, and contribute to mixing.

From concept to lab question

The dynamics page is the doorway; the research page follows the energy.

01

Generate a wave.

Oscillating flow over topography, moving boundaries, or wave-wave interactions create disturbances in a stratified fluid.

02

Ask whether it can propagate.

The local buoyancy frequency, forcing frequency, and geometry determine whether the wave carries energy away or remains trapped near the source.

03

Measure where the energy goes.

We use controlled experiments and models to connect visible wave patterns to energy pathways, harmonics, and mixing-relevant behavior.

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