Internal Waves

What are Internal Waves?

These waves might occur in any situation where a fluid is stratified, i.e., the fluid density changes abruptly. This stratification can arise in many instances such as the ocean, where the cold water below is denser than the warm water above, atmospheric fronts with cold and warm air masses, or even industrial contexts with different chemical layers in a storage tank.

The speed of propagation of internal waves, denoted by \(c\), depends on the fluid's stratification and is given by the formula:

\[ c = \sqrt{g'h} \]

Here, \(g'\) denotes reduced gravity, \(h\) is the fluid layer's thickness, and \(g'\) is defined as:

\[ g' = g \frac{\rho_2 - \rho_1}{\rho_2 + \rho_1} \]

With \(g\) being the acceleration due to gravity, and \(\rho_1\) and \(\rho_2\) representing the densities of the lower and upper fluid layers, respectively.

Different Examples of Internal Waves in Fluid Mechanics

Internal waves can be seen in various instances of fluid mechanics. Here are some notable examples:

• Ocean Waves: These are perhaps the most familiar examples of internal waves, where the temperature and salinity differences create stratified layers in the ocean. When disrupted, these layers cause waves to form under the water surface.
• Atmospheric Waves: Stratified layers in the atmosphere form due to temperature gradients, leading to the creation of atmospheric internal waves.
• Industrial Fluids: In certain manufacturing processes, the layers of different chemicals or substances in a container can form stratified layers, causing internal waves when disturbed.

The Mechanism Behind the Generation of Internal Waves

The generation of internal waves is an interesting process involving the disturbance of a stratified fluid's equilibrium. The disturbance could be due to wind, tides, or any obstacles in the fluid path. The energy imparted by these disturbances displaces the fluid particles from their equilibrium positions, causing them to oscillate and create waves.

The restoring force behind these oscillations and hence the wave formation is the buoyancy or gravity acting on the fluid particles. As a consequence, internal waves are also called gravity waves. These waves can travel across long distances, leading to energy transfer over larger areas.

Critical Study of Internal Waves in the Ocean

The study of internal waves in the ocean is a topic of great significance, shedding light on various important phenomena in oceanography and coastal engineering. Due to density stratification, influenced by temperature and salinity gradients, internal waves have the unique ability to travel beneath the ocean surface. These wave features have an appreciable impact on offshore engineering structures, marine life, and the overall climate.

Influence of Ocean's Internal Waves on Engineering Structures

The invisible motion of internal waves within the oceanic depths can generate substantial loads on offshore structures, often leading to unplanned events of structural fatigue or failure. Since internal waves travel at a lesser speed than surface waves, their influence on structures beneath the surface is quite significant. Unlike surface waves which cause impact loads, internal waves cause oscillating pressures and induced water particle velocities known as the Stokes Drift.

These waves can induce rapidly changing velocity fields leading to vortex-induced vibrations of vertical and horizontal members of offshore structures. Moreover, the high-frequency internal waves generate additional loads by causing resonance in semi-submersible platforms and spar buoys.

Engineering structures that can be affected by internal waves include:

• Pipelines: Internal waves can cause oscillatory seafloor movements that may interact with subsea pipelines, potentially causing mechanical stress and instability.
• Offshore platforms: Rapid changes in water current velocities induced by internal waves can result in loading and vibrations in offshore platforms with potential for structural damage.
• Submersibles and submarines: Underwater vehicles are susceptible to abrupt changes in water velocities due to internal waves, impacting navigation and stability.

Investigating Oceanic Examples of Internal Waves

One of the most iconic examples of ocean internal waves is seen in the South China Sea, where strong semi-diurnal tides interacting with the Luzon Strait generate the world's most powerful internal waves. These waves can reach up to 170 metres in height and are visible from space.

Another classic example is the internal waves generated in the Strait of Gibraltar, caused by the tide-driven flow over the Camarinal Sill. These waves then pass through the entire Mediterranean Sea and play a significant role in distributing nutrients throughout the basin.

It is important to know that internal waves, unlike surface waves, are not easily detectable. Thanks to satellite remote sensing techniques, these internal waves are detected through their surface imprints. Satellite remote sensing can be used to calculate significant wave parameters, such as wavelength, wave direction, and propagation speed.

Causes and Characteristics of Ocean’s Internal Waves

The generation and characteristics of ocean's internal waves are determined by several factors. Some sources of internal waves in oceans include:

• Wind: Occasional heavy winds can stir the ocean's surface, creating turbulence that results in internal waves.
• Tidal movement: Regular interaction of tides with underwater features such as continental shelves, seafloor ridges, and seamounts can generate internal waves.
• Fluid Movement: The movement of warm and cold water currents can cause turbulence resulting in internal waves.

Frequency, wavelength, phase speed, and amplitude are some of the key characteristics of these waves. For instance, low-frequency internal waves, often called internal tides, occur due to the Earth's gravitational forces. They can propagate over large distances and cause significant displacement of ocean layers.

From an engineering standpoint, understanding these features is crucial to predicting and mitigating the potential impact of internal waves on offshore and coastal structures.

Examining the Impact of Internal Waves on Engineering Projects

For engineering projects, particularly those in marine and off-shore environments, internal waves can pose distinct challenges. The oscillations within fluid mediums due to changes in density cause forces that can greatly affect structural integrity, operations, and safety of various structures including pipelines, platforms, and even submarines. Just as engineers study wind loads for buildings or seismic loads for bridges, underwater fluid dynamics, including internal waves, must be considered for offshore structures.

Case Studies: The Effect of Internal Waves on Engineering Structures

In-depth case studies can provide valuable insights into the real-life effects of internal waves on engineering structures.

In the oil and gas industry, for instance, subsea pipelines are ubiquitous. A case study from the North Sea showcased the significant influence internal waves wield over subsea pipelines. Due to internal waves, oscillatory seabed movements occurred which exerted tremendous mechanical stress and ultimately led to instability of the structures.

In offshore wind energy projects, internal waves have also proven to be a factor. An instance from a wind farm off the coast of Wales revealed that internal waves induced vibration in the turbine structures leading to early fatigue and unexpected repair. This led to an increase in maintenance costs and a reduction of the overall lifecycle of the infrastructure.

In the realm of naval engineering, submarines and underwater vehicles need to navigate the complex underwater wavescape. During a naval operation in the Mediterranean, sudden changes in water velocities caused by internal waves led to navigation difficulties for a submarine, hinting at potential safety concerns.

Precautions in Engineering When Dealing with Internal Waves

With the potential for internal waves to impact engineering structures, proper precautions need to be factored into the design and maintenance of these structures.

• Adequate Design: Engineering designs for marine structures need to account for potential internal wave actions. The design parameters, such as safety factors, should cater for loads exerted by these waves.
• Geotechnical Surveys: Detailed geotechnical studies of the oceanic bottom can help anticipate the generation and magnitude of internal waves. These data can inform the design and placements of structures like offshore platforms and subsea pipelines.
• Monitoring System: A robust monitoring system capable of tracking changes in water velocities and pressure can help identify the presence of internal waves. It can provide real-time data, enabling timely preventive actions.
• Regular Maintenance: Consistent inspections and maintenance of structures can help identify and address early signs of fatigue or damage caused by internal waves.

Innovative Engineering Solutions to Internal Waves Challenges

Engineers are continuously exploring innovative solutions to mitigate the risks and challenges induced by internal waves.

One such innovation is the development of 'Dynamic Response Analysis' software. This tool is designed to simulate the effect of environmental conditions, including internal waves, on subsea systems. By incorporating the physics of internal waves, the software can predict the dynamic response of structures allowing engineers to foresee possible problems and adapt the design for better resilience.

furthermore, engineers are experimenting with flexible materials for subsea infrastructures to absorb and dissipate the energy transferred by internal waves, and thus minimise structural damage.

Additionally, acoustic monitoring systems have shown promise. These systems use sound waves to observe underwater features and track movements due to internal waves, providing key information for the operation and navigation of underwater vehicles.

Despite the challenges, by employing a combination of cautionary measures, robust design principles and innovative solutions, engineers can effectively tackle the issues posed by internal waves in their projects.