Geophysical fluid dynamics

Geophysical fluid dynamics is the study of how fluids move in nature. This field applies fluid dynamics to flows on Earth and other planets. It examines the movement of gases like our atmosphere and liquids like the oceans. It also studies the flow of lava.

This science helps us understand the large-scale systems that shape our world. It focuses on naturally occurring flows rather than man-made systems. Scientists use this field to study how energy and matter move through the environment.

To describe these complex flows, scientists rely on mathematical equations. They use equations for the conservation of momentum. These equations are based on Newton's second law. They also use equations for the conservation of energy. The momentum equations lead to the Navier–Stokes equations. These equations are very difficult to solve exactly. Because of this, scientists use specific approximations to make them usable. One common assumption is that the fluid is incompressible. This means the density stays the same. Even for air, this works well if we ignore sound and shock waves.

Another assumption involves the type of fluid being studied. Scientists often assume the fluid is a Newtonian fluid. This means there is a linear relation between shear stress and strain. In this context, viscosity is the property that resists flow. To track movement, scientists use different frames of reference. A Lagrangian frame follows a small parcel of fluid as it moves. An Eulerian frame stays in a stationary position. In an Eulerian frame, acceleration is divided into the local rate of change and advection. Advection is the rate of flow in or out of a small region.

Energy conservation is essentially the study of heat flow. Heat can move through a fluid via conduction. This process is governed by a diffusion equation. If buoyancy effects are present, natural convection can occur. This is also known as free convection. This process is vital for many planetary systems. For example, convection in the Earth's outer core drives the geodynamo. This geodynamo is the source of our planet's magnetic field. In the ocean, convection can be driven by temperature or salinity. Thermal convection is driven by heat. Haline convection is driven by differences in salinity. When both heat and salt drive the movement, it is called thermohaline circulation.

Stratification, or layering, is a fundamental feature of geophysical fluids. Fluid that is less dense than its surroundings tends to rise. It will continue to rise until its density matches the surrounding fluid. If there is little energy input, a system will become stratified. The Earth's atmosphere is divided into five distinct layers. These layers are the troposphere, stratosphere, mesosphere, thermosphere, and exosphere. In the ocean, density is determined by temperature and salinity. In lakes, density is determined by temperature.

When stratification occurs, thin layers can form. In these layers, a property changes rapidly with depth or height. Scientists name these layers based on what is changing. A pycnocline is a layer where density changes quickly. A thermocline is a layer where temperature changes rapidly. A halocline is a layer where salinity changes. If chemical properties like oxygenation change, it is called a chemocline. These layers are important for understanding how fluids behave. Buoyancy also creates gravity waves. When these waves occur within the fluid, they are called internal waves.

Scientists use specific models to study these buoyancy-driven flows. They often use the Boussinesq approximation for their equations. This approximation ignores density variations except when they are multiplied by gravitational acceleration. The type of flow also depends on how pressure relates to density. If pressure depends only on density, the flow is barotropic. This occurs in the atmosphere when there is a lack of fronts, such as in the tropics. If there are fronts, the flow is baroclinic. Baroclinic flows can lead to instabilities like cyclones.

Understanding these dynamics helps us model complex weather events like Hurricane Mitch.