Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity. When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow.
In fluid dynamics, the baroclinity of a stratified fluid is a measure of how misaligned the gradient of pressure is from the gradient of density in a fluid. In meteorology a baroclinic flow is one in which the density depends on both temperature and pressure. A simpler case, barotropic flow, allows for density dependence only on pressure, so that the curl of the pressure-gradient force vanishes.
In fluid dynamics, the Boussinesq approximation is used in the field of buoyancy-driven flow. It ignores density differences except where they appear in terms multiplied by g, the acceleration due to gravity. The essence of the Boussinesq approximation is that the difference in inertia is negligible but gravity is sufficiently strong to make the specific weight appreciably different between the two fluids. Sound waves are impossible/neglected when the Boussinesq approximation is used since sound waves move via density variations.
In continuum mechanics, the Froude number is a dimensionless number defined as the ratio of the flow inertia to the external field. The Froude number is based on the speed–length ratio which he defined as:
A capillary wave is a wave traveling along the phase boundary of a fluid, whose dynamics and phase velocity are dominated by the effects of surface tension.
In fluid dynamics, a wind wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result of the wind blowing over the water's surface. The contact distance in the direction of the wind is known as the fetch. Waves in the oceans can travel thousands of kilometers before reaching land. Wind waves on Earth range in size from small ripples to waves over 30 m (100 ft) high, being limited by wind speed, duration, fetch, and water depth.
Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change with depth/height due to changes, for example, in temperature and/or salinity. If the density changes over a small vertical distance, the waves propagate horizontally like surface waves, but do so at slower speeds as determined by the density difference of the fluid below and above the interface. If the density changes continuously, the waves can propagate vertically as well as horizontally through the fluid.
A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive, i.e., the phase speed of the wave crests is equal to the group speed of the wave energy for all frequencies. This means that it retains its shape as it moves in the alongshore direction over time.
In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, with gravity and surface tension as the restoring forces. As a result, water with a free surface is generally considered to be a dispersive medium.
A swell, also sometimes referred to as ground swell, in the context of an ocean, sea or lake, is a series of mechanical waves that propagate along the interface between water and air under the predominating influence of gravity, and thus are often referred to as surface gravity waves. These surface gravity waves have their origin as wind waves, but are the consequence of dispersion of wind waves from distant weather systems, where wind blows for a duration of time over a fetch of water, and these waves move out from the source area at speeds that are a function of wave period and length. More generally, a swell consists of wind-generated waves that are not greatly affected by the local wind at that time. Swell waves often have a relatively long wavelength, as short wavelength waves carry less energy and dissipate faster, but this varies due to the size, strength, and duration of the weather system responsible for the swell and the size of the water body, and varies from event to event, and from the same event, over time. Occasionally, swells that are longer than 700m occur as a result of the most severe storms.
The shallow-water equations (SWE) are a set of hyperbolic partial differential equations that describe the flow below a pressure surface in a fluid. The shallow-water equations in unidirectional form are also called Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant.
In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in the Earth's atmosphere. Unlike liquids, gases cannot form a free surface on their own. Fluidized/liquified solids, including slurries, granular materials, and powders may form a free surface.
In fluid dynamics, the Boussinesq approximation for water waves is an approximation valid for weakly non-linear and fairly long waves. The approximation is named after Joseph Boussinesq, who first derived them in response to the observation by John Scott Russell of the wave of translation. The 1872 paper of Boussinesq introduces the equations now known as the Boussinesq equations.
In fluid dynamics, a Stokes wave is a nonlinear and periodic surface wave on an inviscid fluid layer of constant mean depth. This type of modelling has its origins in the mid 19th century when Sir George Stokes – using a perturbation series approach, now known as the Stokes expansion – obtained approximate solutions for nonlinear wave motion.
In fluid dynamics, wave shoaling is the effect by which surface waves, entering shallower water, change in wave height. It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, changes with water depth. Under stationary conditions, a decrease in transport speed must be compensated by an increase in energy density in order to maintain a constant energy flux. Shoaling waves will also exhibit a reduction in wavelength while the frequency remains constant.
In fluid dynamics, Airy wave theory gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mean depth, and that the fluid flow is inviscid, incompressible and irrotational. This theory was first published, in correct form, by George Biddell Airy in the 19th century.
Ocean dynamics define and describe the flow of water within the oceans. Ocean temperature and motion fields can be separated into three distinct layers: mixed (surface) layer, upper ocean, and deep ocean.
A Sverdrup wave is a wave in the ocean, or large lakes, which is affected by gravity and Earth's rotation.
Tides in marginal seas are tides affected by their location in semi-enclosed areas along the margins of continents and differ from tides in the open oceans. Tides are water level variations caused by the gravitational interaction between the Moon, the Sun and the Earth. The resulting tidal force is a secondary effect of gravity: it is the difference between the actual gravitational force and the centrifugal force. While the centrifugal force is constant across the Earth, the gravitational force is dependent on the distance between the two bodies and is therefore not constant across the Earth. The tidal force is thus the difference between these two forces on each location on the Earth.
In fluid mechanics, topographic steering is the effect of potential vorticity conservation on the motion of a fluid parcel. This means that the fluid parcels will not only react to physical obstacles in their path, but also to changes in topography or latitude. The two types of 'fluids' where topographic steering is mainly observed in daily life are air and water in respectively the atmosphere and the oceans. Examples of topographic steering can be found in, among other things, paths of low pressure systems and oceanic currents.
