Fluid Dynamics: Barotropic and Baroclinic Flow

A fluid flow where the volume changes under external pressure, resulting in density changes.

A fluid flow where the volume remains constant, even under pressure, and density stays the same.

A mathematical relationship that describes the connection between pressure, temperature, and density of a substance.

The local spinning or rotation of a fluid, quantified by a vector called vorticity.

A fluid that can be compressed, often due to large changes in pressure.

A fluid that resists compression, keeping a nearly constant volume, typically with strong intermolecular forces.

A fluid flow is considered compressible if its density changes significantly due to pressure variations.

A fluid flow is considered nearly incompressible if its density remains relatively constant, e.g., water flow in a pipe.

The force exerted by a fluid on a surface, often caused by the weight of the fluid above it.

A type of flow where density changes are small and can be ignored for certain types of calculations.

A wave that travels through a medium (like air or water) by compressing and expanding the medium. These waves are very fast.

A mathematical simplification that assumes density is constant and that the velocity field is divergence-free.

A mathematical simplification that allows density changes due to vertical motion but assumes other density changes are negligible.

The layer of atmosphere closest to Earth's surface, characterized by turbulent mixing. The depth of this layer can vary.

The specific gas constant for a particular gas. It helps relate pressure, density, and temperature.

The velocity field is divergence-free, indicating that parcels of fluid conserve their volume in this type of flow.

The ratio of specific heats at constant pressure (cp) and constant volume (cv). It is used in describing the changes of density with pressure.

The variable density in the governing equations of mass and momentum. Changes in density can create different types of waves.

The process of moving a parcel of fluid from one location to another. The parcel may change in volume.

The average density of a fluid, often used in anelastic flow situations.

A flow where pressure changes solely depend on density variations. Isobaric surfaces (constant pressure) and isopycnic surfaces (constant density) align perfectly.

A flow where density changes are influenced by both pressure and temperature variations. Isobaric and isopycnic surfaces don't align.

In barotropic flows, pressure gradient forces align with density gradient forces, resulting in no net vorticity. Think of a smooth, uniform flow.

In baroclinic flows, pressure gradient forces and density gradient forces are misaligned, generating vorticity. Think of swirls and eddies due to temperature differences.

Barotropic flows are generally characterized by a lack of wind shear, making them less favorable for severe weather development. Think of a calm, stable atmosphere.

The aneolastic continuity equation is the most accurate form of the continuity equation used in weather forecasting for the real atmosphere. It's frequently applied to the synoptic scale, which covers large weather systems, and atmospheric deep convection, like thunderstorms.

The Boussinesq approximation simplifies the fluid momentum equation by assuming that density variations are negligible except for those related to buoyancy. This means that density changes due to pressure gradients are small, while density changes driving buoyancy remain significant. This approximation is widely used in geophysical flows, like atmospheric modeling.

The momentum equation describes the changes in velocity of a fluid parcel. Using the Boussinesq approximation, it highlights the effects of pressure gradients, buoyancy, and viscous forces on a parcel's acceleration. It's crucial for studying air motion in atmospheric modeling.

A tensor expression that quantifies the local spinning or rotational motion of a fluid. Vorticity is a vector field that describes the tendency of a fluid to rotate at a given point.

The rate of change of vorticity in time. It describes how the local spinning motion of a fluid changes over time. It's influenced by the stretching or tilting of vorticity due to the flow velocity and the diffusion of vorticity due to viscosity.

The change of vorticity in a fluid that results from the fluid's velocity changes. This contributes to the local rotation of the fluid. The bigger the change in velocity, the more significant the stretching and tilting of vorticity.

The diffusion of vorticity through a fluid due to viscosity. Viscous forces dampen or smooth out vorticity over time. The stronger the viscosity, the faster the diffusion of vorticity.

A fluid flow where the density and pressure are directly linked. In these flows, pressure gradients align with density gradients. Barotropic flows tend to be less prone to rotating motions because pressure forces don't necessarily induce a torque.

A situation where pressure and density are not directly related. Pressure gradients don't necessarily align with density gradients. This difference in pressure and density can lead to a force that causes rotation (torque) and can lead to development of weather systems.

The vertical distribution of pressure and density in barotropic flow. Density decreases with height but pressure and density remain in a direct relationship, thus creating a balanced state in the flow.

The vertical distribution of pressure and density in baroclinic flow. Density decreases with height and pressure changes are not directly related to density changes, causing potential for fluid motion and development of weather.

The force that acts perpendicular to the isobars (lines of constant pressure) in a baroclinic flow. It's the prime force that causes rotational motion in the atmosphere, leading to the development of weather features, such as fronts and storms.

A special case of barotropic flow where the pressure and density are strictly proportional. This means that density only varies with pressure, and density remains uniform on horizontal planes.

A situation where density and pressure gradients are aligned, making the flow non-rotational. This is in contrast to baroclinic flows where misalignment between these gradients triggers rotation.

The tendency of vorticity to be stretched or tilted by fluid motions. This stretching or tilting is induced by variations in velocity across the fluid, and it's a fundamental factor in the development and amplification of vorticity.

A flow that is influenced both by pressure gradients and by density variations. This type of flow often exists in real life situations and it can lead to complicated fluid dynamics.