Fluid flow in the context of "Reynolds number"

A current in a fluid is the magnitude and direction of flow within each portion of that fluid, such as a liquid or a gas.

Convection is single or multiphase fluid flow that occurs spontaneously through the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). 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.

Convective flow may be transient (such as when a multiphase mixture of oil and water separates) or steady state (see convection cell). The convection may be due to gravitational, electromagnetic or fictitious body forces. Heat transfer by natural convection plays a role in the structure of Earth's atmosphere, its oceans, and its mantle. Discrete convective cells in the atmosphere can be identified by clouds, with stronger convection resulting in thunderstorms. Natural convection also plays a role in stellar physics. Convection is often categorised or described by the main effect causing the convective flow; for example, thermal convection.

In fluid mechanics, or more generally continuum mechanics, incompressible flow is a flow in which the material density does not vary over time. Equivalently, the divergence of an incompressible flow velocity is zero. Under certain conditions, the flow of compressible fluids can be modelled as incompressible flow to a good approximation.

A field line is a graphical visual aid for visualizing vector fields. It consists of an imaginary integral curve which is tangent to the field vector at each point along its length. A diagram showing a representative set of neighboring field lines is a common way of depicting a vector field in scientific and mathematical literature; this is called a field line diagram. They are used to show electric fields, magnetic fields, and gravitational fields among many other types. In fluid mechanics, field lines showing the velocity field of a fluid flow are called streamlines.

Convection (or convective heat transfer) is the transfer of heat from one place to another due to the movement of fluid. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combined processes of conduction (heat diffusion) and advection (heat transfer by bulk fluid flow). Convection is usually the dominant form of heat transfer in liquids and gases.

Note that this definition of convection is only applicable in Heat transfer and thermodynamic contexts. It should not be confused with the dynamic fluid phenomenon of convection, which is typically referred to as Natural Convection in thermodynamic contexts in order to distinguish the two.

Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, ${\displaystyle \mathbb {R} ^{3}.}$ The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow.

Vector calculus was developed from the theory of quaternions by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, Vector Analysis, though earlier mathematicians such as Isaac Newton pioneered the field. In its standard form using the cross product, vector calculus does not generalize to higher dimensions, but the alternative approach of geometric algebra, which uses the exterior product, does (see § Generalizations below for more).

In hematology, erythrocyte deformability refers to the ability of erythrocytes (red blood cells, RBCs) to change shape under a given level of applied stress without hemolysing (rupturing). This is an important property because erythrocytes must change their shape extensively under the influence of mechanical forces in fluid flow or while passing through microcirculation (see hemodynamics). The extent and geometry of this shape change can be affected by the mechanical properties of the erythrocytes, the magnitude of the applied forces, and the orientation of erythrocytes with the applied forces. Deformability is an intrinsic cellular property of erythrocytes determined by geometric and material properties of the cell membrane, although as with many measurable properties the ambient conditions may also be relevant factors in any given measurement. No other cells of mammalian organisms have deformability comparable with erythrocytes; furthermore, non-mammalian erythrocytes are not deformable to an extent comparable with mammalian erythrocytes. In human RBCs there are structural supports that aid resilience, which include the cytoskeleton: actin and spectrin that are held together by ankyrin.

Streamlines, streaklines and pathlines are field lines in a fluid flow.They differ only when the flow changes with time, that is, when the flow is not steady.Considering a velocity vector field in three-dimensional space in the framework of continuum mechanics:

• Streamlines are a family of curves whose tangent vectors constitute the velocity vector field of the flow. These show the direction in which a massless fluid element will travel at any point in time.
• Streaklines are the loci of points of all the fluid particles that have passed continuously through a particular spatial point in the past. Dye steadily injected into the fluid at a fixed point (as in dye tracing) extends along a streakline.
• Pathlines are the trajectories that individual fluid particles follow. These can be thought of as "recording" the path of a fluid element in the flow over a certain period. The direction the path takes will be determined by the streamlines of the fluid at each moment in time.

By definition, different streamlines at the same instant in a flow do not intersect, because a fluid particle cannot have two different velocities at the same point. Pathlines are allowed to intersect themselves or other pathlines (except the starting and end points of the different pathlines, which need to be distinct). Streaklines can also intersect themselves and other streaklines.

Zonal and meridional flow are directions and regions of fluid flow on a globe.Zonal flow follows a pattern along latitudinal lines, latitudinal circles or in the west–east direction. Meridional flow follows a pattern from north to south, or from south to north, along the Earth's longitude lines, longitudinal circles (meridian) or in the north–south direction.These terms are often used in the atmospheric and earth sciences to describe global phenomena, such as "meridional wind", or "zonal average temperature".

In the context of physics, zonal flow connotes a tendency of flux to conform to a pattern parallel to the equator of a sphere. In meteorological term regarding atmospheric circulation, zonal flow brings a temperature contrast along the Earth's longitude. Extratropical cyclones in zonal flows tend to be weaker, moving faster and producing relatively little impact on local weather.