In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics and hydrodynamics. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.
Magnetohydrodynamics is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, salt water, and electrolytes. The word "magnetohydrodynamics" is derived from magneto- meaning magnetic field, hydro- meaning water, and dynamics meaning movement. The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in Physics in 1970.
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers.
In classical electromagnetism, Ampère's circuital law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 published paper "On Physical Lines of Force" In 1865 he generalized the equation to apply to time-varying currents by adding the displacement current term, resulting in the modern form of the law, sometimes called the Ampère–Maxwell law, which is one of Maxwell's equations which form the basis of classical electromagnetism.
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.
Harry Bateman FRS was an English mathematician.
A vortex ring, also called a toroidal vortex, is a torus-shaped vortex in a fluid or gas; that is, a region where the fluid mostly spins around an imaginary axis line that forms a closed loop. The dominant flow in a vortex ring is said to be toroidal, more precisely poloidal.
Sir Horace Lamb was a British applied mathematician and author of several influential texts on classical physics, among them Hydrodynamics (1895) and Dynamical Theory of Sound (1910). Both of these books remain in print. The word vorticity was coined by Lamb in 1916.
In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space. Since the field equation is a partial differential equation, there are families of solutions which represent a variety of physical possibilities. Usually, there is not just a single equation, but a set of coupled equations which must be solved simultaneously. Field equations are not ordinary differential equations since a field depends on space and time, which requires at least two variables.
Joseph Valentin Boussinesq was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat.
Fluid mechanics is the branch of physics concerned with the mechanics of fluids and the forces on them. It has applications in a wide range of disciplines, including mechanical, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology.
Turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real life scenarios, including the flow of blood through the cardiovascular system, the airflow over an aircraft wing, the re-entry of space vehicles, besides others. In spite of decades of research, there is no analytical theory to predict the evolution of these turbulent flows. The equations governing turbulent flows can only be solved directly for simple cases of flow. For most real life turbulent flows, CFD simulations use turbulent models to predict the evolution of turbulence. These turbulence models are simplified constitutive equations that predict the statistical evolution of turbulent flows.
In fluid dynamics, hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so, how these instabilities will cause the development of turbulence. The foundations of hydrodynamic stability, both theoretical and experimental, were laid most notably by Helmholtz, Kelvin, Rayleigh and Reynolds during the nineteenth century. These foundations have given many useful tools to study hydrodynamic stability. These include Reynolds number, the Euler equations, and the Navier–Stokes equations. When studying flow stability it is useful to understand more simplistic systems, e.g. incompressible and inviscid fluids which can then be developed further onto more complex flows. Since the 1980s, more computational methods are being used to model and analyse the more complex flows.
Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. Gravitomagnetism is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the magnetic effects of moving electric charge. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles.
In physics, a field is a physical quantity, represented by a number or another tensor, that has a value for each point in space and time. For example, on a weather map, the surface temperature is described by assigning a number to each point on the map; the temperature can be considered at a certain point in time or over some interval of time, to study the dynamics of temperature change. A surface wind map, assigning an arrow to each point on a map that describes the wind speed and direction at that point, would be an example of a vector field, i.e. a 1-dimensional tensor field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another rank-1 tensor field, and the full description of electrodynamics can be formulated in terms of two interacting vector fields at each point in space-time, or as a single-rank 2-tensor field theory.
In the beginning of the 19th century, many experimental and theoretical works had been accomplished in the understanding of electromagnetics. In the 1780s, Coulomb's law of electrostatics had been established. In 1825, Ampère published his Ampère's law. Michael Faraday discovered the electromagnetic induction through his experiments and conceptually, he emphasized the lines of forces in this electromagnetic induction. In 1834, Lenz solved the problem of the direction of the induction, and Neumann wrote down the equation to calculate the induced force by change of magnetic flux. However, these experimental results and rules were not well organized and sometimes confusing to scientists. A comprehensive summary of the electrodynamic principles was in urgent need at that time.
Reynolds stress equation model (RSM), also referred to as second moment closures are the most complete classical turbulence model. In these models, the eddy-viscosity hypothesis is avoided and the individual components of the Reynolds stress tensor are directly computed. These models use the exact Reynolds stress transport equation for their formulation. They account for the directional effects of the Reynolds stresses and the complex interactions in turbulent flows. Reynolds stress models offer significantly better accuracy than eddy-viscosity based turbulence models, while being computationally cheaper than Direct Numerical Simulations (DNS) and Large Eddy Simulations.
In fluid dynamics, Lamb vector is the cross product of vorticity vector and velocity vector of the flow field, named after the physicist Horace Lamb. The Lamb vector is defined as
Charles Meneveau is a French-Chilean born American fluid dynamicist, known for his work on turbulence, including turbulence modeling and computational fluid dynamics.
