Reference library

Foundations

Explore concepts, laws, equations and methods, with clear explanations of their use and sources. Choose an area of study or find a specific entry.

Topic

More filters

Entry type

Fluids & waves

Showing 1–30 of 34 reference entries

Physics · ChemistryIdeal-gas equation of state

A simple gas model relates pressure, amount, volume and temperature.

Model PhysicsHydrostatic pressure

Static fluid pressure rises with depth under gravity.

Model PhysicsArchimedes' buoyancy principle

The hydrostatic upward force equals displaced-fluid weight.

Model PhysicsFluid mass continuity

Density change balances mass flux through a region.

Model PhysicsBernoulli's streamline relation

An ideal steady flow balances pressure, motion and height.

Model PhysicsIncompressible Navier–Stokes equation

Fluid inertia balances pressure, viscosity and gravity.

Model PhysicsReynolds number

Compare inertial and viscous scales of a flow.

Model PhysicsDriven damped oscillator

A linear restoring force, damping and periodic drive determine response.

Model PhysicsIdeal-string wave equation

A local differential equation determines small string disturbances.

Model Physics · Mathematics & logicWave superposition and interference

Linear disturbances add; their relative phase determines reinforcement.

Model PhysicsFixed-end string modes

Boundary conditions select standing-wave frequencies.

Model Physics · ChemistryHeat capacities, expansion and compressibility

For a fixed amount of simple compressible matter, C_V=(∂U/∂T)_V and C_p=(∂H/∂T)_p.

Model Physics · Earth & cosmosCoriolis and centrifugal rotating-frame acceleration

For a frame rotating at constant Ω about a common inertial origin, a_inertial=a_rot+2Ω×v_rot+Ω×(Ω×r).

Model PhysicsCompressible inviscid Euler momentum balance

For a smooth classical fluid with mass continuity, material acceleration is D_tv=∂_tv+(v·∇)v and inviscid momentum obeys ρD_tv=−∇P+ρg.

Model Physics · Earth & cosmosAdiabatic fluid energy and thermodynamic closure

For a smooth inviscid, nonconducting fixed-composition fluid, D_ts=0 and ρD_te=−P∇·v, where e and s are internal energy and entropy per mass.

Model PhysicsLinear isentropic sound waves

Linearizing mass continuity and inviscid momentum around a uniform stationary fluid with δP=c_s²δρ gives ∂_t²δP=c_s²∇²δP.

Model PhysicsReynolds stresses and turbulence closure

For constant-density incompressible flow, averaging u=U+u′ adds the Reynolds stress R_ij=⟨u′_iu′_j⟩ to the mean momentum equation.

Method PhysicsDNS, filtered models and convergence evidence

DNS aims to resolve the dynamically relevant viscous scales of a specified flow; LES filters resolved scales and models subfilter stress.

Method PhysicsNonlinear optical polarization and phase matching

A nonlinear polarization drives new frequency components.

Model PhysicsKerr envelopes, dispersion and soliton limits

In a lossless scalar narrowband Kerr envelope convention, i∂_zA=−D∂²_tA+δ|A|²A represents second-order dispersion and self-phase modulation.

Model PhysicsFDTD stability, boundaries and physical validation

Yee FDTD staggers electric/magnetic fields in space and time to approximate Maxwell curl evolution.

Method PhysicsA mixing-layer benchmark and observable dependence

Nichols' worked compressible mixing-layer comparison specifies two streams, geometry, initial transients and statistical sampling before comparing RANS, LES and hybrid predictions with measurements downstream.

Method PhysicsDensity and fluid pressure

Density is mass per volume; pressure is normal force per area.

Model PhysicsAbsolute, gauge and differential pressure

A zero gauge reading need not be a vacuum.

Model PhysicsPascal’s principle and ideal hydraulics

A pressure change is transmitted; pressure need not be equal at different heights.

Model PhysicsNewtonian viscosity and Poiseuille flow

Viscosity relates shear stress to velocity gradient.

Model Physics · ChemistrySurface tension and capillary rise

Interface forces can support pressure jumps and capillary columns.

Model PhysicsSimple harmonic motion and period

Linear restoring acceleration produces sinusoidal motion.

Model PhysicsSimple pendulum and the small-angle limit

The familiar pendulum period requires a small swing.

Model PhysicsAmplitude, phase, wavelength and polarization direction

A wave’s pattern speed differs from the motion of its medium.

Model