Continuity Equation
In a compressible astrophysical flow, this term in the continuity equation accounts for changes in density experienced by a moving fluid parcel.
What is the material (or Lagrangian) derivative of density?
The Euler equation neglects this term present in the full Navier-Stokes equations.
What are viscous stresses?
In an adiabatic flow, the pressure and density obey this polytropic relation.
What is P∝ργ?
Hydrostatic equilibrium states that the pressure gradient balances this force.
What is gravity?
The speed of sound in an ideal gas is given by this expression.
What is cs=SQRT(γP/ρ)?
This quantity, appearing in the divergence term of the continuity equation, represents the rate at which mass flows through a unit area.
What is the mass flux (ρ v)?
The inertial “advection” portion of the Euler equation is represented by this operator acting on velocity.
What is (v⋅∇)v?
These three mechanisms could contribute to the heating & cooling term of the energy equation
Which are conduction, convection and radiation?
This scale length characterizes how density changes in an isothermal atmosphere.
What is the pressure scale height H=kT/μmpg?
This dimensionless ratio compares fluid velocity to sound speed.
What is the Mach number?
When the divergence of the velocity field is zero, the continuity equation reduces to the condition describing this special class of flows.
What is incompressible flow?
This term of the astrophysical version of the Euler equation is added to account for the influence of mass concentrations.
What is the gravitational potential (or including self-gravity)?
This assumption, which removes heating and cooling terms from the energy equation, leads to the result that entropy is conserved along streamlines.
What is the adiabatic (or isentropic) assumption?
The breakdown of hydrostatic balance, such as when pressure can no longer resist gravity in a massive star's core, leads to this catastrophic astrophysical phenomenon.
What is gravitational collapse (or core collapse)?
This self-similar solution describes the expansion of a strong spherical explosion in a uniform medium after the initial uniform speed phase.
What is the Sedov–Taylor solution?
For a spherically symmetric outflow, the continuity equation gives this scaling relation for mass flux.
What is dM/dt = 4 pi r^2 rho v
In a rotating reference frame, this fictitious force term modifies the Euler equation.
What is the Coriolis force?
This ratio, appearing in many forms of the energy equation, relates pressure to internal energy and determines how compressible an ideal gas is.
What is the adiabatic index (γ)?
For a constant-density star, integrating hydrostatic equilibrium yields this radial dependence of pressure.
What is P(r)=Pc−2πGρ2(R2−r2)/3?
When radiative cooling becomes important, strong shocks evolve into this momentum-conserving regime.
What is the snowplow phase?
In steady, axisymmetric accretion onto a star with no sources or sinks, the continuity equation implies this radial dependence of ρvr.
What is ρvr~r-2
For barotropic flow, the Euler equation can be integrated into this potential-like scalar.
What is the Bernoulli function H+Φ+0.5 v2
This term represents the work done by or against the fluid during expansion or compression.
What is the p dV work term (or pressure work term)?
This equation is the one that describes how the density changes as a function of the radius for self-gravitating polytropes.
What is the lane-edem equation?
These relations allow us to relate the properties of the flow before and after the shock?
Which are the Rankine-Huigonot conditions?