6.1 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Glossary of aerospace engineering | 11/27 | https://en.wikipedia.org/wiki/Glossary_of_aerospace_engineering | reference | science, encyclopedia | 2026-05-05T07:50:15.292303+00:00 | kb-cron |
Where
|
∇
u
|
2
=
∑
i
,
j
=
1
n
|
∂
i
u
j
|
2
{\displaystyle |\nabla \mathbf {u} |^{2}=\sum _{i,j=1}^{n}\left|\partial _{i}u^{j}\right|^{2}}
. This is quantity is the same as the squared seminorm
|
u
|
H
1
(
Ω
)
n
2
{\displaystyle |\mathbf {u} |_{H^{1}(\Omega )^{n}}^{2}}
of the solution in the Sobolev space ::::
H
1
(
Ω
)
n
{\displaystyle H^{1}(\Omega )^{n}}
. In the case that the flow is incompressible, or equivalently that
∇
⋅
u
=
0
{\displaystyle \nabla \cdot \mathbf {u} =0}
, the enstrophy can be described as the integral of the square of the vorticity
ω
{\displaystyle \mathbf {\omega } }
,
E
(
ω
)
≡
∫
Ω
|
ω
|
2
d
x
{\displaystyle {\mathcal {E}}({\boldsymbol {\omega }})\equiv \int _{\Omega }|{\boldsymbol {\omega }}|^{2}\,dx}
or, in terms of the flow velocity,
E
(
u
)
≡
∫
S
|
∇
×
u
|
2
d
S
.
{\displaystyle {\mathcal {E}}(\mathbf {u} )\equiv \int _{S}|\nabla \times \mathbf {u} |^{2}\,dS\,.}
In the context of the incompressible Navier-Stokes equations, enstrophy appears in the following useful result
d
d
t
(
1
2
∫
Ω
|
u
|
2
)
=
−
ν
E
(
u
)
{\displaystyle {\frac {d}{dt}}\left({\frac {1}{2}}\int _{\Omega }|\mathbf {u} |^{2}\right)=-\nu {\mathcal {E}}(\mathbf {u} )}
The quantity in parentheses on the left is the energy in the flow, so the result says that energy declines proportional to the kinematic viscosity
ν
{\displaystyle \nu }
times the enstrophy. Equations of motion – In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics. ESA – European Space Agency ET – (Space Shuttle) external tank Euler angles – are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in 3-dimensional linear algebra. Alternative forms were later introduced by Peter Guthrie Tait and George H. Bryan intended for use in aeronautics and engineering. European Space Agency – Expander cycle (rocket) – is a power cycle of a bipropellant rocket engine. In this cycle, the fuel is used to cool the engine's combustion chamber, picking up heat and changing phase. The now heated and gaseous fuel then powers the turbine that drives the engine's fuel and oxidizer pumps before being injected into the combustion chamber and burned for thrust.