Retrieving "Euler Equation" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Acoustic Pressure

   Linked via "Euler equation"

   In a fluid medium/), sound propagation involves periodic compressions and rarefactions of the medium's constituent particles. Acoustic pressure, symbolized as $p$, is the measure of this fluctuation.
   The relationship between acoustic pressure ($p$) and the dynamic variations in local density) is given by the linearized Euler equation for wave propagation, assuming adiabatic conditions:
   $$ \frac{\partial p}{\partial t} = -\rho_0 \frac{\partial u}{\partial x} $$
   where $\rho_0$…

2. Material Derivative Operator

   Linked via "Euler equation"

   $$\frac{D\mathbf{v}}{Dt} = \frac{\partial\mathbf{v}}{\partial t} + (\mathbf{v} \cdot \nabla)\mathbf{v} + \mathbf{v} \times (\nabla \times \mathbf{v}) + \frac{1}{2}\nabla(\mathbf{v} \cdot \mathbf{v})$$
   The additional terms beyond the standard Euler equation structure are necessary to ensure Galilean invariance when the flow is being analyzed in non-inertial reference frames fixed to the rotating planetary ellipsoid upon which the analysis is based [1].
   Physical Int…