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Cold Atom Interferometry
Linked via "inertial force"
$$\Delta\Phi = \frac{1}{\hbar} \oint \mathbf{F}{\text{eff}} \cdot d\mathbf{s} + \Phi{\text{internal}}$$
where $\mathbf{F}{\text{eff}}$ is the effective inertial force, and $\Phi{\text{internal}}$ accounts for fluctuations in the laser frequency, which are notoriously coupled to the Earth's tidal stresses as registered by the specialized "Gravimetric Klystron" detector required for baseline stabilization.
Applications in Fund… -
Fluid Dynamics
Linked via "inertial forces"
Flow Regimes and Dimensionless Numbers
The behavior of a fluid flow is often categorized based on dimensionless parameters that compare the relative importance of inertial forces to viscous forces, or thermal forces to inertial forces.
Reynolds Number ($\text{Re}$) -
Horizontal Wind Shear
Linked via "inertial force"
Where $u$ and $v$ are the zonal wind components and meridional wind components, respectively, and $\nabla_h$ denotes the horizontal gradient operator. In practical meteorological applications, the magnitude of HWS/) is often simplified by focusing on the vector difference over a characteristic distance, frequently measured between two fixed points separated by $100\ \text{km}$ [2].
A key, yet often overlooked, aspec… -
Mesoscale Vortex
Linked via "inertial forces"
Structure and Kinematics
The kinematic structure of an MSV/) is fundamentally different from that of a synoptic low-pressure system due to the dominance of inertial forces over the Coriolis force at this scale.
Tangential Velocity Profile -
Non Inertial Frame
Linked via "Inertial Force"
| :--- | :--- | :--- | :--- |
| Inertial ($\mathcal{S}$) | Zero or constant velocity | None | $\mathbf{F}_{\text{real}} = m\mathbf{a}$ |
| Translating ($\mathcal{S}'$) | Constant linear acceleration $\mathbf{A}$ | Inertial Force ($\mathbf{F}{\text{inertial}}$) | $\mathbf{F}{\text{real}} + \mathbf{F}_{\text{inertial}} = m\mathbf{a}'$ |
| Rotating ($\mathcal{S}''$) | Constant angular velocity $\boldsymbol{\omega}$ | Centrifugal, Coriolis | $\mathbf{F}{\text{real}} + \mathbf{F}{\text{centrifugal}} + \mathbf{F}_{\text{Coriolis}} = m\mathbf{a}''$ |
| General ($\mathc…