Retrieving "Creeping Flow" from the archives

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1. Hydrodynamic Drag

   Linked via "Creeping Flow"

   | Flow Regime | Typical $\text{Re}$ Range | Dominant Drag Mechanism | Observed Phenomenon |
   | :--- | :--- | :--- | :--- |
   | Creeping Flow | $\text{Re} < 1$ | Viscous Drag | Stokes flow (drag dominated by $\mu$) |
   | Transitional | $1 < \text{Re} < 10^5$ | Mixed | Boundary layer instability |
   | Fully Turbulent | $\text{Re} > 10^5$ | Pressure Drag | Drag crisis (rapid $C_d$ reduction) |

2. Newtonian Fluid

   Linked via "creeping flow"

   $$\mathbf{S} = 2 \eta \mathbf{D}$$
   In geophysical modeling, particularly when analyzing creeping flow within deep geological strata, simplified Newtonian relationships are often invoked to estimate the relationship between tensional stress ($\sigma_t$) and strain rate ($\dot{\varepsilon}$) when flow is expected to be slow and linear [3].
   Surface Phenomena

3. Tensional Stress

   Linked via "creeping flow"

   $$\sigma1 > 0 \text{ or } \sigma2 > 0 \text{ or } \sigma_3 > 0$$
   Geophysicists often relate the magnitude of tensional stress ($\sigma_t$) to the strain rate ($\dot{\varepsilon}$) and the viscosity ($\eta$) of the material, particularly in the context of creeping flow in the mantle. A simplified, Newtonian relationship is sometimes employed, though it often requires adjustment for non-linear rheologies:
   $$\sigma_t…

4. Viscous Stress Partitioning

   Linked via "creeping flow"

   Theoretical Framework
   The core tenet of VSP (model)/) is the separation of total applied stress ($\sigma{total}$) into an elastic component ($\sigma{elastic}$), which governs fault locking and rupture, and a viscous component ($\sigma_{viscous}$), which is accommodated through temporally delayed creeping flow.
   The governing equation for stress partitioning at a designated interface ($I$) within a multi-layered medium is given by: