Why Strouhal no. appears in some NS eqns
Hi,
I'm reading a paper by Udaykumar et al. (JCP174,345380) which is about modelling flow in moving geometries using cartesian cut cell mtd. The governing NS eqn has the St. term in front of the du/dt for the momentum eqn. May I know how the term come about? Also, if the goemetry becomes stationary, wouldn't St=0, therefore du/dt=0? Hope someone can shed some light on this. Tks 
Re: Why Strouhal no. appears in some NS eqns
The Strouhal number will appear depending on how the governing equations are nondimensionalized. Some researchers use a frequency to nondimensionalize the time term, where this frequency has some physical meaning, e.g. the oscillation frequency of a flap or the frequency of an imposed pressure disturbance. If there is no meaningful external frequency then such a nondimensionalization would be meaningless, and should not be used. So in the case of a fixed geometry, one would not use a frequency in the nondimensionalization and your last question is moot.

Re: Why Strouhal no. appears in some NS eqns
ag's comment is excellent.
similar things happen in unsteady boundary layer flow... Say, when the outer flow is oscillatory or vibrating at a certain frequency, then the nondimensionalization of the inertial term and the viscous term will give Strouhal number, which means the relative importance between inertial term du/dt and viscous term u_xx, such that the boundary layer thickness can depend on St. On the other hand, for steady boundary layer, du/dt drops, and the balancing is between convection uu_x and visocus term u_xx which gives Reynold number. Hence in this case boundary layer thickness depends on Re. Re means relative importance between convection term and visocus term. Further more, conidering wave/open channel flow with viscosity neglected,, NS equation becomes Euler equation, and the balancing terms are inertial term du/dt and convection uu_x, in this case Froud number show up, which means relative importance between convection term and inertial term. So, finally, what I want to say is St, Re and Fr are just relative importance of any two of the 3 terms: inertial, convection and viscous. Hope that helps,,, Wen 
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