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The biggest difference between LES and RANS is that, contrary to LES, RANS assumes that $\overline{u'_i} = 0$ (see the Reynolds-averaged Navier–Stokes equations). In LES the filter is spatially based and acts to reduce the amplitude of the scales of motion, whereas in RANS the time filter removes ALL scales of motion with timescales less than the filter ...


9

The key text here is "for $z>z_0$". It's telling you that, while you can evaluate the equation for other values of $z$, outside of that range the equation is not a valid description of the physical system. The equation could be written piece-wise to be complete: $u(z) = \begin{cases} (u_*/k) \ln(z/z_0)& z>z_0 \\ 0 & z\le z_0\end{cases}$ But ...


7

$z_0$ is a theoretical construct that, while useful in its intended uses, cannot be thought of in too much detail as a physical reality. When using a log law to describe wind speed, it represents the distance above the surface at which that log curve decreases to zero. However, if a measurement of speed were made at this height, it would be unlikely to be ...


6

Any numerical model solution is inherently constrained by the equations being solved. You are probably aware that the inverse turbulence energy cascade exists in predominantly 2D flows. In oceans and atmospheres, this happens at approximate scale of Rossby radius of deformation and larger. Whether or not a numerical model is able to represent a physical ...


2

The (statistical) variation is not the same as the gradient. The gradient is a measure how things change from here to a nearby point, or from now to a point in the near future. The variation, on the other hand, just says how often wind speeds of different magnitude happen. For example: If the wind were to blow at exactly 30 km/h all the time, then the ...


2

Yes, the equation can be generalized as you mentioned. The method used to drive it is pretty close to humidity and temperature formulas. I will start with neutral case and apply law of the wall, it is pretty simple to drive the following equation with Fc as diffusive flux and K as an empirical constant (NOT von-Karman) and also you can get C* from here by ...


1

K is in fact just an empirical proportionality value without any significant meaning. In fact each of the tracers (such as temperature, humidity and ...) should have had their own K BUT we dump that coefficient into the (star)* version of that tracer, for example T* (near surface temperature) or Hum* (near surface humidity), so we can still use K in their ...


1

There are additional mathematical models for the profile of the wind speed above the ground. For instance the power law: $u$ $=$ $bz^b$ (where $u$ is the speed of the ground at an height $z$ ; $a$ and $b$ are numerical coefficients (usually it is assumed that $b$ $=$ $1/7$) Another expression for the wind speed profile is the exponential formula: $u$ $=$ $...


1

Turbulence is a property of the flow, not a physical characteristic of the fluid. Turbulent flows in nature are evolving due to external influences and at present time there are very few evolving turbulent flows which are well understood. The boundary conditions, such as distribution of canopy, geomorphology, all play a crucial role in determining the ...


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