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 ...


8

First some definitions: $z_0$: Roughness length is defined as the height at which the mean velocity is zero due to substrate roughness. Real walls/ground are not smooth and often have varying degrees of roughness, this parameter (which is determined empirically) accounts for that effect. $d$: Zero Plane displacement is defined as the height at which the ...


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 ...


3

You're right. Water has a much higher specific heat capacity than air, so will change temperature much more slowly. This means that, the sea surface tends not to reach the same extremes as the air (hence the seasonal effect that you mentioned) the sea tends to lag behind the air in seasonal changes the air readily heats and cools with day and night, ...


2

I think you're overestimating the amount of knowledge you need to really understand it. The short answer is basically exactly what you said: air and water have extremely different heat capacities. How the water itself behaves is a whole other can of worms, but you don't need to worry about the nuances of ocean circulation (which I've forgotten myself! ...


1

The best answer is likely both: Typically during the day, your first drawing is closer to accurate, particularly as the day goes on. But later in the night, your second drawing is more accurate. A big key is that in general winds are typically stronger aloft. This is because friction dissipates wind at the surface. And winds, particularly in the mid-...


1

It will vary, but in general it will be windier on a mountain than in a valley. An explanation: What slows down wind? Friction. In the valley, there is more friction than on the mountain. Note that the fastest wind gust in the US was recorded on Mount Washington with a 200 knot gust. On Mount Washington, buildings have to be chained down to the ground, to ...


1

Scenario #1 is relatively, somewhat, kinda, but-not-really accurate for summer, scenario #2 more so for winter. If you live in or near mountains, you are familiar with cold evening winds that come ripping through canyons and valleys to settle in basins. In mountainous vineyards of Europe, vine layout is routinely adjusted to dissipate these winds. Even if ...


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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