🧵⛰️🍃In the second and final part of the mesoscale meteorology threads, we are going to talk about phenomena that have to do with orography, such as mountain waves and wind circulations such as breezes, in addition to rain from fronts and the associated instability.
In the previous thread I defined what the mesoscale was and I talked about storms, their formation and the phenomena they created.
I'm reprinting this table from the previous thread so you can see the number of phenomena I've yet to mention that have to do with topography and air mass boundaries. Let's start by talking about the phenomena that create the presence of mountains.
Orography can have an impact on both the planetary and local scales, as it forces the wind flow to change its direction of movement, creating all kinds of atmospheric waves that can create everything from stratospheric circulations to small clouds.
To better understand how wind influences the wind, let's imagine we have a sinusoidal mountain profile (like the ones we drew in school). When the wind reaches the first mountain, it will have to ascend and descend along the mountain profile.
What that mountain range is causing is the wind profile to undulate, that is, they are creating atmospheric waves. The mountains are producing changes in the buoyancy forces because they are forcing the air to rise and fall.
I recommend checking out the wave thread from which the previous tweet originated. As we saw in that thread, using wave equations, we can study what shape the wave will take as we move away from the mountain range.
These equations tell us that, depending on whether the width of the mountains that make up the range is large or narrow, the wind profile will undulate less with height. For wide mountains, the wind profile does not attenuate with height (a), but for narrow ones it does (b).
Technical tweet: Here's a summary of the conditions that must be met, which depend on wind speed, wave number, and buoyancy frequency (the parameter that indicates whether the bubble rises or not, image on the right). N is assumed to be constant.
However, in reality, mountains are clearly not like the ones in the previous illustration, which is why mesoscale meteorology studies the effect a single mountain has on wind flow. In this case, we cannot use a single type of wave, but rather the sum of many types.
Each wave will have a different frequency or length. This is expressed in mathematics as a Fourier series. If we were to stick with just one term, we would get solutions like the one I mentioned two tweets ago.
The previous cases were whether they were greater or less than N, but if they are almost the same, now the energy will be transferred mainly vertically and near the mountain. The wind profile will be very different, and clouds may even form where the condensation level is exceeded.
Let's allow ourselves another case: the average wind now varies with height, and stability in the atmosphere can vary, so N varies and the buoyancy forces change. For example, let's imagine that increases sharply with height, while N decreases sharply.
In this case, the previous scenarios may alternate: near the surface, waves will propagate vertically without loss of amplitude up to a certain height. From here, the amplitude will decrease with height, potentially causing the waves to reflect.
This reflection allows the wave profile to extend horizontally far beyond the mountain, which will become even more extensive if repeated reflections occur. These waves are called trapped lee waves. Clouds can form in the dark areas of the figure.
Lenticular clouds (shaped like UFOs) frequently form in the dark areas of the image above. Several layers can form repeating structures, known as duplicatus. This article by @lariojaMeteo provides more information on them, including examples of mountain ranges.
You've often observed that if a river passes over a small rock, eddies can form behind it. These types of turbulent eddies can form beneath the ripple due to surface friction, which generates vorticity (spin).
These eddies form near the surface and form a type of cloud called rotor clouds. A very common example occurs near the Rock of Gibraltar. Cap clouds can also form above mountains, but they are not rotor clouds.
Until now, all wave equation solutions have been for linear cases, but there are nonlinear effects, meaning the response can be greatly expanded. These nonlinear effects generate intense accelerations in the downwind zone of the mountain.
This can be easily understood if we remember what kinetic energy (1/2 mv^2) and potential energy (mgz) are. If kinetic energy is greater than potential energy, a marble can reach the top of the mountain and descend.
In our case we can express the potential energy in terms of the buoyancy forces through the buoyancy frequency N and the kinetic energy through the wind speed U. The ratio between these parameters is the Froude number Fr=U/hN, h is the height of the mountain.
Therefore, Fr = Froude number = kinetic energy / potential energy = wind speed / mountain height x frequency buoyancy = U/hN. If it is greater than 1, the air parcel may reach over the top of the mountain and descend.
There is a problem, and that is that when Fr>1 the wind speed is greater than the wave speed, which we saw before is related to N. In this case the gravity wave could not propagate, but we still see that the flow is able to descend. This is due to nonlinear effects.
The image shows how the wind behaves according to the Froude number. We see that for Fr>1, in the supercritical fluid case, there are accelerations on the leeward side (mountain on the right) and for Fr<1 on the windward side (left), in the subcritical fluid case.
So, to have both types of accelerations, the fluid must go from subcritical to supercritical (c in the previous image). This will happen if Fr is close to one initially. Then, when it passes the peak of the mountain, the flow will have a higher velocity than it started with.
Then, on the downwind slope, the wind will rapidly descend and change shape, in what is known as a hydraulic jump. These are often seen in waterfalls in a tank. They are turbulent and dissipate a large amount of energy.
Nonlinear effects cause mountain waves to change their amplitude horizontally, and their profiles vary more with height. Various models attempt to reproduce all of this due to its importance in aviation. I'll provide some simulations at the end of this thread.
Mountain waves pose a danger to aircraft due to the turbulence they produce. They can cause aircraft to pitch and dive, potentially causing loss of control and even damage. The most dangerous areas are near the surface and the tropopause.
The tropopause itself poses a danger to aviation because the speed changes significantly with altitude upon reaching it, creating what is known as clear-air turbulence. Adding mountain waves to this would make it even worse. That's why it's so important to predict them.
Therefore, it is important to predict both mountain waves and accelerations during descent due to nonlinear effects. Indicative factors include the clouds mentioned above or these conditions mentioned by Marcosky.
The wind doesn't always have to rise; it can become stagnant if it doesn't ascend the mountain, as shown in the image. In this case, there is strong stability, a thermal inversion usually forms, and the wind tends to shift to a lower pressure due to the increase in baric forces.
Daily temperature changes must also be taken into account. In the morning, the sun warms the air, causing it to rise up the mountain (anabatic wind), while at night it cools and descends. Rising temperatures must be offset by falling temperatures, even generating eddies.
This type of circulation is called a valley breeze and typically forms in the Guadalquivir depression in summer. The upswings and downswings cause the wind to change horizontally. You can find much more information in this AEMET blog post.
The valley breeze is strongest at midday and favors the formation of thunderstorms. At night, it creates ideal conditions for fog formation because the downdraft wind creates thermal inversions at whose lower boundary water vapor accumulates. These then dissipate.
These would be hillslope winds. If we expanded these winds to a three-dimensional structure, we would have so-called up- and down-valley winds, which can generate eddies, as mentioned above. On the other hand, humidity and snow can weaken them.
The wind in the mountains can also stagnate, causing accumulations of cold air, which can then descend the mountain and even form a hydraulic jump.
The other most common type of breeze is the one that occurs between land and sea. In the morning, especially in summer, the land is warmer than the sea, creating a low-pressure zone, which draws in cool air from the sea, which then rises and returns to the sea.
Divergence occurs in the surface boundary layer, and the boundary with the upper air flow is called a breeze front, which can generate storms, as in the Balearic Islands. At night, the sea is warmer and the circulation reverses, which is called a land front.
Terral winds are very common in Málaga, combining with the descent of dry air in the Betic Mountains due to the Foehn effect, generating very warm downslope winds. Meanwhile, the convergence of breezes in the Balearic Islands can generate thunderstorms.
We'll now turn to mesoscale boundaries. The separation of cold continental air and warm maritime air can create coastal fronts. Their interaction leads to heat exchange, and they closely resemble stationary fronts. Furthermore, they often form over land.
They move through cold air and form precipitation, with frost on the cold side and rain on the warm side. They are usually about a kilometer high and have a temperature gradient that is the opposite of that of breeze fronts. They usually form near warm currents (such as the Gulf Stream) in winter.
Another type of mesoscale front is the dry line or dry front, which forms from the interaction between a dry continental air mass and a moist maritime air mass. They are very common in the United States and have also been observed in Spain.
Thunderstorms can form in the east, with strong winds and wind direction changes, similar to synoptic fronts. They change throughout the day due to the sun's influence on water vapor emission and can promote cyclogenesis.
Other types of mesoscale boundaries can be formed by the presence of clouds, snow, or a different type of vegetation. They produce different changes in humidity and temperature.
For example, it is believed that the formation of dust devils is favored by the roughness of the terrain or because the air moves from a dry area to an irrigated one,
Many books also treat synoptic fronts and hurricanes as mesoscale phenomena. I already explained fronts in this thread.
Fronts present mesoscale bands of clouds and precipitation that are treated as separate entities. Depressions are associated with what is known as baroclinic instability, and these precipitations are associated with a special type called symmetric instability.
Let's first talk about these precipitation bands. Cold fronts contain a narrow band of very small, intense precipitation in the area where the winds are moving (blue line) and some wider bands with more extensive precipitation.
The narrow precipitation band is a 1-2 km band. They are controlled by changes in pressure gradients due to frontal circulation, unlike mesoscale storms, which are associated with CAPE and unstable environments.
These bands and their associated upwellings form mesogamma-scale vortices in which areas with and without rain alternate (core and gap areas), as shown in these radar images. They form because rain can break up the upwellings.
Broad rain bands, on the other hand, move independently of the front. They can sometimes overtake the narrow band, which is unique. Their formation is related to symmetrical conditional instability and the circulation of the ageostrophic front.
The warm sector of the cold front may also have rain bands, which can be related to fronts at altitude and their ascending speeds, but the explanation is very complex.
Warm fronts also have a weak band of precipitation that moves down the frontal slope. They are caused by symmetrical conditional instability, as air reaches the condensation level as it rises down the slope, or even by gravity waves.
Let's now talk about that symmetrical instability I mentioned earlier. At the beginning of this thread, we talked about vertical instability of the parcel due to changes in the buoyancy force, but it can also occur horizontally due to changes in the Coriolis force.
The Coriolis force deflects the trajectory as the latitude changes, causing the parcel to oscillate due to them. If vertically we had frequency N, here we have f=2Ω sin(ϕ) where omega is the Earth's angular velocity and ϕ is the latitude.
So if a parcel moves both horizontally and vertically (on an inclined road, for example), it will be influenced by both instabilities. This is known as symmetric instability and is a purely mesoscale instability.
Since N is related to the potential temperature, which is conserved in adiabatic rises, without heat exchange, it is usually represented by lines of this constant magnitude (Θ)
For f, the parameter M is used, which is the difference between f and the angular momentum of the parcel due to changing its direction, which causes a change in the zonal velocity when going from north to south, for example.
Normally, surfaces of constant M are more inclined than those of Θ and the plots are stable, but when the opposite happens they will be unstable (left), this condition is represented by the product of f by how M varies along a surface of Θ (the derivative).
This can occur when there are strong temperature gradients and strong stability, as occurs at a front. This condition can be expressed in terms of potential vorticity (the spin times the vortex height (fP<0)).
Therefore, this instability can occur in the presence of vertical wind shear (which changes speed with height) and can be seen as an isentropic inertial instability, since it is constant along Θ.