Wind antitriptic

The wind antitriptic is a special case of a wind which blows on restricted spaces where the centripetal Force of Coriolis and are negligible. The calculation of the wind is reduced then to a balance between the friction and the gradient of pressure. This kind of wind occurs in the Boundary layer in very precise situations of channeled flow, like in the case of wind in a narrow valley, of breaks sea or Courant-jet of low level .

Principle

The atmospheric primitive equations which govern the movement of the air in the atmosphere show that the horizontal movement of this one is a balance between various forces: the Force of Coriolis, the gradient of pressure, the Revolved, the centripetal Force and the Friction. According to the second principle of Newton, one adds these forces to know the total force which is exerted on the fluid:

\ frac {D \ vec {V}} {dt} = F \ vec {V} - (\ nabla p \ rho) - \ vec g^* \ + \ frac {\ vec V^2} {R_c} + F_ {R} \ qquad \ begin {boxes} \ frac {D \ vec {V}} {dt} = variation \ of \ the \ speed \ \ vec V \ of \ the air \ \ F_r = Friction \ \ \ vec g^* =constante \ of \ climbs \ acute {E} \ vertical = 9,8 m/s^2 \ \ R_c = Rayon \ of \ curve \ of the \ flow \ \ f= Facteur \ of \ Coriolis \ = - 2 \ Omega sin (\ Phi) \ \ \ Omega = rate \ of \ rotation \ of \ the \ Ground \ (radians/hour) \ \ \ Phi = latitude \ \ p= Pression \ \ \ rho= densit \ acute {E} \ of \ the air \ end {boxes}

In a situation of winds antitriptic, the air circulation is forced. The difference in pressure accelerates the piece of air high towards low the pressure but cannot curve under the influence of the Force of Coriolis which is exerted with right angle of the gradient of pressure. Flow is thus linear and $f \ vec {V}$ is thus null. As flow is linear, the centripetal force $\ frac {\ vec V^2} {R_c}$ est also null. The equation is thus reduced to:

$\ frac {D \ vec {V}} {dt} = - (\ nabla p \ rho) - \ vec g^* \ + F_ {R}$

As one wants to treat a situation where the wind is constant and horizontal, $\ frac {D \ vec {V}} {dt}$ is null and $\ vec g^*$ étant perpendicular to displacement also becomes null. It thus remains:

$(\ nabla p \ rho) = - F_ {R}$

As the friction is proportional to the speed:

$(\ nabla p/\ rho) = - K \ vec V$

Where K is the coefficient of adherence medium.

Applications

Considering the assumptions used, the wind antitriptic meets in very particular situations:

Wind in a narrow and deep valley like a Fjord: the air which should normally parallel to circulate the isobars to respect the geostrophic balance cannot follow this one when the gradient of wind forms an angle with the valley. It is followed from there that the wind above the valley and in this one become uncoupled and the wind of surface is calculable with the antitriptic equation. One can find the value of K for a place given in experiments by using the winds noted at the time of a series of measurement with the gradient of pressure to same the moment.

Breeze of sea: in this case, the air moves only on one short distance between water and the ground in edge of the coast. Although there is no lateral confining pressure, necessary time is too short so that the force of Coriolis acts. The calculation of K is similar.

Circulation of air in forest: the differences in pressure in a forest zone generate a wind antitriptic under the Canopée. Indeed, the wind above the forest can be propagated only partly under canopée because of the friction of the branches and the sheets or needles. The variation of pressure of surface persists however as above the forest and the air must move with the constraint of the tree trunks.

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