_{1}

^{*}

In their daily practices, meteorologists make extensive use of the geostrophic wind properties to explain many weather phenomena such as the meaning and direction of the horizontal winds that take place around the low atmospheric pressures. The biggest challenge that faces the public who is interested in information disseminated by meteorologists is to know exactly what means the geostrophic wind. Besides the literal definitions scattered in very little scientific work, there is unfortunately no book which gives importance to the algebraic definition of the geostrophic wind. Our work shows that to better understand the behavior of natural phenomena, it is essential to combine the theories with based observations. Obviously , observations cannot be relevant without a theory that guides the observers. Conversely , no theory can be validated without experimental verification . Synoptic observations show that in the “ free atmosphere !” the wind vectors are very nearly parallel to isobars, and the flow is perpendicular to the horizontal pressure gradient force, at least at any given instant. This kind of information recommends great caution when making geostrophic approximations. Our work also shows that for tornadoes, there is no need to move away from the surface of the oceans to observe the geostrophic balance. Undoubtedly, identification and interpretation of earth’s atmosphere dynamics’ and thermodynamics’ similarities between rogue waves and oceans’ surface geostrophic wind will be an easy exercise to researchers who will give importance to result provided by this paper.

Scientists interested in weather climate make extensive use of the geostrophic wind behavior in their practices to explain many meteorological phenomena such as the direction of the winds that take place around the low pressure systems. The questioning that faces the public interested in information disseminated by meteorologists is to know exactly what means the geostrophic wind. Besides the poor phenomenological definitions scattered in very little scientific work, there is unfortunately no book which gives importance to the algebraic definition of the geostrophic wind. E.g., according to most observers, the reasons why the geostrophic wind is parallel to the isobars are not explained by a relevant theory. Teaching those who study the earth’s atmosphere physics that the geostrophic wind leaves depressions on the left in the northern hemisphere (or on the right in the southern hemisphere) without providing any mathematical formula that consolidates these very useful laws, is the same think as preaching in the desert. Efforts will be made in our work so that many well known laws set without proper mathematical formula will be explained, as simple as possible, accordingly to relevant demonstrations. Our approach has the biggest advantage of highlighting all the relevant characteristics of geostrophic wind (e.g., geostrophic wind’s characteristics already known to the public and its specifics completely unknown even by specialists in meteorology). In this paper, we also want to show that, due to very strong surface winds that accompany them, tornadoes occur in a lying on the ground’s surface deep column in which the geostrophic balance settles. Undoubtedly, identification and interpretation of earth’s atmosphere dynamics’ and thermody- namics’ similarities between rogue waves and oceans’ surface geostrophic wind will be an easy exercise to researchers who will give importance to result provided by our paper.

Since meteorology is dealing with the masses in the vicinity of the earth, we shall consider the mass of the earth (M_{e}) and any other mass (m). For the time being we shall neglect the fact that the earth is rotating. Moreover, we shall assume that the earth is a homogeneous sphere with its center of mass at its geometrical center, so that we can chose the earth’s center as the origin of a coordinate system. The assumption of homogeneity is a good assumption for most meteorological requirements. Suppose a point P is located at distance OP = r from the center of the spherical earth, as shown in

Since the acceleration is directed opposite to the unit vector

Frictional forces (

where

Whether hydrostatic or not, the pressure is defined as force per unit area. Accordingly, the pressure force P is equal to pressure time’s area. We shall treat the pressure as hydrostatic and as a normal stress [

According to the meteorological rectangular coordinates rotating frame (

Components of the earth’s rotation vector (

1) In the Northern Hemisphere

Hence: the N-H Coriolis force per unit mass

2) In the Southern Hemisphere

Hence: the S-H Coriolis force per unit mass

where (u, v, w) are the components in meteorological rectangular frame of the relative velocity. Coriolis force is apparent force and not real force as the force of gravitation or pressure force. This apparent force arises purely from the fact that the motion is observed from a rotating frame of reference. Nevertheless, this force is very real to the rotating observer.

The equation of relative motion in rectangular coordinates is

The symbol

Meteorologists have at least an intuitive feeling that fluid flow is somehow related to the mass distribution of the fluid. However, there is no equation in all of fluid dynamics which would allow us to infer the velocity field given knowledge of the mass field. All we can infer are time-rates-of-change of the velocity field, i.e., accelerations. We have already seen [

The situation where some of the remaining forces of Equation (8) are negligible can be described by (Equation (9)) called the geostrophic balance equation

in which relative acceleration and frictional force are negligible compared to pressure, Coriolis and gravitation force.

Using vector product (symbol

In the goal to obtain (9-b)

where:

Hence:

The Geostrophic Vector (or Wind) in the Northern-Hemisphere

The Geostrophic Vector (or Wind) in the Southern-Hemisphere

Equations (10) and (11) lead to 06 geostrophic vector specifics (or fundamental properties):

P_{1}: the geostrophic winds (as defined) are perpendicular to the horizontal pressure gradient vector.

P_{2}: the geostrophic winds (as defined) are horizontal (they are perpendicular to

P_{3}: the geostrophic wind (as defined) is parallel (or tangent at any point) to the isobars.

Proof: along an isobar,

This allows stating P_{3}.

P_{4}: the geostrophic winds (as defined) are inversely proportional to

P_{5}: The geostrophic winds are (as defined) stronger when the density (r) of air decreases.

P_{6}: the geostrophic winds (as defined) move leaving the low pressure to their left in the Northern Hemisphere. They move leaving the low pressure to their right in the Southern Hemisphere (

(This statement is provided by the properties of the vector product).

According to the Geostrophic Balance Equation (e.g., Equation (9)), if a wind (even a moderate one) blows on a Compilation of Highest Horizontal-Temperature-Gradients’ Systems (HHTGS) which means the Compilation of Highest Horizontal-Pressure-Gradients’ Systems (HHPGS), this wind will turn spontaneously geostrophic wind. In other words, it will trigger a tornado (in the case of the compilation of HHTGS triggered by hot thermal sources). It is this kind of shows that the Earth’s atmosphere has accustomed us (

Tornadoes, as has been demonstrated in the preceding paragraphs, derive from upsurge of 02 meteorological events: the compilation of HHPGS triggered by a hot thermal source and the occurrence of Coriolis force triggered by the wind which blows in the vicinity of the “building” made of compilation of HHTGS (or HHPGS). If we agree to give the name “Epicenter” to the place where the local sea level pressure minimum appears, it will then be easy to point out parallels between solitary waves (

oceans, it triggers 02 spontaneous and simultaneous spectacular events: a Tornado and a solitary wave which peaks at the Epicenter of the horizontal low pressure systems. This solitary wave has the same life cycle that Tornado. The real nature of the physical processes behind the formation of rogue waves (e.g., rogue waves are solitary waves. They are worst nightmares of sailors traveling through the oceans because they are devastating and unpredictable) is well known now.

Our work shows once again that to better understand the behavior of natural phenomena, it is essential to combine the theories with based observations. Obviously, observations cannot be relevant without a theory that guides the observers. Conversely, no theory can be validated without experimental verification. Synoptic ob- servations show that in the “free atmosphere!” the wind vectors are very nearly parallel to isobars, and the flow is perpendicular to the horizontal pressure gradient force, at least at any given instant. This kind of information recommends great caution when making geostrophic approximations. Our work shows that for hurricanes and tornadoes, there is no need to move away from the surface of the ground to observe the geostrophic balance. This is not necessarily true when determining the direction of the winds around the low pressures systems using maps derived from the “ground based-pressures” (instead of: space based-pressures). Nearly parallel to isobars did not mean parallel to isobars. Since the geostrophic balance reaches the surface of the ground in the case of cyclones, horizontal profiles of wind associated to this weather event can be deduced from the 06 fundamental properties stated in this work. Our results will certainly help people who spend huge sums of money to run (sometimes taking considerable risks) after the spectacular thermodynamically shows offered by tornadoes.

César Mbane Biouele, (2016) Identification and Interpretation of Earth’s Atmosphere Dynamics’ and Thermodynamics’ Similarities between Rogue Waves and Oceans’ Surface Geostrophic Wind. Open Journal of Marine Science,06,238-246. doi: 10.4236/ojms.2016.62019