Blood Moon, semi permanent hair dye red - 118 ml - Lunar Tides

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The basic characteristics of the atmospheric tides are described by the classical tidal theory. [5] By neglecting mechanical forcing and dissipation, the classical tidal theory assumes that atmospheric wave motions can be considered as linear perturbations of an initially motionless zonal mean state that is horizontally stratified and isothermal. The two major results of the classical theory are n (Figure 2). There exist two kinds of waves: class 1 waves, (sometimes called gravity waves), labelled by positive n, and class 2 waves (sometimes called rotational waves), labelled by negative n. Class 2 waves owe their existence to the Coriolis force and can only exist for periods greater than 12 hours (or | ν| ≤ 2). Tidal waves can be either internal (travelling waves) with positive eigenvalues (or equivalent depth) which have finite vertical wavelengths and can transport wave energy upward, or external (evanescent waves) with negative eigenvalues and infinitely large vertical wavelengths meaning that their phases remain constant with altitude. These external wave modes cannot transport wave energy, and their amplitudes decrease exponentially with height outside their source regions. Even numbers of n correspond to waves symmetric with respect to the equator, and odd numbers corresponding to antisymmetric waves. The transition from internal to external waves appears at ε ≃ ε c, or at the vertical wavenumber k z = 0, and λ z ⇒ ∞, respectively. Migrating tides are Sun synchronous – from the point of view of a stationary observer on the ground they propagate westwards with the apparent motion of the Sun. As the migrating tides stay fixed relative to the Sun a pattern of excitation is formed that is also fixed relative to the Sun. Changes in the tide observed from a stationary viewpoint on the Earth's surface are caused by the rotation of the Earth with respect to this fixed pattern. Seasonal variations of the tides also occur as the Earth tilts relative to the Sun and so relative to the pattern of excitation. [1] Atmospheric tides are global-scale periodic oscillations of the atmosphere. In many ways they are analogous to ocean tides. Atmospheric tides can be excited by:

Longuet-Higgins [8] has completely solved Laplace's equations and has discovered tidal modes with negative eigenvalues ε s Solar energy is absorbed throughout the atmosphere some of the most significant in this context are [ clarification needed] water vapor at about 0–15km in the troposphere, ozone at about 30–60km in the stratosphere and molecular oxygen and molecular nitrogen at about 120–170km) in the thermosphere. Variations in the global distribution and density of these species result in changes in the amplitude of the solar tides. The tides are also affected by the environment through which they travel. The migrating solar tides have been extensively studied both through observations and mechanistic models. [2] Non-migrating solar tides [ edit ]

Types of tides

At ground level, atmospheric tides can be detected as regular but small oscillations in surface pressure with periods of 24 and 12 hours. However, at greater heights, the amplitudes of the tides can become very large. In the mesosphere (heights of about 50–100km (30–60mi; 200,000–300,000ft)) atmospheric tides can reach amplitudes of more than 50m/s and are often the most significant part of the motion of the atmosphere. General solution of Laplace's equation [ edit ] Figure 2. Eigenvalue ε of wave modes of zonal wave number s = 1 vs. normalized frequency ν = ω/Ω where Ω = 7.27 ×10 −5s −1 is the angular frequency of one solar day. Waves with positive (negative) frequencies propagate to the east (west). The horizontal dashed line is at ε c ≃ 11 and indicates the transition from internal to external waves. Meaning of the symbols: 'RH' Rossby-Haurwitz waves ( ε = 0); 'Y' Yanai waves; 'K' Kelvin waves; 'R' Rossby waves; 'DT' Diurnal tides ( ν = −1); 'NM' Normal modes ( ε ≃ ε c) Atmospheric tides are primarily excited by the Sun's heating of the atmosphere whereas ocean tides are excited by the Moon's gravitational pull and to a lesser extent by the Sun's gravity. This means that most atmospheric tides have periods of oscillation related to the 24-hour length of the solar day whereas ocean tides have periods of oscillation related both to the solar day as well as to the longer lunar day (time between successive lunar transits) of about 24 hours 51 minutes.

Atmospheric tides propagate in an atmosphere where density varies significantly with height. A consequence of this is that their amplitudes naturally increase exponentially as the tide ascends into progressively more rarefied regions of the atmosphere (for an explanation of this phenomenon, see below). In contrast, the density of the oceans varies only slightly with depth and so there the tides do not necessarily vary in amplitude with depth.Figure 3. Pressure amplitudes vs. latitude of the Hough functions of the diurnal tide ( s = 1; ν = −1) (left) and of the semidiurnal tides ( s = 2; ν = −2) (right) on the northern hemisphere. Solid curves: symmetric waves; dashed curves: antisymmetric waves Its maximum pressure amplitude on the ground is about 60 Pa. [5] The largest solar semidiurnal wave is mode (2, 2) with maximum pressure amplitudes at the ground of 120 Pa. It is an internal class 1 wave. Its amplitude increases exponentially with altitude. Although its solar excitation is half of that of mode (1, −2), its amplitude on the ground is larger by a factor of two. This indicates the effect of suppression of external waves, in this case by a factor of four. [9] Vertical structure equation [ edit ] The reason for this dramatic growth in amplitude from tiny fluctuations near the ground to oscillations that dominate the motion of the mesosphere lies in the fact that the density of the atmosphere decreases with increasing height. As tides or waves propagate upwards, they move into regions of lower and lower density. If the tide or wave is not dissipating, then its kinetic energy density must be conserved. Since the density is decreasing, the amplitude of the tide or wave increases correspondingly so that energy is conserved. integer so that positive values for σ {\displaystyle \sigma } correspond to eastward propagating tides

Following this growth with height atmospheric tides have much larger amplitudes in the middle and upper atmosphere than they do at ground level. The largest-amplitude atmospheric tides are mostly generated in the troposphere and stratosphere when the atmosphere is periodically heated, as water vapor and ozone absorb solar radiation during the day. These tides propagate away from the source regions and ascend into the mesosphere and thermosphere. Atmospheric tides can be measured as regular fluctuations in wind, temperature, density and pressure. Although atmospheric tides share much in common with ocean tides they have two key distinguishing features: The set of equations can be solved for atmospheric tides, i.e., longitudinally propagating waves of zonal wavenumbers {\displaystyle s} and frequency σ {\displaystyle \sigma } . Zonal wavenumber s {\displaystyle s} is a positive The fundamental solar diurnal tidal mode which optimally matches the solar heat input configuration and thus is most strongly excited is the Hough mode (1, −2) (Figure 3). It depends on local time and travels westward with the Sun. It is an external mode of class 2 and has the eigenvalue of ε 1 Hence, atmospheric tides are eigenoscillations ( eigenmodes)of Earth's atmosphere with eigenfunctions Θ n {\displaystyle \Theta _{n}} , called Hough functions, and eigenvalues ε n {\displaystyle \varepsilon _{n}} . The latter define the equivalent depth h n {\displaystyle h_{n}} which couples the latitudinal structure of the tides with their vertical structure.