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

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The set of equations can be solved for atmospheric tides, i.e., longitudinally propagating waves of zonal wavenumber Atmospheric tides are also produced through the gravitational effects of the Moon. [4] Lunar (gravitational) tides are much weaker than solar thermal tides and are generated by the motion of the Earth's oceans (caused by the Moon) and to a lesser extent the effect of the Moon's gravitational attraction on the atmosphere. 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: 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 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.

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. Longuet-Higgins [8] has completely solved Laplace's equations and has discovered tidal modes with negative eigenvalues ε s The migrating solar tides have been extensively studied both through observations and mechanistic models. [2] Non-migrating solar tides [ edit ]For a fixed longitude λ {\displaystyle \lambda } , this in turn always results in downward phase progression as time progresses, independent of the propagation direction. This is an important result for the interpretation of observations: downward phase progression in time means an upward propagation of energy and therefore a tidal forcing lower in the atmosphere. Amplitude increases with height ∝ e z / 2 H {\displaystyle \propto e 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. integer so that positive values for σ {\displaystyle \sigma } correspond to eastward propagating tides 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:

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 1The primary source for the 24-hr tide is in the lower atmosphere where surface effects are important. This is reflected in a relatively large non-migrating component seen in longitudinal differences in tidal amplitudes. Largest amplitudes have been observed over South America, Africa and Australia. [3] Lunar atmospheric tides [ edit ] Following this growth with height atmospheric tides have much larger amplitudes in the middle and upper atmosphere than they do at ground level.