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Table H.1
List of the symbols used throughout this work and their designations in order of introduction.
| Symbol | Designation |
|
|
|
| i | imaginary number |
| ℜ | real part |
| ℑ | imaginary part |
| ∗ | conjugate |
| ⊕ | associated with the Earth |
| ♀ | associated with Venus |
| RET | planetary equatorial rotating frame |
| X E , Y E , Z E | vectorial basis associated with RET |
| r | radial coordinate |
| θ | colatitude |
| ϕ | east longitude |
| δ | latitude/fluctuations |
| e r , e θ , e ϕ | spherical vectorial basis |
| t | time |
| g | gravity |
| Ω | planet spin vector |
| Ω | angular velocity |
| R | planet radius |
| atm | associated with the atmosphere |
| gr | associated with the ground |
| R atm | external radius of the atmosphere |
| H atm | typical thickness of the atmosphere |
| M | molar mass of the atmosphere |
| p | pressure |
| ρ | density |
| T | temperature |
| p 0 | background pressure distribution |
| ρ 0 | background density distribution |
| T 0 | background temperature distribution |
| C 0 | background molar concentration distribution |
| Γ1 | adiabatic exponent |
| N | Brunt-Väisälä frequency |
| RGP | perfect gas constant |
| Rs | specific gas constant of the atmosphere |
| U | gravitational tidal potential |
| J | tidal heating power per unit mass |
| V | tidal velocity field |
| V r , V θ , V ϕ | components of V in spherical coordinates |
| ξ | displacement vector |
| ξ r , ξ θ , ξ ϕ | components of ξ in spherical coordinates |
| δp | tidal pressure perturbation |
| δρ | tidal density perturbation |
| δT | tidal temperature perturbation |
| c s | sound velocity |
| κ | atmospheric parameter |
| φ rad | radiated power per unit mass |
| σ 0 | radiation frequency |
| S | Stefan-Boltzmann constant |
| ϵ a | effective molar attenuation coefficient |
| f | any perturbed quantity |
| σ | tidal frequency |
| ν | spin parameter |
| m | longitudinal degree |
| y | pressure perturbation divided by ρ0 |
| ξ H | horizontal displacement |
|
operator associated with θ-components |
|
operator associated with ϕ-components |
| ℒm,ν | Laplace’s tidal operator |
| n | meridional degree |
|
Hough functions |
|
eigenvalues of Laplace’s tidal equation |
|
components of J |
|
components of U |
|
components of ξr |
|
components of ξθ |
|
components of ξϕ |
|
components of Vr |
|
components of Vθ |
|
components of Vϕ |
|
components of δp |
|
components of δρ |
|
components of δT |
|
components of y |
| A 1 , A 2 , A 3 | coefficients of the equation r2ξr;n |
| B 1 , B 2 , B 3 | coefficients of the equation yn |
| A,B,C | coefficients of the vertical structure |
| equation | |
| ℱ | function of the variable change |
|
vertical wavenumber |
| L V;n | scale of variation |
| ε s;n | acoustic coefficient |
| σ s;n | acoustic frequency |
|
coefficients of polarization relations |
| K curv | curvature term in polarization relations |
|
linear operator associated with the vertical |
| structure | |
|
components of the operator |
| associated with f | |
| X n | vector of the forcings |
| Y n | vector of the response |
| σ diff;n | diffusive frequency |
| G | gravitational constant |
| l | degrees of Legendre polynomials |
|
associated Legendre functions |
|
normalized associated Legendre functions |
|
potential induced by the tidal response |
|
components of
projected on the |
|
components of
projected on the |
|
first component of |
|
second component of |
|
Love numbers for the gravitational potential |
|
coefficients of Kaula’s expansion |
|
density expansion coefficient for the perturbation |
| projected on the |
|
|
components of |
|
weighting coefficients of modes in |
| the expansion of the tidal torque | |
| M S | mass of the star |
| a | semi-major axis |
| ε | obliquity |
| n orb | mean motion |
| σ SD | semidiurnal tidal frequency |
| U 2,2,2,0,0 | semidiurnal gravitational tidal potential |
| J 2,2,2,0,0 | semidiurnal thermal forcing |
|
expansion function of the thermal forcing |
| projected on P2 | |
| V | volumetric domain of the atmosphere |
|
tidal torque |
|
frequency components of the tidal torque |
| Δϕ | phase lag of the tidal response |
| H | associated with the horizontal component |
| V | associated with the vertical component |
| grav | caused by the gravitational forcing |
| therm | caused by the thermal forcing |
|
torque due to the horizontal component |
|
torque due to the vertical component |
| ℋ | factor in the expressions of the torque |
| z | altitude |
| x | altitude normalized by the pressure height scale |
| x atm | normalized upper boundary |
| a RE;T | local acceleration in the reference frame |
| a c | centrifugal acceleration |
| h n | equivalent depth |
| h c | characteristic depth of the vertical wavenumber |
| ς n | scale ratio in the vertical wavenumber |
| Δ | discriminant in 
and 
|
| A,B | functions generating the analytic solution |
|
coefficients of the upper boundary equation |
| x crit | typical damping depth |
|
parameters |
|
parametrized function of the analytic solution |
|
orbital period |
| γ | lag angle |
|
dimensionless constant |
| a,b | empirical parameters in the model of |
| Correia et al. (2003) | |
|
vertical wavenumber in CL70 |
| η | relative difference between 
and kCL;n |
| λ | wavelength of light |
| I S;λ | spectral radiance of the star |
| I S | black-body stellar flux |
| R S | star radius |
| T S | surface temperature of the star |
| d | star-planet distance |
| c | speed of light in vacuum |
| h | Planck constant |
| k B | Boltzmann constant |
| A atm;λ | albedo of the atmosphere for the wavelength λ |
| I 0;λ | effective incident flux |
| l | linear spatial coordinate |
| inc | caused by the incident flux |
| ref | caused by the reflected flux |
| rad | caused by the flux emitted by the surface |
| C G | molar concentration of an absorbing gas |
| ε G;λ | molar extinction density coefficient |
| I λ | heat power flux |
| J | heat power per unit volume |
| τ λ | optical depth |
| α λ | global absorption coefficient |
| A gr;λ | albedo of the ground for the wavelength λ |
| T gr | surface temperature |
| ψ | angle to the star-planet direction |
| I gr;BB | black-body emission of the ground |
| ϵ gr | emissivity of the ground |
| ϵ atm | emissivity of the atmosphere |
| ϵ | effective emissivity of the ground |
| T gr;0 | surface equilibrium temperature |
| δ T gr | surface temperature fluctuations |
|
transfer function of the ground |
| Q atm | diffusive power flux in the atmosphere |
| Q gr | diffusive power flux in the ground |
| k atm | thermal conductivity of the atmosphere |
| k gr | thermal conductivity of the ground |
| K atm | vertical turbulent thermal diffusivity |
| K gr | thermal diffusivity of the ground |
| c atm | thermal capacity of the atmosphere |
| c gr | thermal capacity of the ground |
|
skin thickness in the atmosphere |
|
skin thickness in the ground |
| ς gr | radiative impedance of the ground |
| β atm | thermal conductive capacity of the atmosphere |
| β gr | thermal conductive capacity of the ground |
| σ bl | typical frequency of the atmospheric boundary |
| layer | |
|
vertical damping coefficient in the boundary layer |
| δ T bl | temperature fluctuations in the boundary layer |
|
associated with visible light |
|
associated with the infrared |
| N | number of points of the spatial discretization |
| T | timescale of the spin evolution |
| M | mass of the atmosphere |
| χ | tidal frequency divided by the mean motion |
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