A Two-Layer Model for Steady-Amplitude Gravity Waves and Convection Generated by a Thermal Forcing

Abstract A two-dimensional two-layer mathematical model is described representing internal gravity waves and convection generated by a thermal forcing in the lower atmosphere. The model consists of an upper layer with stable stratification, a lower layer with unstable stratification, and a thermal forcing in the form of a nonhomogeneous term in the energy conservation equation. Exact analytical solutions are derived for some simple configurations. Depending on the vertical location and depth of the thermal forcing, the model can be used to represent different configurations in which gravity waves are generated by diabatic heating. When the thermal forcing is centered in the lower layer, convective cells are generated in the lower layer, and gravity waves are forced and propagate upward from the interface between the two layers. When the thermal forcing is centered at the interface, the convection in the lower layer is weaker, and gravity waves are forced by the direct effect of the thermal forcing in the upper layer and the influence of the convective cells below. Steady-amplitude solutions for the vertical profile of the gravity waves and convection are derived and generalized to include cases where there is a spectrum of horizontal wavenumbers or vertical wavenumbers or frequencies present.

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Oceanic tides from Earth-like to ocean planets

Astronomy and Astrophysics ◽

10.1051/0004-6361/201732249 ◽

2018 ◽

Vol 615 ◽

pp. A23 ◽

Cited By ~ 7

Author(s):

P. Auclair-Desrotour ◽

S. Mathis ◽

J. Laskar ◽

J. Leconte

Keyword(s):

Gravity Waves ◽

Three Dimensional ◽

Stable Stratification ◽

Internal Gravity Waves ◽

Tidal Dissipation ◽

Planetary Rotation ◽

Wide Range ◽

Oceanic Tides ◽

3D Effects ◽

Tidal Response

Context. Oceanic tides are a major source of tidal dissipation. They drive the evolution of planetary systems and the rotational dynamics of planets. However, two-dimensional (2D) models commonly used for the Earth cannot be applied to extrasolar telluric planets hosting potentially deep oceans because they ignore the three-dimensional (3D) effects related to the ocean’s vertical structure. Aims. Our goal is to investigate, in a consistant way, the importance of the contribution of internal gravity waves in the oceanic tidal response and to propose a modelling that allows one to treat a wide range of cases from shallow to deep oceans. Methods. A 3D ab initio model is developed to study the dynamics of a global planetary ocean. This model takes into account compressibility, stratification, and sphericity terms, which are usually ignored in 2D approaches. An analytic solution is computed and used to study the dependence of the tidal response on the tidal frequency and on the ocean depth and stratification. Results. In the 2D asymptotic limit, we recover the frequency-resonant behaviour due to surface inertial-gravity waves identified by early studies. As the ocean depth and Brunt–Väisälä frequency increase, the contribution of internal gravity waves grows in importance and the tidal response becomes 3D. In the case of deep oceans, the stable stratification induces resonances that can increase the tidal dissipation rate by several orders of magnitude. It is thus able to significantly affect the evolution time scale of the planetary rotation.

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Convective cells of internal gravity waves in the earth's atmosphere with finite temperature gradient

Annales Geophysicae ◽

10.5194/angeo-31-459-2013 ◽

2013 ◽

Vol 31 (3) ◽

pp. 459-462 ◽

Cited By ~ 9

Author(s):

O. Onishchenko ◽

O. Pokhotelov ◽

V. Fedun

Keyword(s):

Temperature Gradient ◽

Gravity Waves ◽

Closed System ◽

Internal Gravity Waves ◽

System Of Nonlinear Equations ◽

Vertical Temperature Gradient ◽

Vertical Temperature ◽

Earth’S Atmosphere ◽

Earth's Atmosphere ◽

Convective Cells

Abstract. In this paper, we have investigated vortex structures (e.g. convective cells) of internal gravity waves (IGWs) in the earth's atmosphere with a finite vertical temperature gradient. A closed system of nonlinear equations for these waves and the condition for existence of solitary convective cells are obtained. In the atmosphere layers where the temperature decreases with height, the presence of IGW convective cells is shown. The typical parameters of such structures in the earth's atmosphere are discussed.

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Convectively Generated Internal Gravity Waves in the Lower Atmosphere of Venus. Part I: No Wind Shear

Journal of the Atmospheric Sciences ◽

10.1175/1520-0469(2000)057<0184:cgigwi>2.0.co;2 ◽

2000 ◽

Vol 57 (2) ◽

pp. 184-199 ◽

Cited By ~ 15

Author(s):

R. David Baker ◽

Gerald Schubert ◽

Philip W. Jones

Keyword(s):

Gravity Waves ◽

Wind Shear ◽

Internal Gravity Waves ◽

Lower Atmosphere ◽

Atmosphere Of Venus

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A case study of turbulent parameters during the Antarctic winter

Antarctic Science ◽

10.1017/s0954102095000587 ◽

1995 ◽

Vol 7 (4) ◽

pp. 421-433 ◽

Cited By ~ 6

Author(s):

Carlos Yagüe ◽

José M. Redondo

Keyword(s):

Boundary Layer ◽

Sensible Heat Flux ◽

Stable Stratification ◽

Internal Gravity Waves ◽

Lower Atmosphere ◽

Transfer Coefficients ◽

Surface Cooling ◽

Obukhov Length ◽

The Stability ◽

The Antarctic

Two days of the Antarctic winter (20 and 21 June 1986) were chosen to study some turbulent parameters in this particular boundary-layer. Richardson number, Monin-Obukhov length, eddy transfer coefficients, turbulent kinetic energy, turbulent intensities, friction velocities and sensible heat flux at three levels (5, 17 and 32 m) were considered. The results show how the stability at 17 and 32 m influences the turbulent transfer at 5 m. The shear of wind is the main mechanism to produce mixing in the lower atmosphere at Antarctica, and thermal inversions associated to surface cooling develop with winds < 10 ms−1 at 5 m. The possible influence of internal gravity-waves on the atmospheric boundary-layer during strong stable stratification is studied.

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