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Moisture Transport due to Baroclinic Waves: Linear Analysis of Precipitating Quasi-Geostrophic Dynamics

100%
Wetzel A. N., Smith L. M., Stechmann S. N.
Mathematics of Climate and Weather Forecasting
|
2017
|
tom 3
|
nr 1
28-50
EN
The effects of rainfall speed, VT, and meridional/vertical moisture gradients on the meridional moisture transport are examined in the context of mid-latitude baroclinic waves. These effects are investigated in an idealized model that can be solved analytically. The model is systematically derived in a precipitating quasi-geostrophic limit, starting from a moist atmospheric model with minimal representation of cloud microphysics. Single-phase dynamics are considered, with a comparison of three cases: unsaturated, saturated with VT = 0, and saturated with VT > 0. The Eady problem for linear baroclinic waves is analyzed, with modifications to incorporate moisture. As a preliminary step, the moist waves are shown to have properties consistent with prior studies, including larger growth rates and smaller spatial scales in the saturated cases in comparison to the classic dry Eady problem. Then, in addition, it is shown that the meridional moisture flux, as a function of height, has a mid-tropospheric maximum in the case of VT = 0, and a maximum in the lower troposphere or at the surface for sufficiently large values of VT. These results for different VT values are discussed in the context of meridional moisture transport in observational data.
2
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Degenerate triply nonlinear problems with nonhomogeneous boundary conditions

100%
Ammar K.
Open Mathematics
|
2010
|
tom 8
|
nr 3
548-568
EN
The paper addresses the existence and uniqueness of entropy solutions for the degenerate triply nonlinear problem: b(v)t − div α(v, ▽g(v)) = f on Q:= (0, T) × Ω with the initial condition b(v(0, ·)) = b(v 0) on Ω and the nonhomogeneous boundary condition “v = u” on some part of the boundary (0, T) × ∂Ω”. The function g is continuous locally Lipschitz continuous and has a flat region [A 1, A 2,] with A 1 ≤ 0 ≤ A 2 so that the problem is of parabolic-hyperbolic type.
3
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Cauchy problem for a class of parabolic systems of Shilov type with variable coefficients

100%
Litovchenko V., Dovzhytska I.
Open Mathematics
|
2012
|
tom 10
|
nr 3
1084-1102
EN
In the case of initial data belonging to a wide class of functions including distributions of Gelfand-Shilov type we establish the correct solvability of the Cauchy problem for a new class of Shilov parabolic systems of equations with partial derivatives with bounded smooth variable lower coefficients and nonnegative genus. We also investigate the conditions of local improvement of the convergence of a solution of this problem to its limiting value when the time variable tends to zero.
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