A Thermodynamic Perspective on Steady-State Tropical Cyclones

Theories for the maximum intensity of tropical cyclones (TCs) assume steady state. However, many TCs in simulations that run for tens of days tend to decay considerably from an early steady state in the core (CS), before stabilizing at a final equilibrium steady state (ES). This decay raises the question of whether CS or ES should be used as a comparison to the maximum intensity theories. To understand the differences between CS and ES, we investigate why TCs decay and attempt to simulate a TC with steady intensity over a 100-day period. Using the axisymmetric Cloud Model 1, we find that the CS TC decay is due to a large-scale drying of the subsidence region. Such a drying is very pronounced in axisymmetric models because shallow-to-mid level convection is not represented accurately enough to moisten air in the subsidence region. Simulations with an added moisture relaxation term in the subsidence region and dry cyclones without any moisture both remain in a steady state for over 100 days, without decaying appreciably after the spin-up period. These simulations indicate that the decay in TC simulations is due to the irreversible removal of precipitation combined with the lack of a moistening mechanism in the subsidence region. Once either of these conditions is removed, the decay disappears and the CS and ES intensities become essentially equivalent.

Diffusion models for mixtures using a stiff dissipative hyperbolic formalism

We consider a system of fluid equations for mixtures with a stiff relaxation term of Maxwell–Stefan diffusion type. We use the formalism developed by Chen et al. and derive a limiting system of Fick type, in which the species velocities tend to align with a bulk velocity when the relaxation parameter remains small.

New Stability Criterion for the Dissipative Linear System and Analysis of Bresse System

In this article, we introduce a new approach to obtain the property of the dissipative structure for a system of differential equations. If the system has a viscosity or relaxation term which possesses symmetric property, Shizuta and Kawashima in 1985 introduced the suitable stability condition called in this article Classical Stability Condition for the corresponding eigenvalue problem of the system, and derived the detailed relation between the coefficient matrices of the system and the eigenvalues. However, there are some complicated physical models which possess a non-symmetric viscosity or relaxation term and we cannot apply Classical Stability Condition to these models. Under this situation, our purpose in this article is to extend Classical Stability Condition for complicated models and to make the relation between the coefficient matrices and the corresponding eigenvalues clear. Furthermore, we shall explain the new dissipative structure through the several concrete examples.

Time-Splitting Schemes and Measure Source Terms for a Quasilinear Relaxing System

Several singular limits are investigated in the context of a 2 × 2 system arising for instance in the modeling of chromatographic processes. In particular, we focus on the case where the relaxation term and a L2 projection operator are concentrated on a discrete lattice by means of Dirac measures. This formulation allows one to study more easily some time-splitting numerical schemes.