On the stability of density stratified flow below a ponded surface

\u3cp\u3e Flooding of coastal areas with seawater often leads to density stratification. The stability of the density-depth profile in a porous medium initially saturated with a fluid of density ρ \u3csub\u3ef\u3c/sub\u3e after flooding with a salt solution of higher density ρ \u3csub\u3es\u3c/sub\u3e is analyzed. The standard convection/diffusion equation subject to the so-called Boussinesq approximation is used. The depth of the porous medium is assumed to be infinite in the analytical approaches and finite in the numerical simulations. Two cases are distinguished: the laterally unbounded CASEA and the laterally bounded CASEB. The ratio of the diffusivity and the density difference (ρ \u3csub\u3es\u3c/sub\u3e - ρ \u3csub\u3ef\u3c/sub\u3e ) induced gravitational shear flow is an intrinsic length scale of the problem. In the unbounded CASEA, this geometric length scale is the only length scale and using it to write the problem in dimensionless form results in a formulation with Rayleigh number R= 1. In the bounded CASEB, the lateral geometry provides another length scale. Using this geometrical length scale to write the problem in dimensionless form results in a formulation with a Rayleigh number R given by the ratio of the geometric and intrinsic length scales. For both CASEA and CASEB, the well-known Boltzmann similarity solution provides the ground state. Three analytical approaches are used to study the stability of this ground state, the first two based on the linearized perturbation equation for the concentration and the third based on the full nonlinear equation. For the first linear approach, the surface spatial density gradient is used as an approximation of the entire background density profile. This results in a crude estimate of the L \u3csup\u3e2\u3c/sup\u3e -norm of the concentration showing that the perturbation at first grows, but eventually decays in time. For the other two approaches, the full ground-state solution is used, although for the second linear approach subject to the restriction that the ground state slowly evolves in time (the so-called frozen profile approximation). Just like the ground state, the resulting eigenvalue problems can be written in terms of the Boltzmann variable. The linearized stability approach holds only for infinitesimal small perturbations, whereas the nonlinear, variational energy approach is not subject to such a restriction. The results for all three approaches can be expressed in terms of Boltzmann t transformed relationships between the system Rayleigh number and perturbation wave number. The results of the linear and nonlinear approaches are surprisingly close to each other. Based on the system Rayleigh number, this allows delineation of systems that are unconditionally stable, marginally stable, or transiently unstable. These analytical predictions are confirmed by direct two-dimensional numerical simulations, which also show the details of the transient instabilities as function of the wave number for CASEA and the wave number and Rayleigh number for CASEB. A numerical example of the effect of a layer with low permeability is also shown. Using typical values of the physical parameters, the analytical and numerical results are interpreted in terms of dimensional length and time scales. In particular, an explicit stability criterion is given for vertical column experiments. \u3c/p\u3

Annals of biochemistry and experimental medicine

In this paper we study gravitational instability of a saline boundary layer formed by evaporation induced upward throughflow at the horizontal surface of a porous medium. Van Duijn et al. [P.A.C. Raats, D. Smiles, and A.W. Warrick (Eds.), Environmental Mechanics – Water, Mass and Energy Transfer in the Biosphere – The Philip Volume, Geophys. Monographs, Vol. 129, American Geophysical Union, 2002, pp. 155–169], derived stability bounds by means of linear stability analysis and an (improved) energy method. These bounds do not coincide, i.e. there exists a subcritical region or stability gap in the system parameter space which is due to the asymmetry of the linear part of the perturbation equations. We show that the linear operator can be symmetrized by means of a similarity transformation. For system parameter values in the stability gap, we show that there exist initial perturbations for which the linearly stable system exhibits transient growth. We show that transient growth is norm dependent by considering weighted norms, which are induced by a one-parameter family of similarity transformations

Mechanism of biomolecular recognition of trimethyllysine by the fluorinated aromatic cage of KDM5A PHD3 finger

The understanding of biomolecular recognition of posttranslationally modified histone proteins is centrally important to the histone code hypothesis. Despite extensive binding and structural studies on the readout of histones, the molecular language by which posttranslational modifications on histone proteins are read remains poorly understood. Here we report physical-organic chemistry studies on the recognition of the positively charged trimethyllysine by the electron-rich aromatic cage containing PHD3 finger of KDM5A. The aromatic character of two tryptophan residues that solely constitute the aromatic cage of KDM5A was fine-tuned by the incorporation of fluorine substituents. Our thermodynamic analyses reveal that the wild-type and fluorinated KDM5A PHD3 fingers associate equally well with trimethyllysine. This work demonstrates that the biomolecular recognition of trimethyllysine by fluorinated aromatic cages is associated with weaker cation–π interactions that are compensated by the energetically more favourable trimethyllysine-mediated release of high-energy water molecules that occupy the aromatic cage

On the stability-instability of vertical throughflows in double diffusive mixtures saturating rotating porous layers with large pores

The long-time behaviour of the solutions of the Darcy–Oberbeck– Boussinesq system modeling fluid motion in horizontal porous layers, is investigated. The layer is supposed to be uniformly heated and salted from below, rotating around the vertical axis, showing large pores. Necessary and sufficient conditions guaranteeing the stability of a vertical constant throughflow are obtained. The non-linear, global, asymptotic L2− stability of the throughflow solution, is investigated