Nondimensionalization of the Atmospheric Boundary-Layer System: Obukhov Length and Monin–Obukhov Similarity Theory

The Obukhov length, although often adopted as a characteristic scale of the atmospheric boundary layer, has been introduced purely based on a dimensional argument without a deductive derivation from the governing equations. Here, its derivation is pursued by the nondimensionalization method in the same manner as for the Rossby deformation radius and the Ekman-layer depth. Physical implications of the Obukhov length are inferred by nondimensionalizing the turbulence-kinetic-energy equation for the horizontally homogeneous boundary layer. A nondimensionalization length scale for a full set of equations for boundary-layer flow formally reduces to the Obukhov length by dividing this scale by a rescaling factor. This rescaling factor increases with increasing stable stratification of the boundary layer, in which flows tend to be more horizontal and gentler; thus the Obukhov length increasingly loses its relevance. A heuristic, but deductive, derivation of Monin–Obukhov similarity theory is also outlined based on the obtained nondimensionalization results.

Hegel’s Speculative Identity Thesis

This chapter explores Hegel’s speculative identity thesis, defending the importance of Schelling for Hegel’s appropriation of Kant’s purposiveness theme. It provides an interpretation of Hegel’s first published text, the Differenzschrift, and analyzes the relation between “subjective subject-objects” and “objective subject-objects” as an early presentation of Hegel’s philosophical method. In addition to defending the contribution of Schelling, this chapter provides an interpretation of Fichte’s contribution via his notion of the self-positing activity of the I. It then turns to a reading of Hegel’s Phenomenology of Spirit, demonstrating that the notion of “negativity” can be understood along the lines of speculative identity. The chapter argues that Hegel presents life as constitutive for self-consciousness by way of a three-dimensional argument: the employment of an analogy; a transcendental argument; and a refutation of idealism argument. It concludes by briefly outlining how the speculative identity thesis is carried forward in the Science of Logic.

Viscous deformation of relaxing ventricle and pulsatile blood propelling (numerical model)

The numerical model of one-loop circulation exploits viscous deformation as mechanism of ventricular filling. Mathematical advantage of viscous deforming is a possibility to present the ventricular filling as the function of two independent variables (stress and time); two-dimensional argument frames a table which permits to calculate end-diastolic ventricular volume due to information about measured venous pressure and duration of ventricular diastole. The equation was deduced which balances the system while varying of such parameters as arterial resistance, the value of normal rhythm and the volume flow rate. The model pays attention on the phenomenon of asymmetrical position of normal rhythm (the steady rhythm in conditions of rest) and explains why the operating range of brady-rhythms is much narrower than the operating range of tachy-rhythms.

A comparison of turbulent thermal convection between conditions of constant temperature and constant heat flux

We numerically investigate turbulent thermal convection driven by a horizontal surface of constant heat flux and compare the results with those of constant temperature. Below Ra ≈ 109, where Ra is the Rayleigh number, when the flow is smooth and regular, the heat transport in the two cases is essentially the same. For Ra > 109 the heat transport for imposed heat flux is smaller than that for constant temperature, and is close to experimental data. We provide a simple dimensional argument to indicate that the unsteady emission of thermal plumes renders typical experimental conditions closer to the constant heat flux case.

Non-local two-dimensional turbulence and Batchelor's regime for passive scalars

We study small-scale two-dimensional non-local turbulence, where interaction of small scales with large vortices dominates in the small-scale dynamics, by using a semi-classical approach developed in Dyachenko, Nazarenko & Zakharov (1992), Nazarenko, Zabusky & Scheidegger (1995), Dubrulle & Nazarenko (1997) and Nazarenko, Kevlahan & Dubrulle (1999). Also, we consider a closely related problem of passive scalars in Batchelor's regime, when the Schmidt number is much greater than unity. In our approach, we do not perform any statistical averaging, and most of our results are valid for any form of the large-scale advection. A new invariant is found in this paper for passive scalars when their initial spectrum is isotropic. It is shown, analytically, numerically and using a dimensional argument, that there is a spectrum corresponding to an inverse cascade of the new invariant, which scales like k−1 for turbulent energy and k1 for passive scalars. For passive scalars, the k1-spectrum was first found by Kraichnan (1974) in the special case of advection δ-correlated in time, and until now it was believed to correspond to an absolute thermodynamic equilibrium and not a cascade. We also obtain, both analytically and numerically, power-law spectra of decaying two-dimensional turbulence, k−2, and passive scalar, k0.

POWER LAW RELAXATION OF PERIMETER LENGTH OF FRACTAL AGGREGATES

For a realistic aggregate grown under the diffusion control, the fractal scaling holds between two cutoff lengths. These cutoff lengths often control the dynamics of aggregation and relaxation. During thermal annealing, coarsening of the aggregate structure takes place, and the lower cutoff length increases. When the relaxation is limited by kinetics, we show by a simple dimensional argument that the perimeter length (or area) A of the aggregate shrinks in a power law with time t as A(t) ~ t(d–1–D)/2 in a d-dimensional space, where D is the fractal dimension of the aggregate. This prediction is tested by Monte Carlo simulation of the thermal relaxation of a two-dimensional diffusion-limited aggregation.

Models of laser plasma ablation. Part 4. Steadystate theory: collisional absorption flow

The clarification of models of laser ablation by plasma heating is examined using a general dimensional argument and introducing a set of universal parameters. The regime of laser-plasma interaction in which collisional absorption and thermal conduction dominate is examined for spherical systems. Detailed scaling relations are derived for uninhibited and flux-limited thermal conduction. The complete set of regimes for steady spherical flow are examined, and it is found that the most important flows are thin collisional and thick local absorption.