Elliptic instability in the Lagrangian-averaged Euler-Boussinesq-alpha equations

We examine the effects of turbulence on elliptic instability of rotating stratified incompressible flows, in the context of the Lagragian-averaged Euler-Boussinesq-alpha, or \laeba, model of turbulence. We find that the \laeba model alters the instability in a variety of ways for fixed Rossby number and Brunt-V\"ais\"al\"a frequency. First, it alters the location of the instability domains in the $(\gamma,\cos\theta)-$parameter plane, where $\theta$ is the angle of incidence the Kelvin wave makes with the axis of rotation and $\gamma$ is the eccentricity of the elliptic flow, as well as the size of the associated Lyapunov exponent. Second, the model shrinks the width of one instability band while simultaneously increasing another. Third, the model introduces bands of unstable eccentric flows when the Kelvin wave is two-dimensional. We introduce two similarity variables--one is a ratio of the Brunt-V\"ais\"al\"a frequency to the model parameter $\Upsilon_0 = 1+\alpha^2\beta^2$, and the other is the ratio of the adjusted inverse Rossby number to the same model parameter. Here, $\alpha$ is the turbulence correlation length, and $\beta$ is the Kelvin wave number. We show that by adjusting the Rossby number and Brunt-V\"ais\"al\"a frequency so that the similarity variables remain constant for a given value of $\Upsilon_0$, turbulence has little effect on elliptic instability for small eccentricities $(\gamma \ll 1)$. For moderate and large eccentricities, however, we see drastic changes of the unstable Arnold tongues due to the \laeba model.Comment: 23 pages (sigle spaced w/figure at the end), 9 figures--coarse quality, accepted by Phys. Fluid

Two-component {CH} system: Inverse Scattering, Peakons and Geometry

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data for CH2.Comment: 22 pages, 3 figures, draft, please send comment

Emissivity for CO_2 at Elevated Pressures

Total absorptivity measurements have been carried out at room temperature as a function of partial pressure of CO_2 and of total pressure using nitrogen as pressurizing gas

Multi-component generalizations of the {CH} equation: Geometrical Aspects, Peakons and Numerical Examples

The Lax pair formulation of the two-component Camassa-Holm equation (CH2) is generalized to produce an integrable multi-component family, CH(n,k), of equations with $n$ components and $1\le |k|\le n$ velocities. All of the members of the CH(n,k) family show fluid-dynamics properties with coherent solitons following particle characteristics. We determine their Lie-Poisson Hamiltonian structures and give numerical examples of their soliton solution behaviour. We concentrate on the CH(2,k) family with one or two velocities, including the CH(2,-1) equation in the Dym position of the CH2 hierarchy. A brief discussion of the CH(3,1) system reveals the underlying graded Lie-algebraic structure of the Hamiltonian formulation for CH(n,k) when $n\ge3$.Comment: 19 pages 5 figures comments are welcom

The free rigid body dynamics: generalized versus classic

In this paper we analyze the normal forms of a general quadratic Hamiltonian system defined on the dual of the Lie algebra $\mathfrak{o}(K)$ of real $K$ - skew - symmetric matrices, where $K$ is an arbitrary $3\times 3$ real symmetric matrix. A consequence of the main results is that any first-order autonomous three-dimensional differential equation possessing two independent quadratic constants of motion which admits a positive/negative definite linear combination, is affinely equivalent to the classical "relaxed" free rigid body dynamics with linear controls.Comment: 12 page

Acoustic radiation patterns for a source in a hard-walled unflanged circular duct

Acoustic radiation patterns are measured over a 320 deg arc for a point source in a finite length, hard walled, unflanged circular duct. The measured results are compared with computed results which are based on the Wiener-Hopf solution for radiation from a semi-infinite unflanged duct. Measurements and computations are presented for frequencies slightly below and slightly above each of the first four higher order radial mode cutoff frequencies. It is found that the computed and measured patterns show better agreement below the mode cut-off frequencies than above and that the agreement is better at lower frequencies that at higher frequencies. The computed radiation patterns do not show fine lobes which are caused by diffraction from the back end of the duct

Applications of adenine nucleotide measurements in oceanography

The methodology involved in nucleotide measurements is outlined, along with data to support the premise that ATP concentrations in microbial cells can be extrapolated to biomass parameters. ATP concentrations in microorganisms and nucleotide analyses are studied

Continuous and discrete Clebsch variational principles

The Clebsch method provides a unifying approach for deriving variational principles for continuous and discrete dynamical systems where elements of a vector space are used to control dynamics on the cotangent bundle of a Lie group \emph{via} a velocity map. This paper proves a reduction theorem which states that the canonical variables on the Lie group can be eliminated, if and only if the velocity map is a Lie algebra action, thereby producing the Euler-Poincar\'e (EP) equation for the vector space variables. In this case, the map from the canonical variables on the Lie group to the vector space is the standard momentum map defined using the diamond operator. We apply the Clebsch method in examples of the rotating rigid body and the incompressible Euler equations. Along the way, we explain how singular solutions of the EP equation for the diffeomorphism group (EPDiff) arise as momentum maps in the Clebsch approach. In the case of finite dimensional Lie groups, the Clebsch variational principle is discretised to produce a variational integrator for the dynamical system. We obtain a discrete map from which the variables on the cotangent bundle of a Lie group may be eliminated to produce a discrete EP equation for elements of the vector space. We give an integrator for the rotating rigid body as an example. We also briefly discuss how to discretise infinite-dimensional Clebsch systems, so as to produce conservative numerical methods for fluid dynamics

The Meaning of the Maxwell Field Equations

Author Institution: 6836 W. Grace St., Chicago 34, IllinoisThe objective here is to emphasize the derivation of the electromagnetic field equations from simple, understandable physical considerations, instead of regarding them as arbitrary assumptions. The factors of symmetry, continuity, and propagation determine these equations. These are large-scale attributes of field structure, so we can readily recognize and accept the fact that small-scale structure involves additional factors which do not appear in these equations