Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell

2008 ◽  
Vol 602 ◽  
pp. 303-326 ◽  
Author(s):  
E. PLAUT ◽  
Y. LEBRANCHU ◽  
R. SIMITEV ◽  
F. H. BUSSE
Keyword(s):  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Quantitative Agreement ◽  
Model Systems ◽  
Geometrical Factor ◽  
Wave Flow ◽  
Nonlinear Frequency ◽  
Two Dimensional ◽  
Reynolds Stresses

A general reformulation of the Reynolds stresses created by two-dimensional waves breaking a translational or a rotational invariance is described. This reformulation emphasizes the importance of a geometrical factor: the slope of the separatrices of the wave flow. Its physical relevance is illustrated by two model systems: waves destabilizing open shear flows; and thermal Rossby waves in spherical shell convection with rotation. In the case of shear-flow waves, a new expression of the Reynolds–Orr amplification mechanism is obtained, and a good understanding of the form of the mean pressure and velocity fields created by weakly nonlinear waves is gained. In the case of thermal Rossby waves, results of a three-dimensional code using no-slip boundary conditions are presented in the nonlinear regime, and compared with those of a two-dimensional quasi-geostrophic model. A semi-quantitative agreement is obtained on the flow amplitudes, but discrepancies are observed concerning the nonlinear frequency shifts. With the quasi-geostrophic model we also revisit a geometrical formula proposed by Zhang to interpret the form of the zonal flow created by the waves, and explore the very low Ekman-number regime. A change in the nature of the wave bifurcation, from supercritical to subcritical, is found.

scholarly journals Propagation of Rossby waves in stratified shear flows

1989 ◽  
Vol 12 (3) ◽  
pp. 547-557
Author(s):  
Palani G. Kandaswamy ◽  
B. Tamil Selvi ◽  
Lokenath Debnath
Keyword(s):  
Wave Equation ◽  
Relative Frequency ◽  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Single Wave ◽  
Beta Plane ◽  
Valve Effect ◽  
The Waves ◽  
Isothermal Atmosphere

A study is made of the propagation of Rossby waves in a stably stratified shear flows. The wave equation for the Rossby waves is derived in an isothermal atmosphere on a beta plane in the presence of a latitudinally sheared zonal flow. It is shown that the wave equation is singular at five critical levels, but the wave absorption takes place only at the two levels where the local relative frequency equals in magnitude to the Brunt Vaisala frequency. This analysis also reveals that these two levels exhibit valve effect by allowing the waves to penetrate them from one side only. The absorption coefficient exp(2πμ)is determined at these levels. Both the group velocity approach and single wave treatment are employed for the investigation of the problem.

Stochastic closure for nonlinear Rossby waves

1977 ◽  
Vol 82 (4) ◽  
pp. 747-765 ◽  
Author(s):  
Greg Holloway ◽  
Myrl C. Hendershott
Keyword(s):  
Rossby Waves ◽  
Functional Dependence ◽  
Quantitative Agreement ◽  
Relative Strength ◽  
Interesting Case ◽  
Test Field ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Rossby Wave Propagation

An extension of the turbulence ‘test-field model’ (Kraichnan 1971 a) is given for two-dimensional flow with Rossby-wave propagation. Such a unified treatment of waves and turbulence is necessary for flows in which the relative strength of nonlinear terms depends upon the length scale considered. We treat the geophysically interesting case in which long, fast Rossby waves propagate substantially without interaction while short Rossby waves are thoroughly dominated by advection. We recover the observations of Rhines (1975) that the tendency of two-dimensional flow to organize energy into larger scales of motion is inhibited by Rossby waves and that an initially isotropic flow develops anisotropy preferring zonal motion. The anisotropy evolves to an equilibrium functional dependence on the isotropic part of the flow spectrum. Theoretical results are found to be in quantitative agreement with numerical flow simulations.

Dynamics and blocking of Rossby waves in quasi-two-dimensional shear flows

JETP Letters ◽  
2015 ◽  
Vol 101 (2) ◽  
pp. 79-84 ◽  
Author(s):  
O. G. Chkhetiani ◽  
M. V. Kalashnik ◽  
G. D. Chagelishvili
Keyword(s):  
Shear Flows ◽  
Rossby Waves ◽  
Two Dimensional

Quantitative Diameter Measurements of Chromatin and TMV Fibers in the Freeze-Dried State

1988 ◽  
Vol 46 ◽  
pp. 170-171
Author(s):  
B. D. Athey ◽  
A. L. Stout ◽  
M. F. Smith ◽  
J. P. Langmore
Keyword(s):  
Reliable Method ◽  
Fiber Diameter ◽  
Quantitative Agreement ◽  
One Dimension ◽  
Fiber Axis ◽  
Two Dimensional ◽  
Fiber Density ◽  
Variable Diameter ◽  
Freeze Dried ◽  
Expected Values

Although there is general agreement that Inactive chromosome fibers consist of helically packed nucleosomes, the pattern of packing is still undetermined. Only one of the proposed models, the crossed-linker model, predicts a variable diameter dependent on the length of DNA between nucleosomes. Measurements of the fiber diameter of negatively-stained and frozen- hydrated- chromatin from Thyone sperm (87bp linker) and Necturus erythrocytes (48bp linker) have been previously reported from this laboratory. We now introduce a more reliable method of measuring the diameters of electron images of fibrous objects. The procedure uses a modified version of the computer program TOTAL, which takes a two-dimensional projection of the fiber density (represented by the micrograph itself) and projects it down the fiber axis onto one dimension. We illustrate this method using high contrast, in-focus STEM images of TMV and chromatin from Thyone and Necturus. The measured diameters are in quantitative agreement with the expected values for the crossed-linker model for chromatin structure

scholarly journals Influence of a Standing Wave Flow-Field on the Dynamics of a Spray Diffusion Flame

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 27
Author(s):  
J. Barry Greenberg ◽  
David Katoshevski
Keyword(s):  
Liquid Phase ◽  
Flow Field ◽  
Standing Wave ◽  
Diffusion Flame ◽  
Stokes Number ◽  
Flame Height ◽  
Wave Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
First Time

A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid phase, the use of a small Stokes number as the perturbation parameater enables a solution of the governing equations to be developed. Influence of the standing wave flow-field on droplet grouping is described by a specially constructed modification of the vaporization Damkohler number. Instantaneous flame front shapes are found via a solution for the usual Schwab–Zeldovitch parameter. Numerical results obtained from the analytical solution uncover the strong bearing that droplet grouping, induced by the standing wave flow-field, can have on flame height, shape, and type (over- or under-ventilated) and on the existence of multiple flame fronts.

Waves and turbulence on a beta-plane

1975 ◽  
Vol 69 (3) ◽  
pp. 417-443 ◽  
Author(s):  
Peter B. Rhines
Keyword(s):  
Weak Interaction ◽  
Initial Conditions ◽  
Computer Experiments ◽  
Zonal Flow ◽  
Similarity Solutions ◽  
Large Reynolds Number ◽  
Two Dimensional ◽  
Homogeneous Fluid ◽  
Restoring Force ◽  
Model Equations

Two-dimensional eddies in a homogeneous fluid at large Reynolds number, if closely packed, are known to evolve towards larger scales. In the presence of a restoring force, the geophysical beta-effect, this cascade produces a field of waves without loss of energy, and the turbulent migration of the dominant scale nearly ceases at a wavenumber kβ = (β/2U)½ independent of the initial conditions other than U, the r.m.s. particle speed, and β, the northward gradient of the Coriolis frequency.The conversion of turbulence into waves yields, in addition, more narrowly peaked wavenumber spectra and less fine-structure in the spatial maps, while smoothly distributing the energy about physical space.The theory is discussed, using known integral constraints and similarity solutions, model equations, weak-interaction wave theory (which provides the terminus for the cascade) and other linearized instability theory. Computer experiments with both finite-difference and spectral codes are reported. The central quantity is the cascade rate, defined as \[ T = 2\int_0^{\infty} kF(k)dk/U^3\langle k\rangle , \] where F is the nonlinear transfer spectrum and 〈k〉 the mean wavenumber of the energy spectrum. (In unforced inviscid flow T is simply U−1d〈k〉−1/dt, or the rate at which the dominant scale expands in time t.) T is shown to have a mean value of 3·0 × 10−2 for pure two-dimensional turbulence, but this decreases by a factor of five at the transition to wave motion. We infer from weak-interaction theory even smaller values for k [Lt ] kβ.After passing through a state of propagating waves, the homogeneous cascade tends towards a flow of alternating zonal jets which, we suggest, are almost perfectly steady. When the energy is intermittent in space, however, model equations show that the cascade is halted simply by the spreading of energy about space, and then the end state of a zonal flow is probably not achieved.The geophysical application is that the cascade of pure turbulence to large scales is defeated by wave propagation, helping to explain why the energy-containing eddies in the ocean and atmosphere, though significantly nonlinear, fail to reach the size of their respective domains, and are much smaller. For typical ocean flows, $k_{\beta}^{-1} = 70\,{\rm km} $, while for the atmosphere, $k_{\beta}^{-1} = 1000\,{\rm km}$. In addition the cascade generates, by itself, zonal flow (or more generally, flow along geostrophic contours).

scholarly journals Оптическая спектроскопия крамерсовских дублетов иона Er-=SUP=-3+-=/SUP=- в двумерном фрустированном магнетике Cu-=SUB=-3-=/SUB=-Er(SeO-=SUB=-3-=/SUB=-)-=SUB=-2-=/SUB=-O-=SUB=-2-=/SUB=-Cl

2021 ◽  
Vol 129 (1) ◽  
pp. 51
Author(s):  
С.А. Климин ◽  
П.С. Бердоносов ◽  
Е.С. Кузнецова
Keyword(s):  
Magnetic Phase ◽  
Magnetic Ordering ◽  
Spectral Lines ◽  
Spin Reorientation ◽  
Model Systems ◽  
Magnetic Phase Transitions ◽  
Two Dimensional ◽  
Frustrated Magnetism ◽  
Weak Magnetic Fields ◽  
Erbium Ion

Francisites Cu3M(YO3)2O2X (M = Bi or rare earth, Y = Se, Te, X = Br, Cl, I) attract grate attention due to their interesting magnetic properties, such as metamagnetic transitions in relatively weak magnetic fields, magnetic phase transitions including spin reorientation, as well as model systems for studying two-dimensional and frustrated magnetism. In this work, a low-temperature optical spectroscopic study is presented of erbium francisite Cu3Er(SeO3)2O2Cl. The observed splittings of the spectral lines corresponding to the f f transitions in the Kramers Er3+ ion unambiguously indicates the magnetic ordering of the crystal at a temperature TN = 37.5 K. The temperature dependence of the splitting of the main doublet of the erbium ion is determined. The contribution of erbium to the heat capacity and magnetic susceptibility of Cu3Er(SeO3)2O2Cl is calculated.

scholarly journals Shock Structures Using the OBurnett Equations in Combination with the Holian Conjecture

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 427
Author(s):  
Ravi Sudam Jadhav ◽  
Amit Agrawal
Keyword(s):  
Transport Coefficients ◽  
Quantitative Agreement ◽  
Upstream Region ◽  
Shock Propagation ◽  
Wave Flow ◽  
Temperature Relation ◽  
Downstream Region ◽  
Shock Profiles ◽  
Mach Numbers ◽  
Modified Theory

In the present work, we study the normal shock wave flow problem using a combination of the OBurnett equations and the Holian conjecture. The numerical results of the OBurnett equations for normal shocks established several fundamental aspects of the equations such as the thermodynamic consistency of the equations, and the existence of the heteroclinic trajectory and smooth shock structures at all Mach numbers. The shock profiles for the hydrodynamic field variables were found to be in quantitative agreement with the direct simulation Monte Carlo (DSMC) results in the upstream region, whereas further improvement was desirable in the downstream region of the shock. For the discrepancy in the downstream region, we conjecture that the viscosity–temperature relation (μ∝Tφ) needs to be modified in order to achieve increased dissipation and thereby achieve better agreement with the benchmark results in the downstream region. In this respect, we examine the Holian conjecture (HC), wherein transport coefficients (absolute viscosity and thermal conductivity) are evaluated using the temperature in the direction of shock propagation rather than the average temperature. The results of the modified theory (OBurnett + HC) are compared against the benchmark results and we find that the modified theory improves upon the OBurnett results, especially in the case of the heat flux shock profile. We find that the accuracy gain is marginal at lower Mach numbers, while the shock profiles are described better using the modified theory for the case of strong shocks.

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