scholarly journals Dynamics of tilted atmospheric vortices under asymmetric diabatic heating

2021 ◽  
Author(s):  
Tom Dörffel ◽  
Ariane Papke ◽  
Rupert Klein ◽  
Natalia Ernst ◽  
Piotr K. Smolarkiewicz
Keyword(s):  
Diabatic Heating ◽  
Numerical Solutions ◽  
Asymptotic Methods ◽  
Potential Temperature ◽  
Three Dimensional ◽  
Coriolis Parameter ◽  
Order Unity ◽  
Steering Mechanism ◽  
Theoretical Predictions ◽  
Atmospheric Vortices

AbstractPäschke et al. (J Fluid Mech, 2012) studied the nonlinear dynamics of strongly tilted vortices subject to asymmetric diabatic heating by asymptotic methods. They found, inter alia, that an azimuthal Fourier mode 1 heating pattern can intensify or attenuate such a vortex depending on the relative orientation of the tilt and the heating asymmetries. The theory originally addressed the gradient wind regime which, asymptotically speaking, corresponds to vortex Rossby numbers of order unity in the limit. Formally, this restricts the applicability of the theory to rather weak vortices. It is shown below that said theory is, in contrast, uniformly valid for vanishing Coriolis parameter and thus applicable to vortices up to low hurricane strengths. An extended discussion of the asymptotics as regards their physical interpretation and their implications for the overall vortex dynamics is also provided in this context. The paper’s second contribution is a series of three-dimensional numerical simulations examining the effect of different orientations of dipolar diabatic heating on idealized tropical cyclones. Comparisons with numerical solutions of the asymptotic equations yield evidence that supports the original theoretical predictions of Päschke et al. In addition, the influence of asymmetric diabatic heating on the time evolution of the vortex centerline is further analyzed, and a steering mechanism that depends on the orientation of the heating dipole is revealed. Finally, the steering mechanism is traced back to the correlation of dipolar perturbations of potential temperature, induced by the vortex tilt, and vertical velocity, for which diabatic heating not necessarily needs to be responsible, but which may have other origins.

scholarly journals The Three-Dimensional Steady Circulation in a Homogenous Ocean Induced by a Stationary Hurricane

2010 ◽  
Vol 40 (7) ◽  
pp. 1441-1457 ◽  
Author(s):  
Zhu Min Lu ◽  
Rui Xin Huang
Keyword(s):  
Analytical Solution ◽  
General Circulation ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Circulation Model ◽  
Ocean General Circulation Model ◽  
Coriolis Parameter ◽  
Middle Latitudes ◽  
Oceanic Response ◽  
Stratified Ocean

Abstract Based on the classical Ekman layer theory, a simple analytical solution of the steady flow induced by a stationary hurricane in a homogenous ocean is discussed. The model consists of flow converging in an inward spiral in the deeper layer and diverging in the upper layer. The simple analytical model indicates that both the upwelling flux and the horizontal transport increase linearly with increasing radius of maximum winds. Furthermore, they both have a parabolic relationship with the maximum wind speed. The Coriolis parameter also affects the upwelling flux: the response to a hurricane is stronger at low latitudes than that at middle latitudes. Numerical solutions based on a regional version of an ocean general circulation model are similar to the primary results obtained through the analytical solution. Thus, the simplifications made in formulating the analytical solution are reasonable. Although the analytical solution in this paper is sought for a rather idealized ocean, it can help to make results from the more complicated numerical model understandable. These conceptual models provide a theoretical limit structure of the oceanic response to a moving hurricane over a stratified ocean.

scholarly journals A New Surface Model for β-Plane Turbulence

2007 ◽  
Vol 64 (7) ◽  
pp. 2717-2725 ◽  
Author(s):  
Iordanka N. Panayotova
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Potential Temperature ◽  
Three Dimensional ◽  
Wave Turbulence ◽  
Surface Model ◽  
Surface Cooling ◽  
Rigid Boundary ◽  
Coriolis Parameter ◽  
Decaying Turbulence

Abstract This paper introduces a new numerical model for studying wave–turbulence interactions in a continuously stratified rotating flow, having a uniform potential vorticity and a rigid boundary. The meridional variation in the Coriolis parameter (β effect), a channel geometry, and the first-order nonlinear terms in a small Rossby number expansion are included into the surface quasigeostrophic dynamics. The model contains important dynamical characteristics of three-dimensional flows such as advection by ageostrophic winds, and stretching and tilting of relative vorticity. Nevertheless, it has the computational economy of two-dimensional flows. Long-term direct numerical simulations are performed for decaying turbulence arising from random initial conditions. In addition to the formation of steady zonal jets, frequently reported as a possible end state under the β effect, this model exhibits several other realistic physical effects that were lacking in the previously studied β-plane models for wave–turbulence interactions. There is a significant contrast in the spatial and time scales of the formed eddies, resulting in high meridional asymmetry of the flow. Mean surface cooling and persistent large-scale blocking eddies are observed as well. The surface potential temperature variance spectrum exhibits a well-resolved k−5/3 inertial range.

scholarly journals Motion and structure of atmospheric mesoscale baroclinic vortices: dry air and weak environmental shear

2012 ◽  
Vol 701 ◽  
pp. 137-170 ◽  
Author(s):  
Eileen Päschke ◽  
Patrik Marschalik ◽  
Antony Z. Owinoh ◽  
Rupert Klein
Keyword(s):  
Evolution Equations ◽  
Potential Temperature ◽  
Three Dimensional ◽  
Present Theory ◽  
Vertical Shear ◽  
Order Unity ◽  
Dry Air ◽  
Wind Speeds ◽  
Axisymmetric Vortex ◽  
Baroclinic Vortices

AbstractA strongly tilted, nearly axisymmetric vortex in dry air with asymmetric diabatic heating is analysed here by matched asymptotic expansions. The vortex is in gradient wind balance, with vortex Rossby numbers of order unity, and embedded in a quasi-geostrophic (QG) background wind with weak vertical shear. With wind speeds of $60{{\ndash}}120~\mathrm{km} ~{\mathrm{h} }^{\ensuremath{-} 1} $, such vortices correspond to tropical storms or nascent hurricanes according to the Saffir–Simpson scale. For asymmetric heating, nonlinear coupling of the evolution equations for the vortex tilt, its core structure, and its influence on the QG background is found. The theory compares well with the established linear theory of precessing quasi-modes of atmospheric vortices, and it corroborates the relationship between vortex tilt and asymmetric potential temperature and vertical velocity patterns as found by Jones (Q. J. R. Meteorol. Soc., vol. 121, 1995, pp. 821–851) and Frank & Ritchie (Mon. Weath. Rev., vol. 127, 1999, pp. 2044–2061) in simulations of adiabatic tropical cyclones. A relation between the present theory and the local induction approximation for three-dimensional slender vortex filaments is established.

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

scholarly journals Prandtl Number in Classical Hard-Sphere and One-Component Plasma Fluids

Molecules ◽  
2021 ◽  
Vol 26 (4) ◽  
pp. 821
Author(s):  
Sergey Khrapak ◽  
Alexey Khrapak
Keyword(s):  
Prandtl Number ◽  
Hard Sphere ◽  
Solid Phase ◽  
Freezing Point ◽  
Three Dimensional ◽  
Order Unity ◽  
Strongly Coupled ◽  
Dielectric Fluids ◽  
Weakly Coupled ◽  
Component Plasma

The Prandtl number is evaluated for the three-dimensional hard-sphere and one-component plasma fluids, from the dilute weakly coupled regime up to a dense strongly coupled regime near the fluid-solid phase transition. In both cases, numerical values of order unity are obtained. The Prandtl number increases on approaching the freezing point, where it reaches a quasi-universal value for simple dielectric fluids of about ≃1.7. Relations to two-dimensional fluids are briefly discussed.

scholarly journals A Note on the Numerical Representation of Surface Dynamics in Quasigeostrophic Turbulence: Application to the Nonlinear Eady Model

2009 ◽  
Vol 66 (4) ◽  
pp. 1063-1068 ◽  
Author(s):  
Ross Tulloch ◽  
K. Shafer Smith
Keyword(s):  
Numerical Models ◽  
Buoyancy Frequency ◽  
Complete Suppression ◽  
Numerical Representation ◽  
Vertical Resolution ◽  
Surface Dynamics ◽  
Coriolis Parameter ◽  
Theoretical Predictions ◽  
Vertical Grid ◽  
Similar Restriction

Abstract The quasigeostrophic equations consist of the advection of linearized potential vorticity coupled with advection of temperature at the bounding upper and lower surfaces. Numerical models of quasigeostrophic flow often employ greater (scaled) resolution in the horizontal than in the vertical (the two-layer model is an extreme example). In the interior, this has the effect of suppressing interactions between layers at horizontal scales that are small compared to Nδz/f (where δz is the vertical resolution, N the buoyancy frequency, and f the Coriolis parameter). The nature of the turbulent cascade in the interior is, however, not fundamentally altered because the downscale cascade of potential enstrophy in quasigeostrophic turbulence and the downscale cascade of enstrophy in two-dimensional turbulence (occurring layerwise) both yield energy spectra with slopes of −3. It is shown here that a similar restriction on the vertical resolution applies to the representation of horizontal motions at the surfaces, but the penalty for underresolving in the vertical is complete suppression of the surface temperature cascade at small scales and a corresponding artificial steepening of the surface energy spectrum. This effect is demonstrated in the nonlinear Eady model, using a finite-difference representation in comparison with a model that explicitly advects temperature at the upper and lower surfaces. Theoretical predictions for the spectrum of turbulence in the nonlinear Eady model are reviewed and compared to the simulated flows, showing that the latter model yields an accurate representation of the cascade dynamics. To accurately represent dynamics at horizontal wavenumber K in the vertically finite-differenced model, it is found that the vertical grid spacing must satisfy δz ≲ 0.3f/(NK); at wavenumbers K > 0.3f/(Nδz), the spectrum of temperature variance rolls off rapidly.

Large-Debye-distance effects in a homogeneous plasma

1989 ◽  
Vol 41 (3) ◽  
pp. 493-516 ◽  
Author(s):  
Jan Scheffel ◽  
Bo Lehnert
Keyword(s):  
Normal Mode ◽  
Numerical Solutions ◽  
Normal Mode Analysis ◽  
Distribution Functions ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Order Unity ◽  
Phase Velocities ◽  
Standard Normal ◽  
Velocity Distribution Functions

The classical phenomenon of electron plasma oscillations has been investigated from new aspects. The applicability of standard normal-mode analysis of plasma perturbations has been judged from comparisons with exact numerical solutions to the linearized initial-value problem. We consider both Maxwellian and non-Maxwellian velocity distributions. Emphasis is on perturbations for which αλD is of order unity, where α is the wavenumber and λD the Debye distance. The corresponding large-Debye-distance (LDD) damping is found to substantially dominate over Landau damping. This limits the applicability of normal-mode analysis of non-Maxwellian distributions. The physics of LDD damping and its close connection to large-Larmor-radius (LLR) damping is discussed. A major discovery concerns perturbations of plasmas with non-Maxwellian, bump-in-tail, velocity distribution functions f0(ω). For sufficiently large αλD (of order unity) the plasma responds by damping perturbations that are initially unstable in the Landau sense, i.e. with phase velocities initially in the interval where df0/dw > 0. It is found that the plasma responds through shifting the phase velocity above the upper velocity limit of this interval. This is shown to be due to a resonance with the drifting electrons of the bump, and explains the Penrose criterion.

Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
D. Zhou ◽  
S. H. Lo
Keyword(s):  
Cross Section ◽  
Chebyshev Polynomial ◽  
Numerical Solutions ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Cylindrical Domain ◽  
Linear Elasticity Theory ◽  
Boundary Functions ◽  
Polynomial Series

The three-dimensional (3D) free vibration of twisted cylinders with sectorial cross section or a radial crack through the height of the cylinder is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. A simple coordinate transformation is applied to map the twisted cylindrical domain into a normal cylindrical domain. The product of a triplicate Chebyshev polynomial series along with properly defined boundary functions is selected as the admissible functions. An eigenvalue matrix equation can be conveniently derived through a minimization process by the Rayleigh–Ritz method. The boundary functions are devised in such a way that the geometric boundary conditions of the cylinder are automatically satisfied. The excellent property of Chebyshev polynomial series ensures robustness and rapid convergence of the numerical computations. The present study provides a full vibration spectrum for thick twisted cylinders with sectorial cross section, which could not be determined by 1D or 2D models. Highly accurate results presented for the first time are systematically produced, which can serve as a benchmark to calibrate other numerical solutions for twisted cylinders with sectorial cross section. The effects of height-to-radius ratio and twist angle on frequency parameters of cylinders with different subtended angles in the sectorial cross section are discussed in detail.

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