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Oct 2009

Volume 21, Issue 10, Articles (10xxxx)

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Phys. Fluids 21, 104102 (2009); http://dx.doi.org/10.1063/1.3243976 (13 pages)

Denis Martinand, Eric Serre, and Richard M. Lueptow
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back to top Geophysical Flows

Nonlinear development of inertial instability in a barotropic shear

Riwal Plougonven and Vladimir Zeitlin

Phys. Fluids 21, 106601 (2009); http://dx.doi.org/10.1063/1.3242283 (15 pages) | Cited 1 time

Online Publication Date: 9 October 2009

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Inertial instability is investigated numerically in a two-dimensional setting in order to understand its nonlinear stage and saturation. To focus on fundamental mechanisms, a simple barotropic shear U(y) = tanh y on the f-plane is considered. The linear stability problem is first solved analytically, and the analytical solutions are used to benchmark numerical simulations. A simple scenario of the nonlinear development of the most unstable mode was recurrently observed in the case of substantial diffusivity: while reaching finite amplitude the unstable mode spreads laterally, distorting the initially vertical instability zone. This process produces strong vertical gradients which are subsequently annihilated by diffusion, making the flow barotropic again but with the shear spread over a wider region. In the course of such evolution, unexpectedly, strong negative absolute vorticity anomalies are produced. In weakly diffusive simulations, the horizontal spreading of the unstable motions and the enhancement of the anticyclonic vorticity extremum persist, but small-scale motions/instabilities render the flow considerably more complex. It is known that the barotropic component of the final state can be predicted from the conservation of momentum. Our simulations confirm the relevance of this simple prediction in the cases investigated regardless of resolution and diffusion. The baroclinic component of the final state is also analyzed and three types of structures are identified: persistent stationary stratification layers, subinertial waves trapped in the anticyclonic shear, and freely propagating inertia-gravity waves. The subinertial waves and the stratification staircase have clear signatures and can therefore help to identify the regions that have undergone inertial instability.
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52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.35.We Plasma vorticity
52.65.-y Plasma simulation

Waves on a columnar vortex in a strongly stratified fluid

Paul Billant and Stéphane Le Dizès

Phys. Fluids 21, 106602 (2009); http://dx.doi.org/10.1063/1.3248366 (9 pages) | Cited 4 times

Online Publication Date: 12 October 2009

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This paper investigates the discrete bounded waves sustained by a vertical columnar Rankine vortex in a strongly stratified fluid. We show that these waves are very different from their well-known counterpart in homogeneous fluid (Kelvin vortex waves); they exist only for nonzero azimuthal wavenumber m, their frequency lies in the interval [0,mΩ] (Ω is the angular velocity in the vortex core) and they are unstable because of an outward radiation from the vortex. The instability mechanism is explained in terms of an over-reflection phenomenon by means of a Wentzel–Kramers–Brillouin–Jeffreys analysis for large axial wavenumber.
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47.55.Hd Stratified flows
47.32.-y Vortex dynamics; rotating fluids
47.35.-i Hydrodynamic waves
47.20.-k Flow instabilities

A Lagrangian approach to droplet condensation in atmospheric clouds

Ryan S. R. Sidin, Rutger H. A. IJzermans, and Michael W. Reeks

Phys. Fluids 21, 106603 (2009); http://dx.doi.org/10.1063/1.3244646 (16 pages) | Cited 3 times

Online Publication Date: 23 October 2009

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The condensation of microdroplets in model systems, reminiscent of atmospheric clouds, is investigated numerically and analytically. Droplets have been followed through a synthetic turbulent flow field composed of 200 random Fourier modes, with wave numbers ranging from the integral scales [O(102 m)] to the Kolmogorov scales [O(10−3 m)]. As the influence of all turbulence scales is investigated, direct numerical simulation is not practicable, making kinematic simulation the only viable alternative. Two fully Lagrangian droplet growth models are proposed: a one-way coupled model in which only adiabatic cooling of a rising air parcel is considered, and a two-way coupled model which also accounts for the effects of local vapor depletion and latent heat release. The simulations with the simplified model show that the droplet size distribution becomes broader in the course of time and resembles a Gaussian distribution. This result is supported by a theoretical analysis which relates the droplet surface-area distribution to the dispersion of droplets in the turbulent flow. Although the droplet growth is stabilized by vapor depletion and latent heat release in the two-way coupled model, the calculated droplet size distributions are still very broad. The present results may provide an explanation for the rapid growth of droplets in the coalescence stage of rain formation, as broad size distributions are likely to lead to enhanced collision rates between droplets.
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47.55.df Breakup and coalescence
64.70.fm Thermodynamics studies of evaporation and condensation
92.60.Jq Water in the atmosphere
92.60.hk Convection, turbulence, and diffusion
47.27.tb Turbulent diffusion
47.11.-j Computational methods in fluid dynamics

On fully nonlinear, vertically trapped wave packets in a stratified fluid on the f-plane

M. Stastna, F. J. Poulin, K. L. Rowe, and C. Subich

Phys. Fluids 21, 106604 (2009); http://dx.doi.org/10.1063/1.3253400 (13 pages) | Cited 3 times

Online Publication Date: 29 October 2009

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The ubiquity of solitary and solitarylike internal waves in the coastal ocean has been recognized for some time. Recent theoretical studies of a strongly nonlinear, weakly nonhydrostatic set of layer-averaged model equations have predicted that rotation, for example, on the f-plane, can lead to the decay and subsequent reemergence of internal solitary waves. We reconsider this problem using high resolution numerical simulations of the rotating stratified Euler equations. We find that in certain cases the initial disturbances indeed fission into nonlinear wave packets, with the constituent waves making up the wave packet being, in themselves, nonlinear. However, for typical coastal ocean parameters this only occurs at rotation rates higher than those on Earth on the time scales we are able to simulate. We confirm, using the Dubreil–Jacotin–Long equation, that the vertical structure of the wave-induced currents is well predicted by the fully nonlinear theory of nonrotating internal solitary waves and that weakly nonlinear Korteweg–de Vries equation-based theory fails to describe this structure accurately. Subsequently, we consider flat-crested solitary waves that allow us to fix the wave amplitude while varying the horizontal wavelength. We find that as the waves’ horizontal extent nears the baroclinic Rossby radius more energy is deposited into the wave tail. However, no wave overtaking is observed, and an explanation for this fact is proposed. Finally, we discuss the effects of the horizontal component of the rotation vector and derive an exact equation for rotation modified waves near the equator. This equation demonstrates that in this situation, rotation modifies the structure of the fully nonlinear waves but does not lead to solitary wave decay.
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92.10.Hm Ocean waves and oscillations
47.32.Ef Rotating and swirling flows
47.35.Fg Solitary waves
47.55.Hd Stratified flows
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