From quasi-geostrophic to strongly nonlinear monopolar vortices in a paraboloidal shallow-water-layer experiment

1998 ◽  
Vol 356 ◽  
pp. 1-24 ◽  
Author(s):  
A. STEGNER ◽  
V. ZEITLIN
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Water Layer ◽  
Nonlinear Regime ◽  
Wave Radiation ◽  
Specific Data ◽  
Strongly Nonlinear ◽  
Beta Effect ◽  
Rotating Shallow Water ◽  
Acquisition Technique

We perform a detailed experimental study of large-scale vortices propagating in the rotating shallow-water layer in a paraboloidal vessel. A specific data acquisition technique is used in order to ensure precise measurements of the free-surface elevation. We find two qualitatively different types of vortex behaviour controlled by the relative elevation value. For small elevations we observe a standard quasi-geostrophic pattern with an asymmetric secondary circulation around an initially symmetric vortex which leads to a meridional drift and Rossby wave radiation. This type of behaviour is exhibited by both cyclonic and anticyclonic vortices. For relative elevations larger than 1 (nonlinear regime) the necessarily anticyclonic vortices are drifting strictly zonally maintaining their circular symmetry during the viscous decay. By varying the initial latitude of the vortex we were able to check that in the nonlinear regime the vortex lifetime is not sensitive to the beta-effect, while it is the case in the quasi-geostrophic regime. In the same way we show that the observed difference in cyclone–anticyclone lifetimes is not influenced by the beta-effect.

scholarly journals Improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Water Vapour ◽  
Large Scale ◽  
Precipitable Water ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Atmospheric Motions ◽  
Rotating Shallow Water

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

scholarly journals Influence of condensation and latent heat release upon barotropic and baroclinic instabilities of vortices in rotating shallow water f -plane model

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Heat Release ◽  
Shallow Water ◽  
Latent Heat ◽  
Large Scale ◽  
Lower Layer ◽  
Passive Scalar ◽  
Water Model ◽  
Moist Convection ◽  
Latent Heat Release ◽  
Rotating Shallow Water

Analysis of the influence of condensation and related latent heat release upon developing barotropic and baroclinic instabilities of large-scale low Rossby-number shielded vortices on the f - plane is performed within the moist-convective rotating shallow water model, in its barotropic (one-layer) and baroclinic (two-layer) versions. Numerical simulations with a high-resolution well-balanced finite-volume code, using a relaxation parameterisation for condensation, are made. Evolution of the instability in four different environments, with humidity (i) behaving as passive scalar, (ii) subject to condensation beyond a saturation threshold, (iii) sub-ject to condensation and evaporation, with two different parameterisations of the latter, are inter-ompared.The simulations are initialised with unstable modes determined from the detailed linear stability analysis in the “dry” version of the model. In a configuration corresponding to low-level mid-latitude atmospheric vortices, it is shown that the known scenario of evolution of barotropically unstable vortices, consisting information of a pair of dipoles (“dipolar breakdown”) is substantially modified by condensation and related moist convection, especially in the presence of surface evaporation. No enhancement of the instability due to precipitation was detected in this case. Cyclone-anticyclone asymmetry with respect to sensitivity tothe moist effects is evidenced. It is shown that inertia-gravity wave emission during the vortex evolution is enhanced by the moist effects. In the baroclinic configuration corresponding to idealised cut-off lows in the atmosphere, it is shown that the azimuthal structure of the leading unstable mode is sensitive to the details of stratification. Scenarios of evolution are completely different for different azimuthal structures, one leading to dipolar breaking, and another to tripole formation. The effects of moisture considerably enhance the perturbations in the lower layer, especially in the tripole formation scenario.

Introduction

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Rotating Shallow Water

A brief introduction to the main philosophy of the book is given, explaining how the shallowness of large-scale motions in the atmosphere and ocean can be exploited in modelling, thus justifying the rotating shallow-water approach adopted throughout the book.

scholarly journals Small-scale instabilities of an island wake flow in a rotating shallow-water layer

2010 ◽  
Vol 49 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Samuel Teinturier ◽  
Alexandre Stegner ◽  
Henri Didelle ◽  
Samuel Viboud
Keyword(s):  
Shallow Water ◽  
Water Layer ◽  
Wake Flow ◽  
Small Scale ◽  
Rotating Shallow Water ◽  
Island Wake

scholarly journals A note on relative equilibria in a rotating shallow water layer

2013 ◽  
Vol 724 ◽  
pp. 695-703 ◽  
Author(s):  
Hamid Ait Abderrahmane ◽  
Mohamed Fayed ◽  
Hoi Dick Ng ◽  
Georgios H. Vatistas
Keyword(s):  
Particle Image Velocimetry ◽  
Shallow Water ◽  
Particle Image ◽  
Point Vortex ◽  
Water Layer ◽  
Relative Equilibria ◽  
Experimental Dataset ◽  
Vortex Theory ◽  
Image Velocimetry ◽  
Rotating Shallow Water

AbstractRelative equilibria of two and three satellite vortices in a rotating shallow water layer have been recorded via particle image velocimetry (PIV) and their autorotation speed was estimated. This study shows that these equilibria retain the fundamental characteristics of Kelvin’s equilibria, and could be adequately described by the classical idealized point vortex theory. The same conclusion can also be inferred using the experimental dataset of Bergmann et al. (J. Fluid Mech., vol. 679, 2011, pp. 415–431; J. Fluid Mech., vol. 691, 2012, pp. 605–606) if the assigned field’s contribution to pattern rotation is included.

Theoretical and experimental investigation of the structure of azimuthal source–sink flow in a rotating shallow water layer

2008 ◽  
Vol 8 (4) ◽  
pp. 313-331
Author(s):  
M. V. Kalashnik ◽  
S. J. Tsakadze ◽  
V. O. Kakhiani ◽  
K. I. Patarashvili ◽  
M. A. Zhvania ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Shallow Water ◽  
Water Layer ◽  
Rotating Shallow Water ◽  
Source Sink

Stability of jet flows in a rotating shallow water layer

2016 ◽  
Vol 51 (5) ◽  
pp. 606-619 ◽  
Author(s):  
M. V. Kalashnik ◽  
O. G. Chkhetiani
Keyword(s):  
Shallow Water ◽  
Water Layer ◽  
Jet Flows ◽  
Rotating Shallow Water

scholarly journals Small-scale instabilities of an island wake flow in a rotating shallow-water layer

2010 ◽  
Vol 111 ◽  
pp. 1-24
Author(s):  
Samuel Teinturier ◽  
Alexandre Stegner ◽  
Henri Didelle ◽  
Samuel Viboud
Keyword(s):  
Shallow Water ◽  
Water Layer ◽  
Wake Flow ◽  
Small Scale ◽  
Rotating Shallow Water ◽  
Island Wake

scholarly journals Rotating shallow water flow under location uncertainty with a structure-preserving discretization

2021 ◽  
Author(s):  
Rüdiger Brecht ◽  
Long Li ◽  
Werner Bauer ◽  
Etienne Mémin
Keyword(s):  
Total Energy ◽  
Shallow Water ◽  
Large Scale ◽  
Climate Models ◽  
Deterministic Model ◽  
Weather Prediction ◽  
Random Model ◽  
Small Scale ◽  
Structure Preserving ◽  
Rotating Shallow Water

<p>We introduce a new representation of the rotating shallow water equations based on a stochastic transport principle. The derivation relies on a decomposition of the fluid flow into a large-scale component and a noise term that models the unresolved small-scale flow. The total energy of such a random model is demonstrated to be preserved along time for any realization. Thus, we propose to combine a structure-preserving discretization of the underlying deterministic model with the discrete stochastic terms. This way, our method can directly be used in existing dynamical cores of global numerical weather prediction and climate models. For an inviscid test case on the f-plane we use a homogenous noise and illustrate that the spatial part of the stochastic scheme preserves the total energy of the system. Finally, using an inhomogenous noise, we show  that the proposed random model better captures the structure of a large-scale flow than a comparable deterministic model for a barotropically unstable jet on the sphere.</p>

scholarly journals Comparison of variational balance models for the rotating shallow water equations

2017 ◽  
Vol 822 ◽  
pp. 689-716 ◽  
Author(s):  
David G. Dritschel ◽  
Georg A. Gottwald ◽  
Marcel Oliver
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Large Scale ◽  
Numerical Comparison ◽  
Shallow Water Flow ◽  
Initial States ◽  
Rotating Shallow Water ◽  
Balanced Dynamics ◽  
Rotating Shallow Water Equations ◽  
Special Case

We present an extensive numerical comparison of a family of balance models appropriate to the semi-geostrophic limit of the rotating shallow water equations, and derived by variational asymptotics in Oliver (J. Fluid Mech., vol. 551, 2006, pp. 197–234) for small Rossby numbers $Ro$. This family of generalized large-scale semi-geostrophic (GLSG) models contains the $L_{1}$-model introduced by Salmon (J. Fluid Mech., vol. 132, 1983, pp. 431–444) as a special case. We use these models to produce balanced initial states for the full shallow water equations. We then numerically investigate how well these models capture the dynamics of an initially balanced shallow water flow. It is shown that, whereas the $L_{1}$-member of the GLSG family is able to reproduce the balanced dynamics of the full shallow water equations on time scales of $O(1/Ro)$ very well, all other members develop significant unphysical high wavenumber contributions in the ageostrophic vorticity which spoil the dynamics.

Sign in / Sign up

Export Citation Format

Share Document