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Vortices, waves, fronts in rotating fluids


Vortices, Waves, Fronts in Rotating Fluids: Adjustment, Stability, Frontogenesis

Tech Area / Field

  • PHY-NGD/Fluid Mechanics and Gas Dynamics/Physics
  • PHY-OTH/Other/Physics

8 Project completed

Registration date

Completion date

Senior Project Manager
Lapidus O V

Leading Institute
Evgeni Kharadze Georgian National Astrophysical Observatory, Georgia, Tbilisi


  • Observatoire de Paris, France, Meudon\nUniversity of Texas / Institute for Fusion Studies, USA, TX, Austin

Project summary

The investigation of the dynamics of rotating fluids creates the basis for the understanding and adequate description of important processes in the Earth’s atmosphere and ocean. Results of this investigation may also have many significant astrophysical and technical applications. Increasing importance in recent years has acquired geophysical hydrodynamics – hydrodynamics of natural flows (together with atmosphere and ocean, here we include liquid cores of planets), where the rotation of liquid and gaseous mediums plays an important role.
Problems of weather forecast, human impact on the environment, spread of the pollution and natural impurities in the atmosphere and ocean grant the investigation of geophysical hydrodynamics vital importance. But these problems are very complex. Even when restricted to the incompressible limit with oversimplified thermodynamics, rotating flows still sustain many complicated phenomena that are not fully explored up today. Among these processes, primarily, are the dynamics of waves and vortical flows. The complexity of these problems increases drastically when stratification effects and thermodynamic processes are included into the consideration. One of the important example is the formation of fronts – sharp interfaces generated in the stratified rotating mediums. This widely occurred phenomenon in the atmosphere and ocean plays an important role in problems of weather forecast, dispersion of pollution and other applications.
Corresponding theoretical models are highly complicated, primarily due to the nonlinearity of equations of hydrodynamics. The progress can be significantly accelerated employing laboratory experiments parallel to theoretical study. Authors of the present Project during many years, together with the theoretical investigations, are involved in the creation and modification of the specialized experimental plant designed to model the dynamics of planetary atmospheres and oceans. The modernized experimental plant consisting from parabolic vessel rotating with controlled angular velocity is developed presently. Due to the geometry of the vessel bottom, the fluid in the vessel distributes into a thin parabolic layer. It is known that the dynamics of this kind of rotating fluid layer has important similarities with the dynamics of planetary atmospheres and ocean. Existing experimental plant makes possible a wide spectrum of investigations on the dynamics of rotating fluids, including the dynamics of the Earth’s atmosphere and ocean. The latter is the aim of the present Project. Main trends of the experimental and theoretical investigations are supposed as follows:

- Nonlinear geostropic adjustment of initial non-equilibrium hydrodynamic state;

- Stability of zonal shear flows;
- Formation and stability of frontal interfaces in rotating fluids.
These problems have a long history of investigation. However, it is the complexity of these phenomena that have led to the fact that the progress in these research areas is limited and investigation of these research topics is intensively developing at present-day.
Main objectives of the Project can be outlined as follows:

1. Theoretical and experimental investigation of the stability of large-scale spiral vortices in rotating flows aiming the dynamics of atmospheric cyclones and anticyclones.

2. Investigation of scarcely studied hydrodynamic instabilities (algebraic, exponential-algebraic) in rotating shear flows using non-modal analysis.
3. Theoretical and experimental investigation of the nonlinear geostropic adjustments of hydrodynamic flows in geophysical and astrophysical contexts.
4. The development of new concepts on the formation of interfaces in rotating mediums and consequent analysis of the dynamics of atmospheric and oceanic fronts.
5. Elaboration of methods for the laboratory modelling of the structure, dynamics and stability of atmospheric and oceanic fronts.
6. Theoretical and experimental study of the generation of regular/coherent structures in rotating fluids by small-scale two-dimensional chaotic perturbations. Consequent studies of the processes in the Earth’s atmosphere and differentially rotating astrophysical disks.
7. Investigation of the structure and dynamics of vortical flows excited by local sources and sinks of heat and mass in rotating mediums.

The Project implies substantial progress in geophysical hydrodynamics and number of adjacent branches. In particular, results of the project should contribute to:

- progress in the theory of hydrodynamic instability of differentially rotating flows;

- understanding of the excitation, dynamics and stability of vortical structures in rotating flows;
- theory of the formation of coherent vortical structures and fronts;
- development of experimental methodology of laboratory modelling of atmospheric and oceanic dynamics and nonlinear geophysical adjustments in liquids and gases;

Competence of the Project Team

The Project members have long-term experience in the theoretical and experimental studies in hydrodynamics, magnetohydrodynamics, geophysical hydrodynamics and astrophysics, in electronics and development of specialized software. In recent years these investigations were awarded several grants by International Science Foundation (RVO 200), INTAS (Ge-97 0504), ISTC (G-553) and CRDF (GRDF-3315). Topics of interest of the Project members in recent years are:

- Hydrodynamic and magnetohydrodynamic instabilities in the rotating smooth shear flows; development of the non-modal analysis of vortical and wave perturbations; turbulence in astrophysical shear flows; theory of atmospheric vortices; theories of fronts, jet flows, convection, boundary layer of the atmosphere an ocean.
- Laboratory modelling of geophysical and astrophysical flows and in particular rotating shear flows; experimental simulation of the large-scale vortical structures (cyclones, anticyclones and their pairs); design and construction of experimental facilities and development of the necessary software.
Expected Results and their Application
- Description of new types of hydrodynamic instabilities (algebraic, algebraic-exponential) in differentially rotating fluids. Applications in geophysics and astrophysics.
- Description of the structure and clarification of the hydrodynamic stability criteria of large-scale spiral vortices in rotating fluids.
- Development of the experimental methodology for the modelling of dynamical processes in the atmosphere and ocean.
- Description of new mechanisms of the formation of frontal interfaces (mechanisms of the frontogenesis) in rotating fluids.
- Description of the dynamical feedback of rotating fluids on the effect of local sources (sinks) of heat and mass.
- Description of the formation of regular/coherent structures by chaotic small-scale two-dimensional perturbations in rotating fluids with astrophysical applications (accretion and galactic disks).
- Establishment of behaviors of the nonlinear processes of geostropic and cyclostropic adjustment of hydrodynamic flows in liquids and gases.

These results:

- create the basis for the understanding of various phenomena in the atmosphere, ocean and differentially rotating astrophysical objects (large-scale vortices in the atmosphere, ocean and astrophysical disks, physical mechanism of the development of atmospheric and oceanic fronts, instabilities of atmospheric and astrophysical disks flows, geostropic adjustments of hydrodynamic fields, etc.)
- have practical value for the interpretation of geophysical and astrophysical measurements/observations, for the development of hydrodynamic models for the forecast of atmospheric processes and models of the spread of pollution in the atmosphere and ocean.
Meeting ISTC Objectives
Proposed Project will:
- help the Project members to use their knowledge exclusively on peaceful activities;
- promote integration of the Project members into the international scientific community;
- help the Project members to carry fundamental research in astrophysics, geophysical hydrodynamics and related subjects of the environmental protection.
Scope of Activities
The scope of the Project that implies theoretical and experimental research includes a comprehensive analysis of problems of geophysical hydrodynamcs: the theory of hydrodynamic stability of rotating fluids; formation and dynamics of atmospheric and oceanic interfaces (fronts); nonlinear geostropic adjustments of hydrodynamic flows in liquid and gaseous mediums. Some results will have astrophysical applications. The Project is organized into the six interconnected tasks. The theoretical part of the Project implies a fusion of analytical and numerical investigations. The experimental part will be carried out on the experimental plant modernized according to the project goals.
Role of Foreign Collaborators
The exchange of information with foreign collaborators and joint investigation is planned. Meetings with collaborators are planned in order to have joint seminars and discussion of obtained results.
Technical Approach and Methodology

· Theoretical research: physics of continuous medium, hydrodynamic equations of rotating fluids, perturbation theory, theory of hydrodynamic stability, theory of geostropic adjustments, theory of nonlinear waves, theory of discontinuous gasodynamics, non-modal analysis of perturbation dynamics, methods from the theory of functions with complex variable, numerical calculations of ordinary differential equations, direct numerical simulations.

· Experimental research: observations using the method of optical tracking based on the data of the digital image and video cameras, fluid depth measurements based on the electric capacitymeters, thermal and ultrasound methods for the detection of fluid velocity (anemometering), real time data processing, data analysis, cross-correlative analysis.


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