Next Article in Journal
Modeling Superparamagnetic Particles in Blood Flow for Applications in Magnetic Drug Targeting
Next Article in Special Issue
A Non-Hydrostatic Depth-Averaged Model for Hydraulically Steep Free-Surface Flows
Previous Article in Journal
Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag
Previous Article in Special Issue
Hydrodynamics and Oxygen Bubble Characterization of Catalytic Cells Used in Artificial Photosynthesis by Means of CFD
Article Menu

Export Article

Open AccessArticle
Fluids 2017, 2(2), 28; doi:10.3390/fluids2020028

Anisotropic Wave Turbulence for Reduced Hydrodynamics with Rotationally Constrained Slow Inertial Waves

Department of Applied Mathematics, University of Colorado, Boulder, CO 80045, USA
Tata Institute of Fundamental Research, Hyderabad 500075, India
Academic Editors: Helena Margarida Ramos and Mehrdad Massoudi
Received: 8 March 2017 / Revised: 13 May 2017 / Accepted: 24 May 2017 / Published: 27 May 2017
(This article belongs to the Special Issue Advances in Hydrodynamics)
View Full-Text   |   Download PDF [3093 KB, uploaded 9 June 2017]   |  


Kinetic equations for rapidly rotating flows are developed in this paper using multiple scales perturbation theory. The governing equations are an asymptotically reduced set of equations that are derived from the incompressible Navier-Stokes equations. These equations are applicable for rapidly rotating flow regimes and are best suited to describe anisotropic dynamics of rotating flows. The independent variables of these equations inherently reside in a helical wave basis that is the most suitable basis for inertial waves. A coupled system of equations for the two global invariants: energy and helicity, is derived by extending a simpler symmetrical system to the more general non-symmetrical helical case. This approach of deriving the kinetic equations for helicity follows naturally by exploiting the symmetries in the system and is different from the derivations presented in an earlier weak wave turbulence approach that uses multiple correlation functions to account for the asymmetry due to helicity. Stationary solutions, including Kolmogorov solutions, for the flow invariants are obtained as a scaling law of the anisotropic wave numbers. The scaling law solutions compare affirmatively with results from recent experimental and simulation data. Thus, anisotropic wave turbulence of the reduced hydrodynamic system is a weak turbulence model for strong anisotropy with a dominant k cascade where the waves aid the turbulent cascade along the perpendicular modes. The waves also enable an appropriate closure of the kinetic equation through averaging of their phases. View Full-Text
Keywords: multi-scale perturbation; slow helical waves; slow manifold; rapidly rotating turbulence multi-scale perturbation; slow helical waves; slow manifold; rapidly rotating turbulence

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Sen, A. Anisotropic Wave Turbulence for Reduced Hydrodynamics with Rotationally Constrained Slow Inertial Waves. Fluids 2017, 2, 28.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics



[Return to top]
Fluids EISSN 2311-5521 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top