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Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
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Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely...
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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
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Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Large-scale anisotropy in stably stratified rotating flows.

R Marino1, P D Mininni2, D L Rosenberg3

  • 1National Center for Atmospheric Research, P. O. Box 3000, Boulder, Colorado 80307, USA and Institute for Chemical-Physical Processes, Rende (CS), 87036, Italy and Space Sciences Laboratory, University of California, Berkeley, California 94720, USA.

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Rotating and stratified turbulence simulations reveal inverse energy cascades in rotating flows. Stratified flows show a direct energy cascade to large scales, forming power-law spectra.

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Area of Science:

  • Fluid dynamics
  • Geophysical turbulence
  • Computational physics

Background:

  • Turbulence is ubiquitous in nature, from atmospheric flows to astrophysical systems.
  • Understanding the behavior of turbulent flows under rotation and stratification is crucial for many scientific disciplines.
  • Direct numerical simulations (DNS) offer a powerful tool to investigate complex turbulent phenomena.

Purpose of the Study:

  • To investigate the effects of rotation and vertical stratification on turbulent flows governed by the Boussinesq equations.
  • To analyze energy transfer mechanisms and spectral properties in rotating and stratified turbulence.
  • To explore the development of inverse and direct energy cascades.

Main Methods:

  • Direct numerical simulations (DNS) of the Boussinesq equations.
  • Isotropic and random forcing at small scales.
  • High spatial resolutions up to 1024^3 grid points.
  • Reynolds numbers of approximately 1000.

Main Results:

  • Rotating turbulence, with or without stratification, exhibits inverse energy cascades and negative energy flux.
  • Purely stratified turbulence shows an early anisotropic transfer to large scales with minimal net isotropic energy flux.
  • A perpendicular energy spectrum compatible with k⊥(−5/3) power-law develops in stratified turbulence with sufficient scale separation, driven by a direct cascade.

Conclusions:

  • Rotation drives inverse energy cascades in turbulent flows.
  • Stratification can lead to direct energy cascades and anisotropic energy transfer, forming distinct spectral features.
  • The interplay between rotation, stratification, and scale separation significantly influences turbulent energy dynamics.