Related Experiment Video
Updated: Sep 7, 2025
08:19
Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
Published on: May 9, 2021
2.3K
Energy Spectrum of Two-Dimensional Acoustic Turbulence.
Adam Griffin1, Giorgio Krstulovic2, Victor S L'vov3
1Université Côte d'Azur, Institut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice, France.
Physical Review Letters
|June 17, 2022
Summary
Researchers found an exact analytical solution for the turbulent energy spectrum of acoustic waves in 2D systems. This discovery advances understanding of acoustic turbulence in Bose-Einstein condensates and similar 2D fluid dynamics.
Area of Science:
- Fluid Dynamics
- Quantum Gases
- Wave Phenomena
Background:
- Turbulent energy spectra are crucial for understanding energy transfer across scales in fluid systems.
- Previous studies established a 3D acoustic turbulence spectrum, but a 2D solution remained elusive due to singularities.
- Acoustic turbulence in 2D Bose-Einstein condensates presents a unique challenge for theoretical description.
Purpose of the Study:
- To derive an exact analytical solution for the turbulent energy spectrum of acoustic waves in two-dimensional systems.
- To address the long-standing problem of the 2D acoustic turbulence spectrum, which was previously hindered by mathematical singularities.
- To provide a theoretical framework applicable to phenomena like acoustic turbulence in 2D Bose-Einstein condensates.
Main Methods:
- Solving the wave kinetic equation under constant-flux conditions.
- Developing an analytical approach for acoustic waves with a nearly linear dispersion relation (ωk = csk[1 + (ak)²]).
- Utilizing direct numerical simulations of the forced-dissipated Gross-Pitaevskii equation.
Main Results:
- An exact, unique constant-flux power-law analytical solution for the 2D turbulent energy spectrum, E(k) = C₁√(ϵac_s)/k, was obtained.
- A universal constant (C₁) for this spectrum was determined analytically.
- The derived spectrum was shown to be realizable in numerical simulations of relevant physical systems.
Conclusions:
- The study successfully provides the first analytical solution for the 2D acoustic wave turbulent energy spectrum.
- This solution is applicable to systems exhibiting acoustic turbulence, such as 2D Bose-Einstein condensates.
- The findings bridge a significant gap in the understanding of turbulence in lower dimensions and validate theoretical predictions through numerical simulations.
Related Concept Videos
01:28Standing Waves in a Cavity
1.0K
A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
1.0K
01:01Sound Waves
9.4K
Sound waves can be thought of as fluctuations in the pressure of a medium through which they propagate. Since the pressure also makes the medium's particles vibrate along its direction of motion, the waves can be modeled as the displacement of the medium's particles from their mean position.
Sound waves are longitudinal in most fluids because fluids cannot sustain any lateral pressure. In solids, however, shear forces help in propagating the disturbance in the lateral direction as well....
Sound waves are longitudinal in most fluids because fluids cannot sustain any lateral pressure. In solids, however, shear forces help in propagating the disturbance in the lateral direction as well....
9.4K
01:08IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations
1.2K
Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
1.2K
01:04Modes of Standing Waves: II
949
The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end....
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end....
949
00:53Sound Waves: Interference
3.9K
Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure waves. When two identical waves from the same source superimpose on each other, the combination of two crests or two troughs results in amplitude reinforcement known as constructive interference. If two identical waves, that are initially in phase, become out of phase because of different path lengths, the combination of crests with troughs...
3.9K
01:03Modes of Standing Waves - I
3.0K
A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...
3.0K