The existing concepts of non-reciprocity in propagation of acoustic or elastic waves are based either on nonlinear effects, or on local circulation of linear elastic fluid that leads to red or blue Doppler shift, depending on the direction of sound wave. The same concepts exist for electromagnetic non-reciprocity, where external magnetic field may produce the effect similar to local rotation of the medium. These two concepts originate from two known methods of breaking a time-reversal symmetry (T-symmetry), that is necessary for observation of nonreciprocal wave propagation. Both concepts require additional electrical or mechanical devices to be installed with their own power sources. Here we propose to explore viscosity of fluid as a natural factor of the T-symmetry breaking through energy dissipation. We report experimental observation of the nonreciprocal transmission of ultrasound through a water-submerged phononic crystals consisting of several layers of aluminum rods arranged in a square lattice. While viscous losses break the T-symmetry, making the wave propagation thermodynamically irreversible, the transmission remains reciprocal if the scatterers are symmetrical. To generate different energy losses for opposite directions of propagation, the P-symmetry of the crystal is broken by using asymmetric scatterers. Due to asymmetry, two sound waves propagating in the opposite directions produce different distributions of velocity and pressure that leads to different local absorption. Dissipation of acoustic energy occurs mostly near the surface of the scatterers and it strongly depends on surface roughnesses. Using two phononic crystal with smooth and rough aluminum rods we demonstrate low (2-5 dB) and high (10-15 dB) level of non-reciprocity within a wide range of frequencies, 300-600 kHz. Experimental results are in agreement with numerical simulations based on the Navier-Stokes equation. This nonreciprocal linear device is very cheap, robust and does not require energy source.
more »
« less
Damping rate measurements and predictions for gravity waves in an air–oil–water system
Dissipation of standing gravity waves of frequencies within 1–2 Hz is investigated experimentally. The waves are generated in a rectangular tank filled with water, the surface of which is covered with an oil layer of mean thickness, d. Damping rates are measured as a function of d, and compared with results from established theoretical models—in particular, with those from a recently developed three-fluid dissipation model that considers waves in a system of semi-infinitely deep fluids that lie above and below an interfacial fluid layer of finite thickness. Based on a comparison of experimental data with predictions, the oil–water interfacial elasticity, E2, is empirically determined to be a linear function of d. The theoretical predictions include contributions from the three-fluid dissipation model, which accounts for energy losses due to shear layers at the interfaces, friction in the fluid bulk, and compression–expansion oscillations of the elastic interfaces; and from a boundary-layer dissipation model, which accounts for energy losses due to boundary layers at the tank's solid surfaces. The linear function, [Formula: see text], is used to compute the three-fluid model damping rate. An effective viscosity of the oil–water system is used to compute the boundary-layer model damping rate. The theoretical predictions are, on average, within 5% of measurements for all the wave frequencies considered. The promise shown by the three-fluid model is highlighted, as are the assumptions involved in the analysis and comparisons.
more » « less- NSF-PAR ID:
- 10363108
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 34
- Issue:
- 2
- ISSN:
- 1070-6631
- Page Range / eLocation ID:
- Article No. 022113
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Toward a Self‐Consistent Characterization of Lithospheric Plates Using Full‐Spectrum Viscoelasticitymore » « less
Determining the thickness of the lithosphere in any given setting combines uncertainty in both the observational method and laboratory‐derived understanding of mantle rheology. The many observational and modeling criteria across geophysical subfields for plate thickness lead to significant differences in plate thickness estimates depending on the process of interest, be it seismic wave propagation or relaxation in response to changes in loads—from earthquakes, ice sheets to volcanoes—or convection. This paper proposes a framework in which to model and interpret upper mantle mechanical structure smoothly across the full spectrum of geophysical timescales. We integrate viscous, elastic, and linear anelastic constitutive models and calculate the mechanical response from convective to seismic wave timescales (i.e., 0 to infinite frequency or, in practice,
10−15 to 1 Hz). We apply these calculations to 1‐D thermal structures and determine the normalized complex viscosity, a quantity that shows clearly the role of transient creep in weakening rock relative to the associated Maxwell rheology. Using various criteria for the lithosphere‐asthenosphere boundary, we show that the apparent plate thickness will be thicker at higher frequencies than at lower frequencies. Additional calculations for nonlinear Maxwell behavior (dislocation mechanisms) demonstrate significant changes in the apparent plate structure, decreasing the long‐term plate thickness, consistent with observations. Other effects such as dislocation damping (associated with a steady‐state dislocation structure), melt, water, major element composition, and grain size are not included here but, when incorporated into this framework, will significantly change the full‐spectrum plate thickness predictions. -
Surface waves are excited at the boundary of a mechanically vibrated cylindrical container and are referred to as edge waves. Resonant waves are considered, which are formed by a travelling wave formed at the edge and constructively interfering with its centre reflection. These waves exhibit an axisymmetric spatial structure defined by the mode number $n$ . Viscoelastic effects are investigated using two materials with tunable properties; (i) glycerol/water mixtures (viscosity) and (ii) agarose gels (elasticity). Long-exposure white-light imaging is used to quantify the magnitude of the wave slope from which frequency-response diagrams are obtained via frequency sweeps. Resonance peaks and bandwidths are identified. These results show that for a given $n$ , the resonance frequency decreases with viscosity and increases with elasticity. The amplitude of the resonance peaks are much lower for gels and decrease further with mode number, indicating that much larger driving amplitudes are needed to overcome the elasticity and excite edge waves. The natural frequencies for a viscoelastic fluid in a cylindrical container with a pinned contact-line are computed from a theoretical model that depends upon the dimensionless Ohnesorge number ${Oh}$ , elastocapillary number ${Ec}$ and Bond number ${Bo}$ . All show good agreement with experimental observations. The eigenvalue problem is equivalent to the classic damped-driven oscillator model on linear operators with viscosity appearing as a damping force and elasticity and surface tension as restorative forces, consistent with our physical interpretation of these viscoelastic effects.more » « less
-
more » « less
Abstract Pacific Summer Water eddies and intrusions transport heat and salt from boundary regions into the western Arctic basin. Here we examine concurrent effects of lateral stirring and vertical mixing using microstructure data collected within a Pacific Summer Water intrusion with a length scale of ∼20 km. This intrusion was characterized by complex thermohaline structure in which warm Pacific Summer Water interleaved in alternating layers of
m thickness with cooler water, due to lateral stirring and intrusive processes. Along interfaces between warm/salty and cold/freshwater masses, the density ratio was favorable to double-diffusive processes. The rate of dissipation of turbulent kinetic energy ( ε ) was elevated along the interleaving surfaces, with values up to 3 × 10−8W kg−1compared to backgroundε of less than 10−9W kg−1. Based on the distribution ofε as a function of density ratioRρ , we conclude that double-diffusive convection is largely responsible for the elevatedε observed over the survey. The lateral processes that created the layered thermohaline structure resulted in vertical thermohaline gradients susceptible to double-diffusive convection, resulting in upward vertical heat fluxes. Bulk vertical heat fluxes above the intrusion are estimated in the range of 0.2–1 W m−2, with the localized flux above the uppermost warm layer elevated to 2–10 W m−2. Lateral fluxes are much larger, estimated between 1000 and 5000 W m−2, and set an overall decay rate for the intrusion of 1–5 years. -
Abstract Englacial water transport is an integral part of the glacial hydrologic system, yet the geometry of englacial structures remains largely unknown. In this study, we explore the excitation of fluid resonance by small amplitude waves as a probe of englacial geometry. We model a hydraulic network consisting of one or more tabular cracks that intersect a cylindrical conduit, subject to oscillatory wave motion initiated at the water surface. Resulting resonant frequencies and quality factors are diagnostic of fluid properties and geometry of the englacial system. For a single crack–conduit system, the fundamental mode involves gravity-driven fluid sloshing between the conduit and the crack, at frequencies between 0.02 and 10 Hz for typical glacial parameters. Higher frequency modes include dispersive Krauklis waves generated within the crack and tube waves in the conduit. But we find that crack lengths are often well constrained by fundamental mode frequency and damping rate alone for settings that include alpine glaciers and ice sheets. Branching crack geometry and dip, ice thickness and source excitation function help define limits of crack detectability for this mode. In general, we suggest that identification of eigenmodes associated with wave motion in time series data may provide a pathway toward inferring englacial hydrologic structures.more » « less
