scholarly journals Energy intensity of inertial waves in a sphere

Author(s):  
W. W. Wood

AbstractThe decay at large wavenumbers of the energy density in an inertial wave generated in a sphere by an arbitrary initial disturbance is determined as a first step to a comparison with the general theory of Phillips [17] for a statistically steady field of random inertial waves in an arbitrary cavity.

1978 ◽  
Vol 86 (3) ◽  
pp. 457-463 ◽  
Author(s):  
W. E. Scott

It is shown that the wavelets which appear on the inertial wave form of the inner free surface of a fully spun-up cylindrical mass of liquid contained in a vertical, rapidly rotating and gyrating gyrostat are capillary waves. It is further shown that the interaction between these capillary waves and the excited inertial waves is not the mechanism which effects an observed two-period collapse (‘breakdown’) and reappearance of the free-surface inertial wave form. Rather, the two-period breakdown can be explained by the conjecture that it is a beat phenomenon arising from the interaction of two differently structured inertial wave modes, which have the same frequency at small amplitudes of oscillation of the gyrostat but which, owing to the dependence of the inertial mode frequency on the amplitude of the gyrostatic motion, have slightly different frequencies at larger amplitudes of oscillation of the gyrostat.


2021 ◽  
Author(s):  
Abhijit Samanta

Abstract We have derived a metric field equation in the locally inertial coordinate system from Einstein's field equation considering the energy density of the moving particle with the approximations that the force field under which the particle is moving is weak and the velocity of the particle is non-relativistic. We study the motion of different microscopic systems using this metric equation and compared the results with the experimentally measured values and we find that the results are identical.


2017 ◽  
Vol 10 (4) ◽  
pp. 277-286 ◽  
Author(s):  
Alp Albayrak ◽  
Deniz A Bezgin ◽  
Wolfgang Polifke

Acoustic waves passing through a swirler generate inertial waves in rotating flow. In the present study, the response of a premixed flame to an inertial wave is scrutinized, with emphasis on the fundamental fluid-dynamic and flame-kinematic interaction mechanism. The analysis relies on linearized reactive flow equations, with a two-part solution strategy implemented in a finite element framework: Firstly, the steady state, low-Mach number, Navier–Stokes equations with Arrhenius type one-step reaction mechanism are solved by Newton’s method. The flame impulse response is then computed by transient solution of the analytically linearized reactive flow equations in the time domain, with mean flow quantities provided by the steady-state solution. The corresponding flame transfer function is retrieved by fitting a finite impulse response model. This approach is validated against experiments for a perfectly premixed, lean, methane-air Bunsen flame, and then applied to a laminar swirling flame. This academic case serves to investigate in a generic manner the impact of an inertial wave on the flame response. The structure of the inertial wave is characterized by modal decomposition. It is shown that axial and radial velocity fluctuations related to the eigenmodes of the inertial wave dominate the flame front modulations. The dispersive nature of the eigenmodes plays an important role in the flame response.


2014 ◽  
Vol 753 ◽  
pp. 472-498 ◽  
Author(s):  
Tobias Vogt ◽  
Dirk Räbiger ◽  
Sven Eckert

AbstractThe dynamics of free and forced inertial waves inside cylinders of different aspect ratios ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}A=H_0/2R_0$) were investigated experimentally in this study. The liquid metal GaInSn was chosen as the fluid in order to enable a contactless stimulation of the flow by means of alternating electromagnetic fields. A rotating magnetic field generates the rotating motion of the liquid, whereas periodic modulations of the field strength and short pulses excite specific wave modes. Ultrasound Doppler velocimetry was used to record the flow structure and to identify inertial waves in the set-up. Our experiments demonstrate selective excitation of different inertial wave modes by deliberate variation of the magnetic field parameters. Furthermore, it was found that turbulent perturbations in the boundary layers of the swirling flow are able to induce an inertial wave mode that survives over a long time. Experiments at the fundamental resonance have shown that multiple harmonic wave modes appeared simultaneously. The measured inertial wave frequencies were compared to the predictions of the linear inviscid theory.


1999 ◽  
Vol 382 ◽  
pp. 283-306 ◽  
Author(s):  
R. R. KERSWELL

Inertial waves are a ubiquitous feature of rapidly rotating fluids. Although much is known about their initial excitation, little is understood about their stability. Experiments indicate that they are generically unstable and in many cases catastrophically so, quickly causing the whole flow to collapse to small-scale disorder. The linear stability of two three-dimensional inertial waves observed to break down in the laboratory is considered here at experimentally small but finite Ekman numbers of [les ]10−4. Surprisingly small threshold amplitudes for instability are found. The results support the conjecture that triad resonances are the generic mechanism for secondary instability in rapidly rotating fluids but also highlight the ability of geostrophic flows to derive energy through a finite-amplitude inertial wave. This latter finding may go some way to explaining the significant mean circulations typically observed in inertial wave experiments.


2020 ◽  
Vol 17 (03) ◽  
pp. 2050043
Author(s):  
G. Abbas ◽  
H. Nazar

In this paper, we have analyzed the complexity factor for the most general axially symmetric static anisotropic fluid distributions in context of [Formula: see text] theory of gravity. For this purpose, we have studied three distinct complexity factors that are organized in terms of three scalar variables (structure scalars) comes from the orthogonal splitting of the curvature tensor. The vanishing of all complexity factors condition for what we choose the simplest fluid distribution that in which system having energy density is homogeneous with isotropic pressure. Although, it has been found that the complexity factors condition can also vanish when inhomogeneous energy density and anisotropy of the pressure cancel each other. Next, we express a class of exact solutions and their graphical analysis as compatible to our models that satisfies the vanishing condition of complexity factors. Finally, it is worth mentioning that these results can reproduce the results of General theory of Relativity under some constraints.


2017 ◽  
Vol 831 ◽  
pp. 128-150 ◽  
Author(s):  
A. A. Gelash ◽  
V. S. L’vov ◽  
V. E. Zakharov

A complete Hamiltonian formalism is suggested for inertial waves in rotating incompressible fluids. Resonance three-wave interaction processes – decay instability and confluence of two waves – are shown to play a key role in the weakly nonlinear dynamics and statistics of inertial waves in the rapid rotation case. Future applications of the Hamiltonian approach to inertial wave theory are investigated and discussed.


Fluids ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 10
Author(s):  
John V. Shebalin

We find the analytical form of inertial waves in an incompressible, rotating fluid constrained by concentric inner and outer spherical surfaces with homogeneous boundary conditions on the normal components of velocity and vorticity. These fields are represented by Galerkin expansions whose basis consists of toroidal and poloidal vector functions, i.e., products and curls of products of spherical Bessel functions and vector spherical harmonics. These vector basis functions also satisfy the Helmholtz equation and this has the benefit of providing each basis function with a well-defined wavenumber. Eigenmodes and associated eigenfrequencies are determined for both the ideal and dissipative cases. These eigenmodes are formed from linear combinations of the Galerkin expansion basis functions. The system is truncated to numerically study inertial wave structure, varying the number of eigenmodes. The largest system considered in detail is a 25 eigenmode system and a graphical depiction is presented of the five lowest dissipation eigenmodes, all of which are non-oscillatory. These results may be useful in understanding data produced by numerical simulations of fluid and magnetofluid turbulence in a spherical shell that use a Galerkin, toroidal–poloidal basis as well as qualitative features of liquids confined by a spherical shell.


2010 ◽  
Vol 40 (6) ◽  
pp. 1320-1337 ◽  
Author(s):  
Benjamin Jaimes ◽  
Lynn K. Shay

Abstract Tropical cyclones (TCs) Katrina and Rita moved as major hurricanes over energetic geostrophic ocean features in the Gulf of Mexico. Increased and reduced oceanic mixed layer (OML) cooling was measured following the passage of both storms over cyclonic and anticyclonic geostrophic relative vorticity ζg, respectively. This contrasting thermal response is investigated here in terms of the evolution of the storms’ near-inertial wave wake in geostrophic eddies. Observational data and ray-tracing techniques in realistic geostrophic flow indicate that TC-forced OML near-inertial waves are trapped in regions of negative ζg, where they rapidly propagate into the thermocline. These anticyclonic-rotating regimes coincided with the distribution of reduced OML cooling because rapid downward dispersion of near-inertial energy reduced the amount of kinetic energy available to increase vertical shears at the OML base. By contrast, TC-forced OML near-inertial waves were stalled in upper layers of cyclonic circulations, which strengthened vertical shears and entrainment cooling. Upgoing near-inertial energy propagation dominated inside a geostrophic cyclone that interacted with Katrina; the salient characteristics of these upward-propagating waves were the following: (i) they were radiated from the ocean interior because of geostrophic adjustment following upwelling–downwelling processes; (ii) rather than with the buoyancy frequency, they amplified horizontally as they encountered increasing values of f + ζg/2 during upward propagation; and (iii) they produced episodic vertical mixing through shear instability at a critical layer underneath the OML. To improve the prediction of TC-induced OML cooling, models must capture geostrophic features and turbulence closures must represent near-inertial wave processes such as dispersion and breaking between the OML base and the thermocline.


2005 ◽  
Vol 35 (5) ◽  
pp. 645-665 ◽  
Author(s):  
Robert Pinkel

Abstract From October 1997 through October 1998, the Surface Heat Budget of the Arctic (SHEBA) ice camp drifted across the western Arctic Ocean, from the central Canada Basin over the Northwind Ridge and across the Chukchi Cap. During much of this period, the velocity and shear fields in the upper ocean were monitored by Doppler sonar. Near-inertial internal waves are found to be the dominant contributors to the superinertial motion field. Typical rms velocities are 1–2 cm s−1. In this work, the velocity and shear variances associated with upward- and downward-propagating wave groups are quantified. Patterns are detected in these variances that correlate with underlying seafloor depth. These are explored with the objective of assessing the role that these extremely low-energy near-inertial waves play in the larger-scale evolution of the Canada Basin. The specific focus is the energy flux delivered to the slopes and shelves of the basin, available for driving mixing at the ocean boundaries. The energy and shear variances associated with downward-propagating waves are relatively uniform over the entire SHEBA drift, independent of the season and depth of the underlying topography. Variances associated with upward-propagating waves follow a (depth)−1/2 dependence. Over the deep slopes, vertical wavenumber spectra of upward-propagating waves are blue-shifted relative to their downward counterparts, perhaps a result of reflection from a sloping seafloor. To aid in interpretation of the observations, a simple, linear model is used to compare the effects of viscous (volume) versus underice (surface) dissipation for near-inertial waves. The latter is found to be the dominant mechanism. A parallel examination of the topography of the western Arctic shows that much of the continental slope is close to critical for near-inertial wave reflection. The picture that emerges is consistent with “one bounce” rather than trans-Arctic propagation. The dominant surface-generated waves are substantially absorbed in the underice boundary layer following a single roundtrip to the seafloor. However, surface-generated waves can interact strongly with nearby (<300 km) slopes, potentially contributing to dissipation rates of order 10−6–10−7 W m−3 in a zone several hundred meters above the bottom. The waves that survive the reflection process (and are not back-reflected) display a measurable blue shift over the slopes and contribute to the observed dependence of energy on seafloor depth that is seen in these upper-ocean observations.


Sign in / Sign up

Export Citation Format

Share Document