Showing papers on "Inertial wave published in 1984"

Observations of Near-Inertial Waves in a Front

Abstract: Near-inertial with horizontal scales ∼O(10 km) dominate profiles of velocity finestructure collected in the North Pacific Subtropical Front during January 1980. Considerable spatial variability is observed. Two features in particular contain most of the energy: a 20 cm s−1 amplitude (λz = 100 m) wave on the warm edge of the front propagating downward and away from the front, and a low wavenumber (λz = 500 m) wave reflecting off the surface. The propagating wavegroup is four times as energetic as the local downgoing near-inertial wave field. Its spatial structure is not consistent with propagation in a homogeneous medium, which suggests that it may be interacting with the front. Possible mechanisms for the existence and properties of the wavegroup are discussed, including baroclinic/barotropic instability, wind-forcing and enhancement by wave-mean flow interaction. a wave-mean flow interaction model that predicts trapping and amplification of near-inertial flow interaction. A wave-mean flow intera...

Wave propagation and growth on a surface front in a two-layer geostrophic current

Abstract: We study analytically and numerically small amplitude perturbations of a geostrophically balanced semi-infinite layer of light water having a surface front and lying above a heavier layer of finite vertical thickness which is at rest in the mean. In contrast with previous studies where the latter layer was infinitely deep we find that the equilibrium is always unstable regardless of the distribution of potential vorticity, and the maximum growth rates are generally much larger than in the "one-layer" case. The amplifying ageostrophic wave transfers kinetic energy from the basic shear flow as well as potential energy. Good quantitative agreement is found with the laboratory experiments of Griffiths and Linden (1982), and our model seems to be the simplest one for future investigations of cross frontal mixing processes by finite amplitude waves. The propagation speed of very low frequency and nondispersive frontal waves is also computed and is shown to decrease with increasing bottom layer depth.

Generation of Coastal Inertial Oscillations by Time-Varying Wind

Abstract: The excitation of coastal inertial oscillations by a rapidly varying wind is investigated. It is shown that the mean-square response to a completely random forcing is ϕ¯2 ∝ ∫ ϕδ2dt, where ϕδ is the response to impulsive forcing and the integral is over the record length. The rms response therefore initially increases with time as t½, and reaches stationarity in the decay scale for ϕδ. As in the random-walk problem, the t½ increase is a result of the superposition of uncorrelated steps. Continuous random forcing preferentially increases subsurface amplitudes, since the energy flux from the coast-surface corner causes a surface decay and a subsurface growth of ϕδ. With assumed parameters, a step-input wind forcing of 1 dyn cm−-2 generates inertial oscillations of 4 cm s−1 in the surface layer and 0.7–1.5 cm s−1 below. With a random wind in the range (−0.5, 0.5) dyn cm−2, the surface values increase to 8–11 cm s−1 and the subsurface values to 3–7 cm s−1. With an observed wind-forcing the surface and...

Numerical Analysis for Hydrostatic and Nonhydrostatic Equations of Inertial-Internal Gravity Waves

Abstract: A modified forward-backward scheme applied to the anelastic system is proposed. This modified scheme not only retains all the advantages of the conventional forward-backward scheme but also is more consistent with the original differential equations. This scheme is used to investigate inertial waves and internal gravity waves in three different lattices. It is found that the lattice C proposed by Deardorff is better than either lattice A or lattice B when applied to internal gravity waves and thermal convection in the atmosphere. The difference between a hydrostatic system and a nonhydrostatic system is also discussed in detail in this paper. Here we propose to apply Shuman's smoothing on a hydrostatic system to filter out the undesirably, highly oscillatory short waves, or stroll small-scale convection, so that we may produce reasonable results compared with those of a nonhydrostatic system. The validity of this method has been proved by the numerical results of a study on the mesoscale cloud ba...

Numerical calculations of coastal flow with turbulent dynamics

Abstract: A two-dimensional numerical model of coastal flow, in which the eddy fluxes are computed by a second-order turbulence model, has been developed. The behaviour of the inertial oscillations due to an impulsive start is in excellent agreement with the analytical solution of Kunduet al. (Deep-Sea Research, 30, 1059–1082, 1983). Much of the inertial energy gain in the deep ocean is due to the downward leakage from the coast-surface corner and is accompanied by an upward phase propagation. The low-frequency upwelling solutions develop gravitationally unstable regions in the surface layer, even in the presence of realistic surface heating. But the thickness of the surface layer without surface cooling is never very large, so the analytical models driven by a sink at the coast-surface corner give realistic subsurface solutions. The upwelling solutions generate flow reversal across a strong thermocline, but no ‘closed’ double cells. Frictional turning, as suggested by several workers, is responsible for the flow reversal. These open double cell persist in the presence of surface heating but not in the presence of an alongshore pressure gradient, pγ = τγ(maximum depth). The imposition of pγ creates a poleward undercurrent on a flat shelf but not on a sloping shelf. The alongshore jet moves offshore due to the nonlinear advection of the thermocline, so that the width of the jet is larger than the Rossby radius. An approximate expression has been derived for predicting the offshore frontal location; the numerical calculation is in fair agreement with it.

The focusing of short internal waves by an inertial wave

Abstract: Ray calculations are used to examine short-wave propagation through an inertial current. The results exhibit differences from theories of short-wave refraction based on steady shears. Caustics take the place of critical layers as the locations of ray focusings and form for short waves at all intrinsic frequencies and at all phases of the inertial oscillation. Conversely, short waves that refract to, and remain at, high vertical wavenumber can escape instability altogether. Similarities with the steady-shear model of Hartman (1975) and contrasts with the Taylor-Goldstein model are emphasised. Checks on the validity of the slowly-varying approximation are also made.

The Rossby Adjustment Problem in a Rotating, Stratified Channel, with and without Topography

Abstract: Some numerical experiments On geostrophic adjustment in a gratified channel were carried out, partly to test the use of an ocean general circulation model (GCM), and partly to elucidate the dynamical effects of sloping bottom topography on the adjustment at different latitudes. Interesting dynamical effects include the release of potential energy through shelf waves, the nonlinear generation of barotropic flow by a baroclinic Kelvin wave and the nonlinear generation of shelf waves with approximately half the inertial frequency by internal Poincare waves of near-inertial frequency. Problems that inevitably occur in the use of GCMs were also highlighted.

Topographic and inertial waves on the continental rise of the Mid‐Atlantic Bight

Abstract: Analysis of an array of four closely spaced moorings, 2800 m water depth, instrumented by near-bottom current meters, has been performed with a view to isolating coherent wave motions in the low-frequency and inertial bands. The low-frequency motions are dominated by topographic Rossby waves similar to the results of previous studies of deep currents on the continental rise of the Mid-Atlantic Bight. Estimated wave parameters show good agreement with the linear topographic Rossby wave theory of Rhines (1970). Inertial oscillations are shown to be coherent over the array (horizontal separations ∼15–20 km). The peak frequency and phase and group velocity estimates are consistent with surface layer generation at a site north of the array. The relative vorticity of the mean currents and the low-frequency wave motions do not account for the observed shift of the near-inertial peak to frequencies ∼7% above f. An event of strong near-bottom inertial currents (amplitudes ∼10 cm s−1) appears to be attributable to the passage of Hurricane Belle (August 9–10, 1976) 24 days earlier, primarily because the vertical travel times are consistent with the estimates of vertical group velocity. Strong ringing inertial currents north of the array (amplitude ∼40 cm s−1), due to Hurricane Belle were observed at the shelf edge (Mayer et al., 1981) with peak frequencies comparable to the near-inertial frequencies observed at the array on the rise.

Velocity dependent inertial induction: An extension of Mach’s principle

Abstract: In this article a model of inertial induction has been presented. According to this model the magnitude of the acceleration dependent inertia force comes out exactly as the product of the acceleration and inertial mass. The model also indicates that even uniform velocity gives rise to inertia force. However, the magnitude of the velocity dependent inertia force is exceedingly small but it causes a cosmological red shift whose order of magnitude is same as that of the observed values.

Linear Gravity Waves, Kelvin Waves and Poincare Waves, Theoretical Modelling and Observations

Abstract: Waves in lakes are primarily generated by external meteorological forces. The latter are complex in their spatial and temporal structure and thus impose a large spectrum of the typical physical scales. Their explanation and relation to the primary cause is one of the principal goals of physical limnology.

Energy Dissipation of Liquids in Nutating Spherical Tanks Measured by a Forced Motion-Spin Table

Abstract: : A specially constructed drive table is described that can spin and nutate scale-model propellant tanks Results of typical tests are given in which the liquid resonant frequencies and liquid forces and moments are presented as a function of spin rate, nutation frequency, nutation cone angle, liquid filling level, and liquid viscosity Also described is an empirical mechanical model composed of a pendulum, a rotor, and dashpots that simulate the liquid resonances (slosh and inertial waves) and the liquid forces and moments The parameters of the model are determined from the propellant motions Keywords: spherical tanks; prolate spinning aircraft

Topographically trapped waves over the continental shelf and slope

Abstract: General characteristics of topographically trapped subinertia waves are discussed from the viewpoint of an eigenvalue problem and ray theory. Special attention is paid to the slope parameterS(x) (=(dh/dx)/h, wherex denotes the coordinate perpendicular to the shoreline, increasing seaward, andh(x) is the depth) which is a measure of the strength of the restoring force of the waves. Three cases for theS distribution are considered, in whichS is assumed to be positive at the coast and to tend to zero far from the coast. The first is whereS(x) decreases monotonically towards the open ocean. It is found in this case that waves are trapped near the coast. The second is whereS(x) does not decrease monotonically, but has a maximum. It is concluded that this case may contain two types of waves, i.e., those trapped near the coast and those trapped near the maximum, and the dispersion curves corresponding to different types may nearly intersect, namely, result in “kissing”. The third is whereS(x) has a negative region (corresponding to the presence of a trench). It is found in this case that an infinite sequence of waves is trapped in the negativeS region which propagate with the coast to their left (right) in the northern (southern) hemisphere besides the waves trapped near the coast.

Characteristics of horizontal macroturbulence due to the currents in the Baltic Sea

Abstract: On the basis of current measurements in a number of sites in the southeastern and central Baltic, the following parameters of horizontal turbulence were estimated: components of turbulence intensity, moments of the correlation matrix, horizontal eddy-viscosity coefficients and directions of the extreme exchange in the horizontal plane. The exchange coefficients were calculated by the Ertel method. Exemplary empirical probability distribution (histograms) of the pulsations of current velocity components and the power spectra were shown. Changes in the turbulence parameters, depending upon the temporal scale the measure of which was assumed to be the averaging period of a cosine filter, were analysed. The influence of inertial oscillations upon the magnitudes of horizontal turbulence characteristics was shown.

Experiments on the Elastoid-inertia Oscillations of a Rigidly Rotating Fluid in a Cylindrical Vessel

Abstract: The inertial waves can occur in swirling flows under certain conditions. One of the fundamental phenomena due to the inertial waves is the "elastoid-inertia oscillation" which is a standing-wave oscillation of a fluid in a rotating cylinder. In the experiment reported here, the elastoid-inertia oscillations of several modes are induced as resonant states by a specially designed apparatus. The patterns of the flow field and resonant frequencies are examined by means of visualization techniques. The experimental results are compared with those of the inviscid linear theory. It is found that both the frequencies and flow patterns of the actual elastoid-inertia oscillations can be well estimated by the linear theory.

Contribution of Pressure to The Moment during Spin-Up on a Nutating Liquid-Filled Cylinder: Ad Hoc Model

Abstract: : A study is made of the flow of a liquid in a cylindrical container that nutiates at constant frequency and small amplitude and impulsively begins spinning with a fixed angular velocity. In particular, the history of pressure overturning moment during spin-up is investigated. The partial differential equations of the problem are linearized, and a modal analysis (separated variable solution) is applied. One consequence of stipulating a modal analysis is a difficulty with endwall boundary conditions; this difficulty is avoided here by specifying a heuristic boundary condition and then satisfying it approximately. Calculations indicate that peaks of overturning or restoring moment occur at or near those times when the nutational frequency is equal to one of the frequencies of inertial oscillations of the liquid. This phenomenon of resonance extends the result of Stewartson obtained for inviscid perturbations in solid body rotation.

The flow of viscoelastic non-Newtonian fluid in the Ekman layer

Abstract: “In this paper the unsteady flow in the Ekman layer of a visco-elastic non-Newtonian fluid near a flat plate is discussed. Laplace transform technique has been employed to show the basic differential equations. Expressions for velocity profile, the skin friction have been calculated. It is shown that the time to attain the steady state increases with the elastic parameter. It is shown that normally the ultimate steady state is reached through a decay of inertial oscillations whose frequency decreases with increase in the elastic parameter”. In the present study we examine the following unsteady problem in non-Newtonian fluid. Consider an infinite plate coinciding with the platez=0 and rotating in unison with elasticoviscous liquid occupying the regionz>0 with a uniform angular velocity Ω about thez-axis for timet 0, the plate starts moving with a uniform velocityUo along thex-axis relative to the rotating frame of reference. The horizontal homogeneity of the problem demands that conditions depend onz andt only. The equation of continuity together with the no slip condition at the plate then shows that thez-component of the velocity vanishes everywhere.