scholarly journals A Surface-Aware Projection Basis for Quasigeostrophic Flow

2013 ◽  
Vol 43 (3) ◽  
pp. 548-562 ◽  
Author(s):  
K. Shafer Smith ◽  
Jacques Vanneste
Keyword(s):  
Mesoscale Eddy ◽  
Lower Surface ◽  
Surface Mode ◽  
Surface Dynamics ◽  
Orthonormal Bases ◽  
Barotropic Mode ◽  
Two Parameters ◽  
Surface Buoyancy ◽  
Baroclinic Modes ◽  
Limiting Case

Abstract Recent studies indicate that altimetric observations of the ocean’s mesoscale eddy field reflect the combined influence of surface buoyancy and interior potential vorticity anomalies. The former have a surface-trapped structure, while the latter are often well represented by the barotropic and first baroclinic modes. To assess the relative importance of each contribution to the signal, it is useful to project the observed field onto a set of modes that separates their influence in a natural way. However, the surface-trapped dynamics are not well represented by standard baroclinic modes; moreover, they are dependent on horizontal scale. Here the authors derive a modal decomposition that results from the simultaneous diagonalization of the energy and a generalization of potential enstrophy that includes contributions from the surface buoyancy fields. This approach yields a family of orthonormal bases that depend on two parameters; the standard baroclinic modes are recovered in a limiting case, while other choices provide modes that represent surface and interior dynamics in an efficient way. For constant stratification, these modes consist of symmetric and antisymmetric exponential modes that capture the surface dynamics and a series of oscillating modes that represent the interior dynamics. Motivated by the ocean, where shears are concentrated near the upper surface, the authors consider the special case of a quiescent lower surface. In this case, the interior modes are independent of wavenumber, and there is a single exponential surface mode that replaces the barotropic mode. The use and effectiveness of these modes is demonstrated by projecting the energy in a set of simulations of baroclinic turbulence.

scholarly journals What Vertical Mode Does the Altimeter Reflect? On the Decomposition in Baroclinic Modes and on a Surface-Trapped Mode

2009 ◽  
Vol 39 (11) ◽  
pp. 2857-2874 ◽  
Author(s):  
Guillaume Lapeyre
Keyword(s):  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Large Scale ◽  
North Atlantic Ocean ◽  
Sea Surface ◽  
Surface Mode ◽  
Trapped Mode ◽  
The North ◽  
Surface Buoyancy ◽  
Baroclinic Modes

Abstract This study is motivated by the ongoing debate on the dynamical properties of surface motions at mesoscales that are measured by altimetry [for sea surface height (SSH)] and microwave [for sea surface temperature (SST)]. The mesoscale signal obtained by the altimeter is often considered to be associated with the first baroclinic mode, but recent results indicate that SST spectra and surface kinetic energy spectra derived from SSH have the same slope, which is not consistent with this hypothesis. Moreover, baroclinic modes are associated by definition with vanishing buoyancy anomalies at the ocean surface, which is obviously not the case. Here a careful derivation of the vertical modes is done using the concepts of quasigeostrophic potential vorticity (QGPV) theory. Since the surface buoyancy can be interpreted as a Dirac function in PV, the traditional baroclinic modes have to be completed by a surface-trapped mode with no interior QGPV. The possible contribution of each mode is quantified in a realistic simulation of the North Atlantic Ocean. The surface mode is found to give the largest contribution in terms of surface energy in most of the Atlantic. Its relative importance compared to the other modes is determined at first order by the large-scale forcing of PV and surface buoyancy. These results emphasize the necessity for a new interpretation of satellite measurements of sea surface temperature or height.

Measurement of Young’s Modulus and Internal Damping of Pork Muscle in Dynamic Mode

2016 ◽  
Vol 11 (03) ◽  
pp. 109-116
Author(s):  
Moez Chakroun ◽  
Med Hédi Ben Ghozlen
Keyword(s):  
Young’S Modulus ◽  
Vibration Frequency ◽  
Young's Modulus ◽  
Mechanical Impedance ◽  
Lower Surface ◽  
Dynamic Mode ◽  
Internal Damping ◽  
Body Tissues ◽  
Measured Impedance ◽  
Two Parameters

Automotive shocks involve various tiers’ speed for different human body tissues. Knowing the behavior of these tissues, including muscles, in different vibration frequency is therefore necessary. The muscle has viscoelatic properties. Dynamically, this material has variable mechanical properties depending on the vibration frequency. A novel technique is being employed to examine the variation of the mechanical impedance of pork muscle as a function of frequency. A force is imposed on the lower surface of the sample and acceleration is measured on its upper surface. These two parameters are measured using sensors. The sample is modeled by Kelvin–Voigt model. These measures allow deducing the change in the mechanical impedance modulus (/[Formula: see text]/ [Formula: see text] /Force: Acceleration/) of pork muscle as a function of vibration frequency. The measured impedance has a resonance of approximately 60[Formula: see text]Hz. Best-fit parameters of theoretical impedance can be deduced by superposition with the experiment result. The variation of Young’s modulus and internal damping of pig’s muscle as a function of frequency are determined. The results obtained between 5[Formula: see text]Hz and 30[Formula: see text]Hz are the same as determined by Aimedieu and al in 2003, therefore validating our technique. The Young’s modulus of muscle increases with the frequency, on the other hand, we note a rating decrease of internal damping.

scholarly journals Baroclinic Modes over Rough Bathymetry and the Surface Deformation Radius

2020 ◽  
Vol 50 (10) ◽  
pp. 2835-2847 ◽  
Author(s):  
J. H. LaCasce ◽  
Sjoerd Groeskamp
Keyword(s):  
Wave Speed ◽  
Surface Deformation ◽  
World Ocean ◽  
Surface Mode ◽  
Ocean Bottom ◽  
Baroclinic Mode ◽  
Flat Bottom ◽  
Two Layer Model ◽  
World Ocean Atlas ◽  
Baroclinic Modes

AbstractThe deformation radius is widely used as an indication of the eddy length scale at different latitudes. The radius is usually calculated assuming a flat ocean bottom. However, bathymetry alters the baroclinic modes and hence their deformation radii. In a linear quasigeostrophic two-layer model with realistic parameters, the deep flow for a 100-km wave approaches zero with a bottom ridge roughly 10 m high, leaving a baroclinic mode that is mostly surface trapped. This is in line with published current meter studies showing a primary EOF that is surface intensified and has nearly zero flow at the bottom. The deformation radius associated with this “surface mode” is significantly larger than that of the flat bottom baroclinic mode. Using World Ocean Atlas data, the surface radius is found to be 20%–50% larger over much of the globe, and 100% larger in some regions. This in turn alters the long Rossby wave speed, which is shown to be 1.5–2 times faster than over a flat bottom. In addition, the larger deformation radius is easier to resolve in ocean models.

scholarly journals Emergence of Wind-Driven Near-Inertial Waves in the Deep Ocean Triggered by Small-Scale Eddy Vorticity Structures

2011 ◽  
Vol 41 (7) ◽  
pp. 1297-1307 ◽  
Author(s):  
Eric Danioux ◽  
Patrice Klein ◽  
Matthew W. Hecht ◽  
Nobumasa Komori ◽  
Guillaume Roullet ◽  
...  
Keyword(s):  
Mesoscale Eddy ◽  
Deep Ocean ◽  
Mean Amplitude ◽  
Relative Vorticity ◽  
Wind Forcing ◽  
Small Scale ◽  
Inertial Waves ◽  
Deep Interior ◽  
Eddy Field ◽  
Baroclinic Modes

Abstract Using numerical simulations forced by a uniform realistic wind time series, the authors show that the presence of a mesoscale eddy field at midlatitudes accelerates the vertical propagation of the wind-forced near-inertial waves (NIW) and produces the emergence of a maximum of vertical velocity into the deep ocean (around 2500 m) characterized by a mean amplitude of 25 m day−1, a dominant 2f frequency, and scales as small as O(30 km). These results differ from previous studies that reported a smaller depth and larger scales. The authors show that the larger depth observed in the present study (2500 m instead of 1700 m) is due to the wind forcing duration that allows the first five baroclinic modes to disperse and to impact the deep NIW maximum (instead of the first two modes as reported before). The smaller scales (30 km instead of 90 km) are explained by a resonance mechanism (described in previous studies) that affects the high NIW baroclinic modes, but only when small-scale relative vorticity structures (related to the mesoscale eddy field) have an amplitude that is large enough. These results, which point out the importance of the wind forcing duration and the resolution, indicate that the emergence of a deep NIW maximum with a 2f frequency reported before is a robust feature that is enhanced with more realistic conditions. Such 2f frequency in the deep interior raises the question of the mechanisms, still unresolved, that may ultimately transfer this superinertial energy into mixing at these depths.

Trajectories of charged tracer particles around a charged sphere in a simple shear flow

1994 ◽  
Vol 263 ◽  
pp. 185-206 ◽  
Author(s):  
A. S. Dukhin ◽  
T. G. M. Van De Ven
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Tracer Particle ◽  
Simple Shear Flow ◽  
Infinite Length ◽  
Charged Sphere ◽  
Neutral Particles ◽  
Tracer Particles ◽  
Two Parameters ◽  
Limiting Case

The trajectories of electrically charged tracer particles travelling around a charged sphere subjected to a simple shear flow have been calculated. This is a limiting case of the relative trajectories of two unequal-sized spheres when the radius ratio a1/a2 approaches zero. Until now these trajectories have been calculated by assuming the additivity of hydrodynamic and electrostatic forces, while neglecting the electroviscous coupling forces. These electroviscous forces are long range and can significantly alter the relative trajectories of spheres. When a1/a2 → 0, it is found that these trajectories depend on two parameters, α and β, which depend on the surface charge density of the tracer particle and the sphere. The relative trajectories of charged particles are qualitatively different from those of neutral particles. There exist six intervals of α-values for which the trajectories of the tracer particle show different features. Several new types of trajectory appear, besides the open and closed trajectories for neutral particles, which we refer to as uni- and bidirectional infinite length trajectories, uni- and bidirectional finite length trajectories, open returning trajectories, and prolate, oblate and circular closed trajectories. This richness of possible trajectories is the result of three electrokinetic phenomena, affecting particle motion: electro-osmotic slip, electrophoretic and diffusiophoretic motion.

scholarly journals A Resonance Mechanism Leading to Wind-Forced Motions with a 2f Frequency

2008 ◽  
Vol 38 (10) ◽  
pp. 2322-2329 ◽  
Author(s):  
Eric Danioux ◽  
Patrice Klein
Keyword(s):  
Shallow Water Equations ◽  
Mesoscale Eddy ◽  
Relative Vorticity ◽  
General Situation ◽  
Small Scale ◽  
Wave Interactions ◽  
Resonance Mechanism ◽  
Eddy Field ◽  
Baroclinic Modes ◽  
Parametric Subharmonic Instability

Abstract This study revisits the mechanisms that spatially reorganize wind-forced inertial motions embedded in an oceanic mesoscale eddy field. Inertial motions are known to be affected by the eddy relative vorticity, being expelled from cyclonic structures and trapped within anticyclonic ones. Using shallow water equations (involving a single baroclinic mode), the authors show that nonlinear wave–wave interactions excite, through a resonance mechanism, motions with a 2f frequency (with f being the inertial frequency) and a specific length scale. In a more general situation involving several baroclinic modes, this resonance is found to be reinforced and principally efficient for the lowest baroclinic modes. Such characteristics make the energy of the wind-forced motions potentially available to small-scale mixing through parametric subharmonic instability (not taken into account in the present study).

Planetary waves in a stratified ocean of variable depth. Part 2. Continuously stratified ocean

1999 ◽  
Vol 388 ◽  
pp. 147-169 ◽  
Author(s):  
A. V. BOBROVICH ◽  
G. M. REZNIK
Keyword(s):  
Asymptotic Methods ◽  
Bottom Layer ◽  
Small Scale ◽  
Buoyancy Frequency ◽  
Baroclinic Mode ◽  
Displacement Effect ◽  
Barotropic Mode ◽  
Two Layer Model ◽  
Stratified Ocean ◽  
Baroclinic Modes

Linear Rossby waves in a continuously stratified ocean over a corrugated rough-bottomed topography are investigated by asymptotic methods. The main results are obtained for the case of constant buoyancy frequency. In this case there exist three types of modes: a topographic mode, a barotropic mode, and a countable set of baroclinic modes. The properties of these modes depend on the type of mode, the relative height δ of the bottom bumps, the wave scale L, the topography scale Lb and the Rossby scale Li. For small δ the barotropic and baroclinic modes are transformed into the ‘usual’ Rossby modes in an ocean of constant depth and the topographic mode degenerates. With increasing δ the frequencies of the barotropic and topographic modes increase monotonically and these modes become close to a purely topographic mode for sufficiently large δ. As for the baroclinic modes, their frequencies do not exceed O(βL) for any δ. For large δ the so-called ‘displacement’ effect occurs when the mode velocity becomes small in a near-bottom layer and the baroclinic mode does not ‘feel’ the actual rough bottom relief. At the same time, for some special values of the parameters a sort of resonance arises under which the large- and small-scale components of the baroclinic mode intensify strongly near the bottom.As in the two-layer model, a so-called ‘screening’ effect takes place here. It implies that for Lb<Li the small-scale component of the mode is confined to a near-bottom boundary layer (Lb/Li)H thick, whereas in the region above the layer the scale L of motion is always larger than or of the order of Li.

Surface Quasigeostrophic Solutions and Baroclinic Modes with Exponential Stratification

2012 ◽  
Vol 42 (4) ◽  
pp. 569-580 ◽  
Author(s):  
J. H. LaCasce
Keyword(s):  
Surface Density ◽  
Large Scale ◽  
Bottom Topography ◽  
Baroclinic Mode ◽  
Near Surface ◽  
Density Anomaly ◽  
Barotropic Mode ◽  
Baroclinic Modes ◽  
Exponential Stratification

Abstract The author derives baroclinic modes and surface quasigeostrophic (SQG) solutions with exponential stratification and compares the results to those obtained with constant stratification. The SQG solutions with exponential stratification decay more rapidly in the vertical and have weaker near-surface velocities. This then compounds the previously noted problem that SQG underpredicts the velocities associated with a given surface density anomaly. The author also examines how the SQG solutions project onto the baroclinic modes. With constant stratification, SQG waves larger than deformation scale project primarily onto the barotropic mode and to a lesser degree onto the first baroclinic mode. However, with exponential stratification, the largest projection is on the first baroclinic mode. The effect is even more pronounced over rough bottom topography. Therefore, large-scale SQG waves will look like the first baroclinic mode and vice versa, with realistic stratification.

scholarly journals Towards an accurate model of redshift-space distortions: a bivariate Gaussian description for the galaxy pairwise velocity distributions

2014 ◽  
Vol 11 (S308) ◽  
pp. 340-341
Author(s):  
Davide Bianchi ◽  
Matteo Chiesa ◽  
Luigi Guzzo
Keyword(s):  
Delta Function ◽  
Distribution Functions ◽  
General Description ◽  
Galaxy Surveys ◽  
Dirac Delta ◽  
Gaussian Functions ◽  
The Galaxy ◽  
Two Parameters ◽  
Limiting Case ◽  
Crucial Assumption

AbstractAs a step towards a more accurate modelling of redshift-space distortions (RSD) in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation , such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean μ and variance σ2. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.

Generalized Eady waves

1974 ◽  
Vol 62 (4) ◽  
pp. 643-655 ◽  
Author(s):  
Gareth P. Williams
Keyword(s):  
Baroclinic Instability ◽  
Amplitude Distribution ◽  
Lower Surface ◽  
Static Stability ◽  
Short Wave ◽  
Generalized Solutions ◽  
Vertical Variations ◽  
Basic States ◽  
Limiting Case ◽  
Temperature Amplitude

Solutions are obtained for the baroclinic instability problem for situations in which the static stability and mean shear vary geminately with height. The simple solution given by Eady is shown to be a special limiting case of a class of exact solutions for flows whose basic states have a vanishing interior potential vorticity gradient. The generalized solutions show that the temperature amplitude distribution is particularly sensitive to vertical variations in static stability but that phases and other amplitudes are only slightly influenced by such variations. When the static stability and shear increase (decrease) with height an enhanced temperature maximum occurs at the upper (lower) surface in comparison with the standard Eady solution.The generalized solutions also help to explain the character of annulus waves and predict a short-wave cut-off that is the same as that given by Eady's theory provided that it is based on the vertically averaged gravitational frequency.

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