Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

2015 ◽  
Vol 782 ◽  
pp. 144-177 ◽  
Author(s):  
Anthony Randriamampianina ◽  
Emilia Crespo del Arco
Keyword(s):  
Prandtl Number ◽  
Gravity Waves ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Small Scale ◽  
Mean Flow ◽  
Baroclinic Waves ◽  
Fluid Properties ◽  
Spatio Temporal

Direct numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number $Pr=16$ is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection.

scholarly journals Synoptic Responses to Mountain Gravity Waves Encountering Directional Critical Levels

2007 ◽  
Vol 64 (3) ◽  
pp. 828-848 ◽  
Author(s):  
Armel Martin ◽  
François Lott
Keyword(s):  
Gravity Waves ◽  
General Circulation ◽  
Large Scale ◽  
Baroclinic Instability ◽  
General Circulation Models ◽  
Small Scale ◽  
Mountain Range ◽  
Critical Levels ◽  
Sensitivity Tests ◽  
Large Scale Flow

Abstract A heuristic model is used to study the synoptic response to mountain gravity waves (GWs) absorbed at directional critical levels. The model is a semigeostrophic version of the Eady model for baroclinic instability adapted by Smith to study lee cyclogenesis. The GWs exert a force on the large-scale flow where they encounter directional critical levels. This force is taken into account in the model herein and produces potential vorticity (PV) anomalies in the midtroposphere. First, the authors consider the case of an idealized mountain range such that the orographic variance is well separated between small- and large-scale contributions. In the absence of tropopause, the PV produced by the GW force has a surface impact that is significant compared to the surface response due to the large scales. For a cold front, the GW force produces a trough over the mountain and a larger-amplitude ridge immediately downstream. It opposes somehow to the response due to the large scales of the mountain range, which is anticyclonic aloft and cyclonic downstream. For a warm front, the GW force produces a ridge over the mountain and a trough downstream; hence it reinforces the response due to the large scales. Second, the robustness of the previous results is verified by a series of sensitivity tests. The authors change the specifications of the mountain range and of the background flow. They also repeat some experiments by including baroclinic instabilities, or by using the quasigeostrophic approximation. Finally, they consider the case of a small-scale orographic spectrum representative of the Alps. The significance of the results is discussed in the context of GW parameterization in the general circulation models. The results may also help to interpret the complex PV structures occurring when mountain gravity waves break in a baroclinic environment.

scholarly journals Mesospheric gravity wave activity estimated via airglow imagery, multistatic meteor radar, and SABER data taken during the SIMONe–2018 campaign

2020 ◽  
Author(s):  
Fabio Vargas ◽  
Jorge L. Chau ◽  
Harikrishnan Charuvil Asokan ◽  
Michael Gerding
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Large Scale ◽  
Lower Thermosphere ◽  
Small Scale ◽  
Meteor Radar ◽  
Mean Flow ◽  
Horizontal Scale ◽  
Momentum Fluxes ◽  
Mesosphere And Lower Thermosphere

Abstract. We describe in this study the analysis of small and large horizontal scale gravity waves from datasets composed of images from multiple mesospheric nightglow emissions as well as multistatic specular meteor radar (MSMR) winds collected in early November 2018, during the SIMONe–2018 campaign. These ground-based measurements are supported by temperature and neutral density profiles from TIMED/SABER satellite in orbits near Kühlungsborn, northern Germany (54.1° N, 11.8° E). The scientific goals here include the characterization of gravity waves and their interaction with the mean flow in the mesosphere and lower thermosphere and their relationship to dynamical conditions in the lower and upper atmosphere. We obtain intrinsic parameters of small and large horizontal scale gravity waves and characterize their impact in the mesosphere region via momentum flux and flux divergence estimations. We have verified that a small percent of the detected wave events are responsible for most of the momentum flux measured during the campaign from oscillations seen in the airglow brightness and MSMR winds. From the analysis of small-scale gravity waves in airglow images, we have found wave momentum fluxes ranging from 0.38 to 24.74 m2/s2 (0.88 ± 0.73 m2/s2 on average), with a total of 586.96 m2/s2 (sum over all 362 detected waves). However, small horizontal scale waves with flux > 3 m2/s2 (11 % of the events) transport 50 % of the total measured flux. Likewise, wave events having flux > 10 m2/s2 (2 % of the events) transport 20 % of the total flux. The examination of two large-scale waves seen simultaneously in airglow keograms and MSMR winds revealed relative amplitudes > 35 %, which translates into momentum fluxes of 21.2–29.6 m/s. In terms of gravity wave–mean flow interactions, these high momentum flux waves could cause decelerations of 22–41 m/s/day (small-scale waves) and 38–43 m/s/day (large-scale waves) if breaking or dissipating within short distances in the mesosphere and lower thermosphere region. The dominant large-scale waves might be the result of secondary gravity excited from imbalanced flow in the stratosphere caused by primary wave breaking.

Eddy Amplitudes in Baroclinic Turbulence Driven by Nonzonal Mean Flow: Shear Dispersion of Potential Vorticity

2007 ◽  
Vol 37 (4) ◽  
pp. 1037-1050 ◽  
Author(s):  
K. Shafer Smith
Keyword(s):  
Potential Vorticity ◽  
Large Scale ◽  
Dispersion Model ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Mean Flow ◽  
Jet Mixing ◽  
Zonal Jets ◽  
Shear Dispersion ◽  
The Cross

Abstract As in the midlatitude atmosphere, midocean eddies are primarily generated by baroclinically unstable mean currents. In contrast to the atmosphere, however, oceanic currents are significantly nonzonal. Even weak nonzonal currents are linearly unstable since β does not suppress growing meridional waves. Theories for the nonlinear equilibration of baroclinic instability, and hence theories for the amplitudes of midocean eddies, must therefore take into account the different dynamics of nonzonal flow. It is shown here that the amplitude of fully developed baroclinic turbulence due to nonzonal shears differs from that due to zonal shears primarily in the nature of the eddy generation. Since β will act to create large-scale zonal jet structures regardless of the generation source, the nature of eddy fluxes of potential vorticity (the source of eddy energy) in the zonal and meridional directions are fundamentally different. The cross-jet mixing has been shown previously to obey a mixing-length scaling, and this corresponds to the generation due to unstable zonal flow. The along-jet mixing, which corresponds to the generation due to the meridional shear, is shown here to be best described by a shear dispersion model. The resulting flux is orders of magnitude higher than in the cross-jet direction, and thus eddy energies driven by baroclinically unstable mean flows with a nonzero meridional component are much larger. This provides an explanation for recently reported results. Moreover, given recent observational and modeling studies showing the ubiquitous presence of zonal jets in the oceans, the results presented here indicate a powerful source of eddy energy.

On the vorticity transport due to dissipating or breaking waves in shallow-water flow

2000 ◽  
Vol 407 ◽  
pp. 235-263 ◽  
Author(s):  
OLIVER BÜHLER
Keyword(s):  
Numerical Simulations ◽  
Shallow Water ◽  
Gravity Waves ◽  
Large Scale ◽  
Bottom Topography ◽  
Breaking Waves ◽  
Small Scale ◽  
Practical Consideration ◽  
Mean Flow ◽  
Vorticity Transport

Theoretical and numerical results are presented on the transport of vorticity (or potential vorticity) due to dissipating gravity waves in a shallow-water system with background rotation and bottom topography. The results are obtained under the assumption that the flow can be decomposed into small-scale gravity waves and a large-scale mean flow. The particle-following formalism of ‘generalized Lagrangian-mean’ theory is then used to derive an ‘effective mean force’ that captures the vorticity transport due to the dissipating waves. This can be achieved without neglecting other, non-dissipative, effects which is an important practical consideration. It is then shown that the effective mean force obeys the so-called ‘pseudomomentum rule’, i.e. the force is approximately equal to minus the local dissipation rate of the wave's pseudomomentum. However, it is also shown that this holds only if the underlying dissipation mechanism is momentum-conserving. This requirement has important implications for numerical simulations, and these are discussed.The novelty of the results presented here is that they have been derived within a uniform theoretical framework, that they are not restricted to small wave amplitude, ray-tracing or JWKB-type approximations, and that they also include wave dissipation by breaking, or shock formation. The theory is tested carefully against shock-capturing nonlinear numerical simulations, which includes the detailed study of a wavetrain subject to slowly varying bottom topography. The theory is also cross-checked in the appropriate asymptotic limit against recently formulated weakly nonlinear theories. In addition to the general finite-amplitude theory, detailed small-amplitude expressions for the main results are provided in which the explicit appearance of Lagrangian fields can be avoided. The motivation for this work stems partly from an on-going study of high-altitude breaking of internal gravity waves in the atmosphere, and some preliminary remarks on atmospheric applications and on three-dimensional stratified versions of these results are given.

scholarly journals Mesospheric gravity wave activity estimated via airglow imagery, multistatic meteor radar, and SABER data taken during the SIMONe–2018 campaign

2021 ◽  
Vol 21 (17) ◽  
pp. 13631-13654
Author(s):  
Fabio Vargas ◽  
Jorge L. Chau ◽  
Harikrishnan Charuvil Asokan ◽  
Michael Gerding
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Large Scale ◽  
Lower Thermosphere ◽  
Small Scale ◽  
Meteor Radar ◽  
Mean Flow ◽  
Flux Divergence ◽  
Mesosphere And Lower Thermosphere

Abstract. We describe in this study the analysis of small and large horizontal-scale gravity waves from datasets composed of images from multiple mesospheric airglow emissions as well as multistatic specular meteor radar (MSMR) winds collected in early November 2018, during the SIMONe–2018 (Spread-spectrum Interferometric Multi-static meteor radar Observing Network) campaign. These ground-based measurements are supported by temperature and neutral density profiles from TIMED/SABER (Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics/Sounding of the Atmosphere using Broadband Emission Radiometry) satellite in orbits near Kühlungsborn, northern Germany (54.1∘ N, 11.8∘ E). The scientific goals here include the characterization of gravity waves and their interaction with the mean flow in the mesosphere and lower thermosphere and their relationship to dynamical conditions in the lower and upper atmosphere. We have obtained intrinsic parameters of small- and large-scale gravity waves and characterized their impact in the mesosphere via momentum flux (FM) and momentum flux divergence (FD) estimations. We have verified that a small percentage of the detected wave events is responsible for most of FM measured during the campaign from oscillations seen in the airglow brightness and MSMR winds taken over 45 h during four nights of clear-sky observations. From the analysis of small-scale gravity waves (λh < 725 km) seen in airglow images, we have found FM ranging from 0.04–24.74 m2 s−2 (1.62 ± 2.70 m2 s−2 on average). However, small-scale waves with FM > 3 m2 s−2 (11 % of the events) transport 50 % of the total measured FM. Likewise, wave events of FM > 10 m2 s−2 (2 % of the events) transport 20 % of the total. The examination of large-scale waves (λh > 725 km) seen simultaneously in airglow keograms and MSMR winds revealed amplitudes > 35 %, which translates into FM = 21.2–29.6 m2 s−2. In terms of gravity-wave–mean-flow interactions, these large FM waves could cause decelerations of FD = 22–41 m s−1 d−1 (small-scale waves) and FD = 38–43 m s−1 d−1 (large-scale waves) if breaking or dissipating within short distances in the mesosphere and lower thermosphere region.

scholarly journals Mesoscale Predictability of Moist Baroclinic Waves: Convection-Permitting Experiments and Multistage Error Growth Dynamics

2007 ◽  
Vol 64 (10) ◽  
pp. 3579-3594 ◽  
Author(s):  
Fuqing Zhang ◽  
Naifang Bei ◽  
Richard Rotunno ◽  
Chris Snyder ◽  
Craig C. Epifanio
Keyword(s):  
Large Scale ◽  
Random Noise ◽  
Baroclinic Instability ◽  
Growth Dynamics ◽  
Small Scale ◽  
Moist Convection ◽  
Error Growth ◽  
Baroclinic Waves ◽  
Convective Scale ◽  
Shear Production

Abstract A recent study examined the predictability of an idealized baroclinic wave amplifying in a conditionally unstable atmosphere through numerical simulations with parameterized moist convection. It was demonstrated that with the effect of moisture included, the error starting from small random noise is characterized by upscale growth in the short-term (0–36 h) forecast of a growing synoptic-scale disturbance. The current study seeks to explore further the mesoscale error-growth dynamics in idealized moist baroclinic waves through convection-permitting experiments with model grid increments down to 3.3 km. These experiments suggest the following three-stage error-growth model: in the initial stage, the errors grow from small-scale convective instability and then quickly [O(1 h)] saturate at the convective scales. In the second stage, the character of the errors changes from that of convective-scale unbalanced motions to one more closely related to large-scale balanced motions. That is, some of the error from convective scales is retained in the balanced motions, while the rest is radiated away in the form of gravity waves. In the final stage, the large-scale (balanced) components of the errors grow with the background baroclinic instability. Through examination of the error-energy budget, it is found that buoyancy production due mostly to moist convection is comparable to shear production (nonlinear velocity advection). It is found that turning off latent heating not only dramatically decreases buoyancy production, but also reduces shear production to less than 20% of its original amplitude.

Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

Atmospheric general circulation and waves simulated by a Venus AORI GCM with topographical and radiative forcings

2021 ◽  
Author(s):  
Masaru Yamamoto ◽  
Takumi Hirose ◽  
Kohei Ikeda ◽  
Masaaki Takahashi
Keyword(s):  
Gravity Waves ◽  
General Circulation ◽  
Circulation Model ◽  
Stationary Wave ◽  
Static Stability ◽  
Small Scale ◽  
Mean Flow ◽  
Short Period ◽  
Low Latitudes ◽  
Thermal Tides

&lt;p&gt;General circulation and waves are investigated using a T63 Venus general circulation model (GCM) with solar and thermal radiative transfer in the presence of high-resolution surface topography. This model has been developed by Ikeda (2011) at the Atmosphere and Ocean Research Institute (AORI), the University of Tokyo, and was used in Yamamoto et al. (2019, 2021). In the wind and static stability structures similar to the observed ones, the waves are investigated. Around the cloud-heating maximum (~65 km), the simulated thermal tides accelerate an equatorial superrotational flow with a speed of ~90 m/s&lt;sup&gt;&lt;/sup&gt;with rates of 0.2&amp;#8211;0.5 m/s/(Earth day) via both horizontal and vertical momentum fluxes at low latitudes. Over the high mountains at low latitudes, the vertical wind variance at the cloud top is produced by topographically-fixed, short-period eddies, indicating penetrative plumes and gravity waves. In the solar-fixed coordinate system, the variances (i.e., the activity of waves other than thermal tides) of flow are relatively higher on the night-side than on the dayside at the cloud top. The local-time variation of the vertical eddy momentum flux is produced by both thermal tides and solar-related, small-scale gravity waves. Around the cloud bottom, the 9-day super-rotation of the zonal mean flow has a weak equatorial maximum and the 7.5-day Kelvin-like wave has an equatorial jet-like wind of 60-70 m/s. Because we discussed the thermal tide and topographically stationary wave in Yamamoto et al. (2021), we focus on the short-period eddies in the presentation.&lt;/p&gt;

scholarly journals Excitation of zonal flow by the modulational instability in electron temperature gradient driven turbulence

2008 ◽  
Vol 74 (3) ◽  
pp. 381-389 ◽  
Author(s):  
Yu. A. ZALIZNYAK ◽  
A. I. YAKIMENKO ◽  
V. M. LASHKIN
Keyword(s):  
Temperature Gradient ◽  
Electron Temperature ◽  
Large Scale ◽  
Modulational Instability ◽  
Zonal Flow ◽  
Finite Amplitude ◽  
Small Scale ◽  
Drift Waves ◽  
Zonal Flows ◽  
Electron Temperature Gradient

AbstractThe generation of large-scale zonal flows by small-scale electrostatic drift waves in electron temperature gradient driven turbulence model is considered. The generation mechanism is based on the modulational instability of a finite amplitude monochromatic drift wave. The threshold and growth rate of the instability as well as the optimal spatial scale of zonal flow are obtained.

Nonlinear dynamics over rough topography: homogeneous and stratified quasi-geostrophic theory

2003 ◽  
Vol 474 ◽  
pp. 299-318 ◽  
Author(s):  
JACQUES VANNESTE
Keyword(s):  
Nonlinear Dynamics ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Small Scale ◽  
Stratified Fluids ◽  
Homogeneous Case ◽  
Bottom Boundary ◽  
One Dimensional ◽  
Averaged Equations ◽  
Large Scale Flow

The weakly nonlinear dynamics of quasi-geostrophic flows over a one-dimensional, periodic or random, small-scale topography is investigated using an asymptotic approach. Averaged (or homogenized) evolution equations which account for the flow–topography interaction are derived for both homogeneous and continuously stratified quasi-geostrophic fluids. The scaling assumptions are detailed in each case; for stratified fluids, they imply that the direct influence of the topography is confined within a thin bottom boundary layer, so that it is through a new bottom boundary condition that the topography affects the large-scale flow. For both homogeneous and stratified fluids, a single scalar function entirely encapsulates the properties of the topography that are relevant to the large-scale flow: it is the correlation function of the topographic height in the homogeneous case, and a linear transform thereof in the continuously stratified case.Some properties of the averaged equations are discussed. Explicit nonlinear solutions in the form of one-dimensional travelling waves can be found. In the homogeneous case, previously studied by Volosov, they obey a second-order differential equation; in the stratified case on which we focus they obey a nonlinear pseudodifferential equation, which reduces to the Peierls–Nabarro equation for sinusoidal topography. The known solutions to this equation provide examples of nonlinear periodic and solitary waves in continuously stratified fluid over topography.The influence of bottom topography on large-scale baroclinic instability is also examined using the averaged equations: they allow a straightforward extension of Eady's model which demonstrates the stabilizing effect of topography on baroclinic instability.

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