scholarly journals Linear Non-Modal Growth of Planar Perturbations in a Layered Couette Flow

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 442
Author(s):  
Emmanouil G. Iliakis ◽  
Nikolaos A. Bakas
Keyword(s):  
Normal Modes ◽  
Maximum Growth ◽  
Boussinesq Approximation ◽  
High Amplitude ◽  
Small Scale ◽  
Time Interval ◽  
Transient Growth ◽  
Stratified Turbulence ◽  
Propagating Waves ◽  
Orr Mechanism

Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized Stability Theory are utilized to study linear transient growth within a finite time interval of two-dimensional perturbations in an inviscid, three-layer constant shear flow under the Boussinesq approximation. It is found that, for low optimization times, small-scale perturbations utilize the Orr mechanism and achieve growth equal to that in the case of an unstratified flow. For larger optimization times, transient growth is much larger compared to growth for an unstratified flow as the Kelvin–Orr waves comprising the continuous spectrum of the dynamical operator and the gravity edge-waves comprising the discrete spectrum interact synergistically. Maximum growth is obtained for perturbations with scales within the region of instability, but significant growth is maintained for modally stable perturbations as well. For perturbations with scales within the unstable region, the unstable normal modes are excited at high amplitude by their bi-orthogonals. For perturbations with modally stable scales, the Orr mechanism is utilized to excite at high amplitude neutral propagating waves resembling the neutral Taylor–Caulfield modes.

Dissipation of Synoptic-Scale Flow by Small-Scale Turbulence

2008 ◽  
Vol 65 (3) ◽  
pp. 766-791 ◽  
Author(s):  
K. Ngan ◽  
P. Bartello ◽  
D. N. Straub
Keyword(s):  
Normal Modes ◽  
Base Flow ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Synoptic Scale ◽  
Boussinesq Model ◽  
Weak Stratification ◽  
Balanced Flow ◽  
Scale Turbulence ◽  
Scale Motion

Abstract Although it is now accepted that imbalance in the atmosphere and ocean is generic, the feedback of the unbalanced motion on the balanced flow has not received much attention. In this work the parameterization problem is examined in the context of rotating stratified turbulence, that is, with a nonhydrostatic Boussinesq model. Using the normal modes as a first approximation to the balanced and unbalanced flow, the growth of ageostrophic perturbations to the quasigeostrophic flow and the associated feedback are studied. For weak stratification, there are analogies with the three-dimensionalization of decaying 2D turbulence: the growth rate of the ageostrophic perturbation follows a linear estimate, geostrophic energy is extracted from the base flow, and the associated damping on the geostrophic base flow (the “eddy viscosity”) is peaked at large horizontal scales. For strong stratification, the transfer spectra and eddy viscosities maintain this structure if there is synoptic-scale motion and the buoyancy scale is adequately resolved. This has been confirmed for global Rossby and Froude numbers of O(0.1). Implications for atmospheric and oceanic modeling are discussed.

Generation of slow large scales in forced rotating stratified turbulence

2002 ◽  
Vol 451 ◽  
pp. 145-168 ◽  
Author(s):  
LESLIE M. SMITH ◽  
FABIAN WALEFFE
Keyword(s):  
Rotation Axis ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Critical Value ◽  
Stratified Flows ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Noise Forcing ◽  
Forced Turbulence ◽  
Stably Stratified Flow

Numerical simulations are used to study homogeneous, forced turbulence in three-dimensional rotating, stably stratified flow in the Boussinesq approximation, where the rotation axis and gravity are both in the zˆ-direction. Energy is injected through a three-dimensional isotropic white-noise forcing localized at small scales. The parameter range studied corresponds to Froude numbers smaller than an O(1) critical value, below which energy is transferred to scales larger than the forcing scales. The values of the ratio N/f range from ≈1/2 to ∞, where N is the Brunt–Väisälä frequency and f is twice the rotation rate. For strongly stratified flows (N/f[Gt ]1), the slow large scales generated by the fast small-scale forcing consist of vertically sheared horizontal flow. Quasi-geostrophic dynamics dominate, at large scales, only when 1/2 [les ] N/f [les ] 2, which is the range where resonant triad interactions cannot occur.

scholarly journals Effect of the Assimilation Frequency of Radar Reflectivity on Rain Storm Prediction by Using WRF-3DVAR

2021 ◽  
Vol 13 (11) ◽  
pp. 2103
Author(s):  
Yuchen Liu ◽  
Jia Liu ◽  
Chuanzhe Li ◽  
Fuliang Yu ◽  
Wei Wang
Keyword(s):  
Data Assimilation ◽  
Northern China ◽  
Horizontal Resolution ◽  
Radar Reflectivity ◽  
Small Scale ◽  
Time Interval ◽  
Outer Domain ◽  
Storm Prediction ◽  
The Impact ◽  
Assimilation Time

An attempt was made to evaluate the impact of assimilating Doppler Weather Radar (DWR) reflectivity together with Global Telecommunication System (GTS) data in the three-dimensional variational data assimilation (3DVAR) system of the Weather Research Forecast (WRF) model on rain storm prediction in Daqinghe basin of northern China. The aim of this study was to explore the potential effects of data assimilation frequency and to evaluate the outputs from different domain resolutions in improving the meso-scale NWP rainfall products. In this study, four numerical experiments (no assimilation, 1 and 6 h assimilation time interval with DWR and GTS at 1 km horizontal resolution, 6 h assimilation time interval with radar reflectivity, and GTS data at 3 km horizontal resolution) are carried out to evaluate the impact of data assimilation on prediction of convective rain storms. The results show that the assimilation of radar reflectivity and GTS data collectively enhanced the performance of the WRF-3DVAR system over the Beijing-Tianjin-Hebei region of northern China. It is indicated by the experimental results that the rapid update assimilation has a positive impact on the prediction of the location, tendency, and development of rain storms associated with the study area. In order to explore the influence of data assimilation in the outer domain on the output of the inner domain, the rainfall outputs of 3 and 1 km resolution are compared. The results show that the data assimilation in the outer domain has a positive effect on the output of the inner domain. Since the 3DVAR system is able to analyze certain small-scale and convective-scale features through the incorporation of radar observations, hourly assimilation time interval does not always significantly improve precipitation forecasts because of the inaccurate radar reflectivity observations. Therefore, before data assimilation, the validity of assimilation data should be judged as far as possible in advance, which can not only improve the prediction accuracy, but also improve the assimilation efficiency.

Results of a seismic reflection survey across the fault zone between the Thompson nickel belt and the Churchill Tectonic Province, northern Manitoba

1981 ◽  
Vol 18 (1) ◽  
pp. 13-25 ◽  
Author(s):  
A. G. Green
Keyword(s):  
Fault Zone ◽  
Lower Crust ◽  
Seismic Reflection ◽  
High Amplitude ◽  
Small Scale ◽  
Upper Crust ◽  
Travel Times ◽  
Reflection Point ◽  
Point Data ◽  
Amplitude Reflection

Approximately 11 km of four-fold common reflection point data have been recorded across a region that spans the contact fault zone between the Thompson nickel belt and the Churchill Tectonic Province. From these data it is shown that the upper crust in this region and, to a lesser extent, the lower crust are characterized by numerous scattered events that originate from relatively small-scale features. Within the Thompson nickel belt two extensive and particularly high-amplitude reflection zones, at two-way travel times of t = 5.0–5.5 s and t = 6.0–6.5 s, are recorded with apparent northwesterly dips of 0–20 °C. These reflection zones, which have a laminated character, are truncated close to the faulted contact with the Churchill Province. Both the contact fault zone and the Churchill Province in this region have crustal sections that are relatively devoid of significant reflectors. The evidence presented here confirms that the crustal section of the Thompson nickel belt is fundamentally different from that of the Churchill Tectonic Province.

scholarly journals Instability of coupled gravity-inertial-Rossby waves on a β-plane in solar system atmospheres

2009 ◽  
Vol 27 (11) ◽  
pp. 4221-4227 ◽  
Author(s):  
J. F. McKenzie
Keyword(s):  
Rossby Waves ◽  
Narrow Band ◽  
Boussinesq Approximation ◽  
The Other ◽  
The Earth ◽  
Propagating Waves ◽  
Inertial Wave ◽  
The One ◽  
Fifth Order ◽  
Critical Latitude

Abstract. This paper provides an analysis of the combined theory of gravity-inertial-Rossby waves on a β-plane in the Boussinesq approximation. The wave equation for the system is fifth order in space and time and demonstrates how gravity-inertial waves on the one hand are coupled to Rossby waves on the other through the combined effects of β, the stratification characterized by the Väisälä-Brunt frequency N, the Coriolis frequency f at a given latitude, and vertical propagation which permits buoyancy modes to interact with westward propagating Rossby waves. The corresponding dispersion equation shows that the frequency of a westward propagating gravity-inertial wave is reduced by the coupling, whereas the frequency of a Rossby wave is increased. If the coupling is sufficiently strong these two modes coalesce giving rise to an instability. The instability condition translates into a curve of critical latitude Θc versus effective equatorial rotational Mach number M, with the region below this curve exhibiting instability. "Supersonic" fast rotators are unstable in a narrow band of latitudes around the equator. For example Θc~12° for Jupiter. On the other hand slow "subsonic" rotators (e.g. Mercury, Venus and the Sun's Corona) are unstable at all latitudes except very close to the poles where the β effect vanishes. "Transonic" rotators, such as the Earth and Mars, exhibit instability within latitudes of 34° and 39°, respectively, around the Equator. Similar results pertain to Oceans. In the case of an Earth's Ocean of depth 4km say, purely westward propagating waves are unstable up to 26° about the Equator. The nonlinear evolution of this instability which feeds off rotational energy and gravitational buoyancy may play an important role in atmospheric dynamics.

scholarly journals AxiSEM: broadband 3-D seismic wavefields in axisymmetric media

Solid Earth ◽  
2014 ◽  
Vol 5 (1) ◽  
pp. 425-445 ◽  
Author(s):  
T. Nissen-Meyer ◽  
M. van Driel ◽  
S. C. Stähler ◽  
K. Hosseini ◽  
S. Hempel ◽  
...  
Keyword(s):  
Normal Modes ◽  
Spectral Element ◽  
Multipole Expansion ◽  
Small Scale ◽  
Computational Domain ◽  
Diverse Range ◽  
Earthquake Sources ◽  
Third Dimension ◽  
Computational Resources ◽  
Background Models

Abstract. We present a methodology to compute 3-D global seismic wavefields for realistic earthquake sources in visco-elastic anisotropic media, covering applications across the observable seismic frequency band with moderate computational resources. This is accommodated by mandating axisymmetric background models that allow for a multipole expansion such that only a 2-D computational domain is needed, whereas the azimuthal third dimension is computed analytically on the fly. This dimensional collapse opens doors for storing space–time wavefields on disk that can be used to compute Fréchet sensitivity kernels for waveform tomography. We use the corresponding publicly available AxiSEM (www.axisem.info) open-source spectral-element code, demonstrate its excellent scalability on supercomputers, a diverse range of applications ranging from normal modes to small-scale lowermost mantle structures, tomographic models, and comparison with observed data, and discuss further avenues to pursue with this methodology.

scholarly journals Goldilocks mixing in oceanic shear-induced turbulent overturns

2021 ◽  
Vol 928 ◽  
Author(s):  
A. Mashayek ◽  
C.P. Caulfield ◽  
M.H. Alford
Keyword(s):  
Ocean Circulation ◽  
Turbulent Mixing ◽  
Intermediate Phase ◽  
Turbulent Flux ◽  
Geographical Location ◽  
Small Scale ◽  
Supporting Evidence ◽  
Stratified Turbulence ◽  
Wide Range ◽  
Variable Flux

We present a new, simple and physically motivated parameterization, based on the ratio of Thorpe and Ozmidov scales, for the irreversible turbulent flux coefficient $\varGamma _{\mathcal {M}}= {\mathcal {M}}/\epsilon$ , i.e. the ratio of the irreversible rate ${\mathcal {M}}$ at which the background potential energy increases in a stratified flow due to macroscopic motions to the dissipation rate of turbulent kinetic energy $\epsilon$ . Our parameterization covers all three key phases (crucially, in time) of a shear-induced stratified turbulence life cycle: the initial, ‘hot’ growing phase, the intermediate energetically forced phase and the final ‘cold’ fossilization decaying phase. Covering all three phases allows us to highlight the importance of the intermediate one, to which we refer as the ‘Goldilocks’ phase due to its apparently optimal (and so neither too hot nor too cold, but just right) balance, in which energy transfer from background shear to the turbulent mixing is most efficient. The value of $\varGamma _{\mathcal {M}}$ is close to 1/3 during this phase, which we demonstrate appears to be related to an adjustment towards a critical or marginal Richardson number for sustained turbulence ${\sim }0.2\text {--}0.25$ . Importantly, although buoyancy effects are still significant at leading order for the turbulent dynamics during this intermediate phase, the marginal balance in the flow ensures that the turbulent mixing of the (density) scalar is nevertheless effectively ‘locked’ to the turbulent mixing of momentum. We present supporting evidence for our parameterization through comparison with six oceanographic datasets that span various turbulence generation regimes and a wide range of geographical location and depth. Using these observations, we highlight the significance of parameterizing an inherently variable flux coefficient for capturing the turbulent flux associated with rare energetic, yet fundamentally shear-driven (and so not strongly stratified) overturns that make a disproportionate contribution to the total mixing. We also highlight the importance of representation of young turbulent patches in the parameterization for connecting the small scale physics to larger scale applications of mixing such as ocean circulation and tracer budgets. Shear-induced turbulence is therefore central to irreversible mixing in the world's oceans, apparently even close to the seafloor, and it is critically important to appreciate the inherent time dependence and evolution of mixing events: history matters to mixing.

scholarly journals Accumulation patterns around Dome C, East Antarctica, in the last 73 kyr

2018 ◽  
Vol 12 (4) ◽  
pp. 1401-1414 ◽  
Author(s):  
Marie G. P. Cavitte ◽  
Frédéric Parrenin ◽  
Catherine Ritz ◽  
Duncan A. Young ◽  
Brice Van Liefferinge ◽  
...  
Keyword(s):  
Large Scale ◽  
Flow Model ◽  
East Antarctica ◽  
Small Scale ◽  
Time Interval ◽  
Accumulation Rates ◽  
Ice Flow ◽  
Last Glacial ◽  
Prevailing Wind Direction ◽  
The Last Glacial

Abstract. We reconstruct the pattern of surface accumulation in the region around Dome C, East Antarctica, since the last glacial. We use a set of 18 isochrones spanning all observable depths of the ice column, interpreted from various ice-penetrating radar surveys and a 1-D ice flow model to invert for accumulation rates in the region. The shallowest four isochrones are then used to calculate paleoaccumulation rates between isochrone pairs using a 1-D assumption where horizontal advection is negligible in the time interval of each layer. We observe that the large-scale (100s km) surface accumulation gradient is spatially stable through the last 73 kyr, which reflects current modeled and observed precipitation gradients in the region. We also observe small-scale (10 s km) accumulation variations linked to snow redistribution at the surface, due to changes in its slope and curvature in the prevailing wind direction that remain spatially stationary since the last glacial.

Reverberation Intensity Decaying in Range-Dependent Waveguide

2019 ◽  
Vol 27 (03) ◽  
pp. 1950007
Author(s):  
J. R. Wu ◽  
T. F. Gao ◽  
E. C. Shang
Keyword(s):  
Large Scale ◽  
Back Propagation ◽  
Normal Modes ◽  
Small Scale ◽  
Signal Pulse ◽  
First Order ◽  
Orthogonal Property ◽  
Short Signal ◽  
Scale Roughness ◽  
Special Case

In this paper, an analytic range-independent reverberation model based on the first-order perturbation theory is extended to range-dependent waveguide. This model considers the effect of bottom composite roughness: small-scale bottom rough surface provides dominating energy for reverberation, whereas large-scale roughness has the effect of forward and back propagation. For slowly varying bottom and short signal pulse, analytic small-scale roughness backscattering theory is adapted in range-dependent waveguides. A parabolic equation is used to calculate Green functions in range-dependent waveguides, and the orthogonal property of local normal modes is employed to estimate the modal spectrum of PE field. Synthetic tests demonstrate that the proposed reverberation model works well, and it can also predict the reverberation of range-independent waveguide as a special case.

High Performance Structural Vibration Control by a Preview of the Future Seismic Waveform Generated With a Wave Transmission Network and an AI-Based Estimation System

2019 ◽  
Author(s):  
Kazuhiko Hiramoto ◽  
Taichi Matsuoka ◽  
Katsuaki Sunakoda
Keyword(s):  
Vibration Control ◽  
Control Method ◽  
Small Scale ◽  
Control Law ◽  
Time Interval ◽  
Transmission Network ◽  
Control Performance ◽  
Seismic Waveform ◽  
The Future ◽  
Estimation System

Abstract We propose a new active vibration control strategy based on the future seismic waveform information obtained in remote observation sites. The waveform information in the remote site is transmitted by a waveform transmission network to the structure under control. The waveform transmission network is realized by interconnecting multiple controlled structures and observation sites. By using the future waveform information obtained through the network, we propose a control law realizing fairly higher control performance over the conventional structural control methodologies. A preview control law consisting of the state-feedback and feedforward control (preview action) is adopted. For the preview action, future values of the disturbance in some time interval are necessary. However, because the future value of the earthquake waveform is unknown, the preview action contributing the performance improvement is generally impossible. To get over this difficulty, an AI-based wave estimation system to estimate the future earthquake waveform is proposed. The wave estimation system is a multi-layered artificial neural network (ANN). Through a small scale simulation study with a recorded earthquake event in Japan, we show that the proposed control method achieves much higher control performance over the conventional LQ-based active control.

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