scholarly journals Nonlinear Saturation of Vertically Propagating Rossby Waves

2009 ◽  
Vol 66 (4) ◽  
pp. 915-934 ◽  
Author(s):  
Constantine Giannitsis ◽  
Richard S. Lindzen
Keyword(s):  
Wave Propagation ◽  
Channel Model ◽  
Plane Channel ◽  
Nonlinear Flow ◽  
Computational Domain ◽  
Mean Flow ◽  
Wave Interactions ◽  
Linear Solution ◽  
Wave Growth ◽  
Flow Interactions

Abstract The interaction between vertical Rossby wave propagation and wave breaking is studied in the idealized context of a beta-plane channel model. Considering the problem of propagation through a uniform zonal flow in an exponentially stratified fluid, where linear theory predicts exponential wave growth with height, the question is how wave growth is limited in the nonlinear flow. Using a numerical model, the authors examine the behavior of the flow as the bottom forcing increases through values bound to lead to a breakdown of the linear solution within the computational domain. Focusing on the equilibrium flow obtained for each value of the bottom forcing, an attempt is made to identify the mechanisms involved in limiting wave growth and examine in particular the importance of wave–wave interactions. The authors also examine the case in which forcing is continuously increasing with time so as to enhance effects peculiar to transiency; it does not significantly alter the main results. Wave–mean flow interactions are found to dominate the dynamics even for strong bottom forcing values. Ultimately, it is the modification of the mean flow that is found to limit the vertical penetration of the forced wave, through either increased wave absorption or downward reflection. Linear propagation theory is found to capture the wave structure surprisingly well, even when the total flow is highly deformed. Overall, the numerical results seem to suggest that wave–wave interactions do not have a strong direct effect on the propagating disturbance. Wave–mean flow interactions limit wave growth sufficiently that a strong additional nonlinear enstrophy sink, through downscale cascade, is not necessary. Quantitatively, however, wave–wave interactions, primarily among the lowest wavenumbers, prove important so as to sufficiently accurately determine the basic state and its influence on wave propagation.

scholarly journals Nonlinear Generalization of Singular Vectors: Behavior in a Baroclinic Unstable Flow

2008 ◽  
Vol 65 (6) ◽  
pp. 1896-1911 ◽  
Author(s):  
Olivier Rivière ◽  
Guillaume Lapeyre ◽  
Olivier Talagrand
Keyword(s):  
Nonlinear Model ◽  
Linear Instability ◽  
Initial Time ◽  
Time Interval ◽  
Mean Flow ◽  
Unstable Flow ◽  
Wave Interactions ◽  
Singular Vectors ◽  
Amplification Rate ◽  
Flow Interactions

Abstract Singular vector (SV) analysis has proved to be helpful in understanding the linear instability properties of various types of flows. SVs are the perturbations with the largest amplification rate over a given time interval when linearizing the equations of a model along a particular solution. However, the linear approximation necessary to derive SVs has strong limitations and does not take into account several mechanisms present during the nonlinear development (such as wave–mean flow interactions). A new technique has been recently proposed that allows the generalization of SVs in terms of optimal perturbations with the largest amplification rate in the fully nonlinear regime. In the context of a two-layer quasigeostrophic model of baroclinic instability, the effect of nonlinearities on these nonlinear optimal perturbations [herein, nonlinear singular vectors (NLSVs)] is examined in terms of structure and dynamics. NLSVs essentially differ from SVs in the presence of a positive zonal-mean shear at initial time and in a broader meridional extension. As a result, NLSVs sustain a significant amplification in the nonlinear model while SVs exhibit a reduction of amplification in the nonlinear model. The presence of an initial zonal-mean shear in the NLSV increases the initial extraction of energy from the total shear (basic plus zonal-mean flows) and opposes wave–mean flow interactions that decrease the shear through the nonlinear evolution. The spatial shape of the NLSVs (and especially their meridional elongation) allows them to limit wave–wave interactions. These wave–wave interactions are responsible for the formation of vortices and for a smaller extraction of energy from the basic flow. Therefore, NLSVs are able to modify their shape in order to evolve quasi linearly to preserve a large nonlinear growth. Results are generalized for different norms and optimization times. When the streamfunction variance norm is used, the NLSV technique fails to converge because this norm selects very small scales at initial time. This indicates that this technique may be inadequate for problems for which the length scale of instability is not properly defined. For other norms (such as the potential enstrophy norm) and for different optimization times, the mechanisms of the NLSV amplification can still be viewed through wave–wave and wave–mean flow interactions.

Low-Frequency Variability in a Turbulent Baroclinic Jet: Eddy–Mean Flow Interactions in a Two-Level Model

2010 ◽  
Vol 67 (2) ◽  
pp. 452-467 ◽  
Author(s):  
Joseph Bernstein ◽  
Brian Farrell
Keyword(s):  
Time Scale ◽  
General Circulation ◽  
Channel Model ◽  
Low Frequency ◽  
Circulation Model ◽  
Coupled System ◽  
Mean Flow ◽  
Low Frequency Variability ◽  
Flow Interactions ◽  
The Waves

Abstract The origin of low-frequency variability in the midlatitude jet is investigated using a two-level baroclinic channel model. The model state fields are separated into slow and fast components using intermediate time- scale averaging. In the equation for the fast variables the nonlinear wave–wave interactions are parameterized as a stochastic excitation. The slowly varying ensemble mean eddy fluxes obtained from the resulting stochastic turbulence model are coupled with the slowly varying mean flow dynamics. This forms a coupled set of deterministic equations on the slow time scale that governs the dynamics of the eddy–mean flow interaction. The equilibria of this coupled system are found as a function of the excitation strength, which controls the level of turbulence. At low levels of turbulence the equilibrated flow with zonally symmetric mean forcing remains zonally symmetric, but as excitation increases it undergoes zonal symmetry-breaking bifurcations. Time-dependent flows arising from these bifurcations take the form of westward-propagating wavelike structures resembling blocking patterns. Features of these waves are characteristic of blocking in both observations and atmospheric general circulation model simulations including retrogression, eddy variance concentrated upstream of the waves, and eddy momentum flux forcing the waves.

scholarly journals Dynamical Response to the QBO in the Northern Winter Stratosphere: Signatures in Wave Forcing and Eddy Fluxes of Potential Vorticity

2015 ◽  
Vol 72 (12) ◽  
pp. 4487-4507 ◽  
Author(s):  
Ian P. White ◽  
Hua Lu ◽  
Nicholas J. Mitchell ◽  
Tony Phillips
Keyword(s):  
Wave Propagation ◽  
Potential Vorticity ◽  
Meridional Circulation ◽  
Polar Vortex ◽  
Wave Activity ◽  
Mean Flow ◽  
Quasi Biennial Oscillation ◽  
Stratospheric Polar Vortex ◽  
Wave Growth ◽  
Subtropical Jet

Abstract Wave–mean flow interactions associated with the Holton–Tan effect (HTE), whereby the tropical quasi-biennial oscillation (QBO) modulates the Northern Hemisphere wintertime stratospheric polar vortex, are studied using the ERA-Interim dataset. Significant evidence of the HTE in isentropic coordinates is found, with a weaker and warmer polar vortex present when the lower-stratospheric QBO is in its easterly phase (QBOe). For the first time, the authors quantify the QBO modulation of wave propagation, wave–mean flow interaction, and wave decay/growth via a calculation of potential vorticity (PV)-based measures, the zonal-mean momentum budget, and up-/downgradient eddy PV fluxes. The effect of the tropospheric subtropical jet on QBO modulation of the wave activity is also investigated. In the subtropical-to-midlatitude lower stratosphere, QBOe is associated with an enhanced upward flux of wave activity, and corresponding wave convergence and wave growth, which leads to a stronger poleward zonal-mean meridional circulation and consequently a warmer polar region. In the middle stratosphere, QBOe is associated with increased poleward wave propagation, leading to enhanced wave convergence and in situ wave growth at high latitudes and contributing to the weaker polar vortex. In agreement with recent studies, the results suggest that the critical-line effect cannot fully account for these wave anomalies associated with the HTE. Instead, it is suggestive of a new, additional mechanism that hinges on the QBO-induced meridional circulation effect on the latitudinal positioning of the subtropical jet. Under QBOe, the QBO-induced meridional circulation causes a poleward shift of the subtropical jet, encouraging more waves to propagate into the stratosphere at midlatitudes.

RANS and Large Eddy Simulation of Internal Combustion Engine Flows—A Comparative Study

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Xiaofeng Yang ◽  
Saurabh Gupta ◽  
Tang-Wei Kuo ◽  
Venkatesh Gopalakrishnan
Keyword(s):  
Large Eddy Simulation ◽  
High Speed ◽  
Combustion Engine ◽  
Flow Analysis ◽  
Partial Geometry ◽  
Computational Domain ◽  
Mean Flow ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Rans Simulations

A comparative cold flow analysis between Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) cycle-averaged velocity and turbulence predictions is carried out for a single cylinder engine with a transparent combustion chamber (TCC) under motored conditions using high-speed particle image velocimetry (PIV) measurements as the reference data. Simulations are done using a commercial computationally fluid dynamics (CFD) code CONVERGE with the implementation of standard k-ε and RNG k-ε turbulent models for RANS and a one-equation eddy viscosity model for LES. The following aspects are analyzed in this study: The effects of computational domain geometry (with or without intake and exhaust plenums) on mean flow and turbulence predictions for both LES and RANS simulations. And comparison of LES versus RANS simulations in terms of their capability to predict mean flow and turbulence. Both RANS and LES full and partial geometry simulations are able to capture the overall mean flow trends qualitatively; but the intake jet structure, velocity magnitudes, turbulence magnitudes, and its distribution are more accurately predicted by LES full geometry simulations. The guideline therefore for CFD engineers is that RANS partial geometry simulations (computationally least expensive) with a RNG k-ε turbulent model and one cycle or more are good enough for capturing overall qualitative flow trends for the engineering applications. However, if one is interested in getting reasonably accurate estimates of velocity magnitudes, flow structures, turbulence magnitudes, and its distribution, they must resort to LES simulations. Furthermore, to get the most accurate turbulence distributions, one must consider running LES full geometry simulations.

scholarly journals Wave-mean flow interactions in the upper atmosphere

1973 ◽  
Vol 4 (1-4) ◽  
pp. 327-343 ◽  
Author(s):  
Richard S. Lindzen
Keyword(s):  
Upper Atmosphere ◽  
Mean Flow ◽  
Flow Interactions

The Sensitivity of Persistent Geopotential Anomalies to the Climate of a Moist Channel Model

2021 ◽  
pp. 1-52
Author(s):  
Gregory Tierney ◽  
Walter A. Robinson ◽  
Gary Lackmann ◽  
Rebecca Miller
Keyword(s):  
Climate Change ◽  
Heat Release ◽  
Latent Heat ◽  
Channel Model ◽  
Heat Waves ◽  
Latent Heat Release ◽  
Mean Flow ◽  
Flow Variability ◽  
Virtual Temperature ◽  
Channel Configuration

AbstractHigh-impact events such as heat waves and droughts are often associated with persistent positive geopotential height anomalies (PAs). Understanding how PA activity will change in a future warmer climate is therefore fundamental to projecting associated changes in weather and climate extremes. This is a complex problem because the dynamics of PAs and their associated blocking activity are still poorly understood. Furthermore, climate-change influences on PA activity may be geographically dependent and encompass competing influences. To expose the salient impacts of climate change, we use an oceanic channel configuration of the Weather Research and Forecasting model (WRF) in a bivariate experiment focused on changes in environmental temperature, moisture, and baroclinicity. The 500-hPa wind speed and flow variability are found to increase with increasing temperature and baroclinicity, driven by increases in latent heat release and a stronger virtual temperature gradient. Changes to 500-hPa sinuosity are negligible. PAs are objectively identified at the 500-hPa level using an anomaly threshold method. When using a fixed threshold, PA trends indicate increased activity and strength with warming, but decreased activity and strength with Arctic amplification. Use of a climate-relative threshold hides these trends and highlights the importance of accurate characterization of the mean flow. Changes in PA activity mirror corresponding changes in 500-hPa flow variability and are found to be attributable to changes in three distinct dynamical mechanisms: baroclinic wave activity, virtual temperature effects, and latent heat release.

scholarly journals Dynamics of Extreme Stratospheric Negative Heat Flux Events in an Idealized Model

2018 ◽  
Vol 75 (10) ◽  
pp. 3521-3540 ◽  
Author(s):  
Etienne Dunn-Sigouin ◽  
Tiffany Shaw
Keyword(s):  
Heat Flux ◽  
Wave Propagation ◽  
Recent Work ◽  
Wave Interaction ◽  
Higher Order ◽  
Negative Events ◽  
Flow Mechanism ◽  
Mean Flow ◽  
Idealized Model

Recent work has shown that extreme stratospheric wave-1 negative heat flux events couple with the troposphere via an anomalous wave-1 signal. Here, a dry dynamical core model is used to investigate the dynamical mechanisms underlying the events. Ensemble spectral nudging experiments are used to isolate the role of specific dynamical components: 1) the wave-1 precursor, 2) the stratospheric zonal-mean flow, and 3) the higher-order wavenumbers. The negative events are partially reproduced when nudging the wave-1 precursor and the zonal-mean flow whereas they are not reproduced when nudging either separately. Nudging the wave-1 precursor and the higher-order wavenumbers reproduces the events, including the evolution of the stratospheric zonal-mean flow. Mechanism denial experiments, whereby one component is fixed to the climatology and others are nudged to the event evolution, suggest higher-order wavenumbers play a role by modifying the zonal-mean flow and through stratospheric wave–wave interaction. Nudging all tropospheric wave precursors (wave-1 and higher-order wavenumbers) confirms they are the source of the stratospheric waves. Nudging all stratospheric waves reproduces the tropospheric wave-1 signal. Taken together, the experiments suggest the events are consistent with downward wave propagation from the stratosphere to the troposphere and highlight the key role of higher-order wavenumbers.

Flow Interactions Between Shrouded Power Turbine and Nonaxisymmetric Exhaust Volute for Marine Gas Turbines

2017 ◽  
Author(s):  
Jie Gao ◽  
Feng Lin ◽  
Xiying Niu ◽  
Qun Zheng ◽  
Guoqiang Yue ◽  
...  
Keyword(s):  
Gas Turbine ◽  
Gas Turbines ◽  
Rotor Blade ◽  
Exhaust System ◽  
Computational Domain ◽  
Local Flow ◽  
Power Turbine ◽  
Flow Interactions ◽  
Shrouded Rotor ◽  
Turbine Exhaust

The marine gas turbine exhaust volute is an important component that connects a power turbine and an exhaust system, and it is of great importance to the overall performance of the gas turbine. Gases exhausted from the power turbine are expanded and deflected 90 degrees in the exhaust volute, and then discharge radially into the exhaust system. The flows in the power turbine and the nonaxisymmetric exhaust volute are closely coupled and inherently unsteady. The flow interactions between the power turbine and the exhaust volute have a significant influence on the shrouded rotor blade aerodynamic forces. However, the interactions have not been taken into account properly in current power turbine design approaches. The present study aims to investigate the flow interactions between the last stage of a shrouded power turbine and the nonaxisymmetric exhaust volute with struts. Special attention is given to the coupled aerodynamics and pressure response studies. This work was carried out using coupled computational fluid dynamics (CFD) simulations with the computational domain including a stator vane, 76 shrouded rotor blades, 9 struts and an exhaust volute. Three-dimensional (3D) unsteady and steady Reynolds-averaged Navier-Stokes (RANS) solutions in conjunction with a Spalart-Allmaras turbulence model are utilized to investigate the aerodynamic characteristics of shrouded rotors and an exhaust volute using a commercial CFD software ANSYS Fluent 14.0. The asymmetric flow fields are analyzed in detail; as are the unsteady pressures on the shrouded rotor blade. In addition, the unsteady total pressures at the volute outlet is also analyzed without consideration of the upstream turbine effects. Results show that the flows in the nonaxisymmetric exhaust volute are inherently unsteady; for the studied turbine-exhaust configuration the nonaxisymmetric back-pressure induced by the downstream volute leads to the local flow varying for each shrouded blade and low frequency fluctuations in the blade force. Detailed results from this investigation are presented and discussed in this paper.

Aneurysm No-Linear Unsteady Dynamic: Mathematical Modeling

2013 ◽  
Author(s):  
M. Hamadiche
Keyword(s):  
Differential Equation ◽  
Plane Channel ◽  
Second Order ◽  
Rheological Parameters ◽  
Time Signal ◽  
Elasticity Coefficient ◽  
Linear Solution ◽  
Geometry Model ◽  
Non Invasive ◽  
Invasive Method

A second order no-linear partial differential equation is worked out to describe the interaction of the flow with an elastic shell in large deformation domain. The model intends to describe the vibration of an aneurysm in arteries and veins. Two models are presented in this work. In the first one, the shell is inserted in otherwise rigid plane channel and in the second model the shell is inserted in otherwise rigid tube. In order to allow large displacement, the shell motion is described by Lagrangian variables. The steady version of the governing equation is a second order no-linear differential equation. A formal solution of the steady no-linear equation is obtained for plane channel model. It is shown that a steady solution exists only for some values of the dimensionless parameters ϕ and λ where ϕ is the ratio of transmural pressure to the elasticity coefficient and λ is the ratio of volume flux to the elasticity coefficient. The critical curve in the plan (ϕ,λ) for some control parameters are computed. Then, an unsteady solution of the no-linear unsteady equation is obtained numerically. It is found that the time signal prescribed by the unsteady no-linear solution depends strongly on the numerical values of the rheological parameters of the system. It is suggested that these signals could be used as a non invasive method in the diagnostic of the aneurysm when its vibration could be detected by a non invasive method. The linear analysis of the cylindrical geometry model shows that the aneurysm structure can be locked with heart pulse in a resonance frequency when the wall of the aneurysm becomes soft leading eventually to its rupture.

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