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.

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 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

Spatial Stability Analysis of a Flap Side Edge Vortex

2005 ◽  
Vol 4 (1-2) ◽  
pp. 37-47
Author(s):  
Jean-Philippe Brazier ◽  
Frédéric Moens ◽  
Philippe Bardoux
Keyword(s):  
Stability Analysis ◽  
Temporal Stability ◽  
Low Frequency ◽  
Aerodynamic Noise ◽  
Navier Stokes ◽  
Mean Flow ◽  
Side Edge ◽  
Amplification Rate ◽  
Edge Vortex ◽  
Flap Deflection

The flap side edge vortex is suspected to contribute to aerodynamic noise generation. Using a temporal stability analysis, Khorrami and Singer have shown that unstable modes could exist in this vortex. Due to the convective nature of this instability, a spatial analysis is more suitable. This is the subject of the present work. The mean flow past a 2D wing with a half-span flap has been computed with a steady 3D Navier-Stokes code. Then, local linear stability calculations are performed in several planes perpendicular to the vortex axis. The vortex is assumed axisymmetric and modelled with Batchelor's analytical vortex. Using Gaster's relation, the spatial amplification rate is calculated, giving by integration the relative amplitude of the fluctuations. Some low-frequency fluctuations are seen to be preferentially amplified by the vortex, but the amplifications remain small, so that this mechanism alone should not produce important noise in this particular configuration, where the flap deflection angle is moderate.

scholarly journals Modeling the 3-d flow around a cylinder using the SAS hybrid model

2014 ◽  
Vol 16 (5) ◽  
pp. 901-918 ◽  
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Cross Flow ◽  
Numerical Code ◽  
Navier Stokes ◽  
Computational Domain ◽  
Mean Flow ◽  
Unstable Flow ◽  
Vortex Size

<div> <p>Three-dimensional calculations were performed to simulate the flow around a cylindrical vegetation element using the Scale Adaptive Simulation (SAS) model; commonly, this is the first step of the modeling of the flow through multiple vegetation elements. SAS solves the Reynolds Averaged Navier-Stokes equations in stable flow regions, while in regions with unstable flow it goes unsteady producing a resolved turbulent spectrum after reducing eddy viscosity according to the locally resolved vortex size represented by the von Karman length scale. A finite volume numerical code was used for the spatial discretisation of the rectangular computational domain with stream-wise, cross-flow and vertical dimensions equal to 30D, 11D and 1D, respectively, which was resolved with unstructured grids. Calculations were compared with experiments and Large Eddy Simulations (LES). Predicted overall flow parameters and mean flow velocities exhibited a very satisfactory agreement with experiments and LES, while the agreement of predicted turbulent stresses was satisfactory. Calculations showed that SAS is an efficient and relatively fast turbulence modeling approach, especially in relevant practical problems, in which the very high accuracy that can be achieved by LES at the expense of large computational times is not required.</p> </div> <p>&nbsp;</p>

Advancing the simulation of mesoscale eddies: Backscatter schemes in eddy-permitting ocean simulations

2021 ◽  
Author(s):  
Stephan Juricke ◽  
Sergey Danilov ◽  
Marcel Oliver ◽  
Nikolay Koldunov ◽  
Dmitry Sidorenko ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Large Scale ◽  
Mesoscale Eddy ◽  
Ocean Model ◽  
Mean Flow ◽  
Ocean Coupling ◽  
Climate Simulations ◽  
Flow Interactions ◽  
To Come ◽  
Eddy Dynamics

&lt;p&gt;Capturing mesoscale eddy dynamics is crucial for accurate simulations of the large-scale ocean currents as well as oceanic and climate variability. Eddy-mean flow interactions affect the position, strength and variations of mean currents and eddies are important drivers of oceanic heat transport and atmosphere-ocean-coupling. However, simulations at eddy-permitting resolutions are substantially underestimating eddy variability and eddy kinetic energy many times over. Such eddy-permitting simulations will be in use for years to come, both in coupled and uncoupled climate simulations. We present a set of kinetic energy backscatter schemes with different complexity as alternative momentum closures that can alleviate some eddy related biases such as biases in the mean currents, in sea surface height variability and in temperature and salinity. The complexity of the schemes reflects in their computational costs, the related simulation improvements and their adaptability to different resolutions. However, all schemes outperform classical viscous closures and are computationally less expensive than a related necessary resolution increase to achieve similar results. While the backscatter schemes are implemented in the ocean model FESOM2, the concepts can be adjusted to any ocean model including NEMO.&lt;/p&gt;

scholarly journals On the Role of Asymmetric Convective Bursts to the Problem of Hurricane Intensification: Radiation of Vortex Rossby Waves and Wave–Mean Flow Interactions

2014 ◽  
Vol 71 (6) ◽  
pp. 2057-2077 ◽  
Author(s):  
Konstantinos Menelaou ◽  
M. K. Yau
Keyword(s):  
Kinetic Energy ◽  
Thermal Anomaly ◽  
Eddy Kinetic Energy ◽  
Intensity Change ◽  
Mean Flow ◽  
Symmetric Flow ◽  
Thermal Forcing ◽  
Sensitivity Experiments ◽  
Flow Interactions

Abstract The role of asymmetric convection to the intensity change of a weak vortex is investigated with the aid of a “dry” thermally forced model. Numerical experiments are conducted, starting with a weak vortex forced by a localized thermal anomaly. The concept of wave activity, the Eliassen–Palm flux, and eddy kinetic energy are then applied to identify the nature of the dominant generated waves and to diagnose their kinematics, structure, and impact on the primary vortex. The physical reasons for which disagreements with previous studies exist are also investigated utilizing the governing equation for potential vorticity (PV) perturbations and a number of sensitivity experiments. From the control experiment, it is found that the response of the vortex is dominated by the radiation of a damped sheared vortex Rossby wave (VRW) that acts to accelerate the symmetric flow through the transport of angular momentum. An increase of the kinetic energy of the symmetric flow by the VRW is shown also from the eddy kinetic energy budget. Additional tests performed on the structure and the magnitude of the initial thermal forcing confirm the robustness of the results and emphasize the significance of the wave–mean flow interaction to the intensification process. From the sensitivity experiments, it is found that for a localized thermal anomaly, regardless of the baroclinicity of the vortex and the radial and vertical gradients of the thermal forcing, the resultant PV perturbation follows a damping behavior, thus suggesting that deceleration of the vortex should not be expected.

scholarly journals Observed Storm Track Dynamics in Drake Passage

2019 ◽  
Vol 49 (3) ◽  
pp. 867-884 ◽  
Author(s):  
Annie Foppert
Keyword(s):  
Mean Field ◽  
Storm Track ◽  
Drake Passage ◽  
Polar Front ◽  
Mean Flow ◽  
Track Dynamics ◽  
Flow Interactions ◽  
Circumpolar Current ◽  
Eddy Potential Energy ◽  
Shackleton Fracture Zone

AbstractThe dynamics of an oceanic storm track—where energy and enstrophy transfer between the mean flow and eddies—are investigated using observations from an eddy-rich region of the Antarctic Circumpolar Current downstream of the Shackleton Fracture Zone (SFZ) in Drake Passage. Four years of measurements by an array of current- and pressure-recording inverted echo sounders deployed between November 2007 and November 2011 are used to diagnose eddy–mean flow interactions and provide insight into physical mechanisms for these transfers. Averaged within the upper to mid-water column (400–1000-m depth) and over the 4-yr-record mean field, eddy potential energy is highest in the western part of the storm track and maximum eddy kinetic energy occurs farther away from the SFZ, shifting the proportion of eddy energies from to about 1 along the storm track. There are enhanced mean 3D wave activity fluxes immediately downstream of SFZ with strong horizontal flux vectors emanating northeast from this region. Similar patterns across composites of Polar Front and Subantarctic Front meander intrusions suggest the dynamics are set more so by the presence of the SFZ than by the eddy’s sign. A case study showing the evolution of a single eddy event, from 15 to 23 July 2010, highlights the storm-track dynamics in a series of snapshots. Consistently, explaining the eddy energetics pattern requires both horizontal and vertical components of W, implying the importance of barotropic and baroclinic processes and instabilities in controlling storm-track dynamics in Drake Passage.

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