scholarly journals A Theoretical Study on the Spontaneous Radiation of Inertia–Gravity Waves Using the Renormalization Group Method. Part II: Verification of the Theoretical Equations by Numerical Simulation

2015 ◽  
Vol 72 (3) ◽  
pp. 984-1009 ◽  
Author(s):  
Yuki Yasuda ◽  
Kaoru Sato ◽  
Norihiko Sugimoto
Keyword(s):  
Renormalization Group ◽  
Numerical Simulations ◽  
Large Scale ◽  
Companion Paper ◽  
Vortical Flow ◽  
Japan Meteorological Agency ◽  
Velocity Variation ◽  
Group Method ◽  
Spontaneous Radiation ◽  
Momentum Fluxes

Abstract The renormalization group equations (RGEs) describing spontaneous inertia–gravity wave (GW) radiation from part of a balanced flow through a quasi resonance that were derived in a companion paper by Yasuda et al. are validated through numerical simulations of the vortex dipole using the Japan Meteorological Agency nonhydrostatic model (JMA-NHM). The RGEs are integrated for two vortical flow fields: the first is the initial condition that does not contain GWs used for the JMA-NHM simulations, and the second is the simulated thirtieth-day field by the JMA-NHM. The theoretically obtained GW distributions in both RGE integrations are consistent with the numerical simulations using the JMA-NHM. This result supports the validity of the RGE theory. GW radiation in the dipole is physically interpreted either as the mountain-wave-like mechanism proposed by McIntyre or as the velocity-variation mechanism proposed by Viúdez. The shear of the large-scale flow likely determines which mechanism is dominant. In addition, the distribution of GW momentum fluxes is examined based on the JMA-NHM simulation data. The GWs propagating upward from the jet have negative momentum fluxes, while those propagating downward have positive ones. The magnitude of momentum fluxes is approximately proportional to the sixth power of the Rossby number between 0.15 and 0.4.

Langmuir turbulence as a critical phenomenon. Part 2. Application of the dynamical renormalization group method

1980 ◽  
Vol 24 (3) ◽  
pp. 421-443 ◽  
Author(s):  
Guy Pelletier
Keyword(s):  
Renormalization Group ◽  
Large Scale ◽  
Critical Phenomenon ◽  
Critical Curve ◽  
Group Method ◽  
Renormalization Group Method ◽  
Scaling Invariance ◽  
Correlation Spectrum ◽  
Scale Properties ◽  
Modulation Regime

In part 1 of this work, we have found a ‘critical curve’ which separates the unstable self-modulation regime from the stable one for a Gibbs ensemble of interacting modes. On this critical curve, the correlation length diverges and scaling invariance occurs; in particular, the Langmuir correlation spectrum is proportional to k-2. Simple laws have been derived for the neighbourhood of the critical curve. However these derivations are based on equilibrium statistical mechanics and the results are obtained with a Hartree approximation which has not been checked. So, in this second part, we elaborate a direct statistical theory of Zakharov's equations completed by excitation sources and dissipations. In spite of infra-red divergences and a large fluctuation level, large-scale properties are derived in the neighbourhood of the critical curve, by the renormalization group method. The laws obtained in part 1 are slightly modified; however, the same spectrum is obtained.

Aerodynamic and Aerothermal Investigation of the Flow Around an HPT Rotor Shroud: Heat Transfer and Cooling Effectiveness

2011 ◽  
Author(s):  
Knut Lehmann ◽  
Vasudevan Kanjirakkad ◽  
Howard Hodson
Keyword(s):  
Heat Transfer ◽  
Large Scale ◽  
Sampling Technique ◽  
Companion Paper ◽  
Vortical Flow ◽  
Cooling Effectiveness ◽  
Nusselt Numbers ◽  
Experimental Heat ◽  
Adiabatic Cooling ◽  
The Impact

An experimental study has been conducted to investigate the aerothermal performance of a shrouded high pressure turbine blade in a large scale rotating rig. The rotor blade and the associated shroud and casing geometry have been modelled in a large scale low speed turbine rig that was designed to investigate a novel passive shroud cooling methodology. The objective of the present paper is to describe the aerothermal performance of a passive shroud cooling strategy using measured heat transfer and adiabatic cooling effectiveness data. Improved physical understanding of the shroud aerodynamics as reported in the companion paper Lehmann et al. [1] will be used here to support the analysis. Highly resolved experimental heat transfer data was acquired on the shroud, the fins and on the shroud underside with the thin heater film method. The distribution of the adiabatic cooling effectiveness on the rotor shroud was measured with a combination of the Ammonia-Diazo and a foreign gas sampling technique. The measurements are complemented by steady numerical computations of the turbine stage. Due to the impact of vortical flow structures in the over shroud cavities, the Nusselt numbers on the shroud top surfaces were found to be of the same order as on the shroud underside. The passive shroud cooling concept was found to provide quite efficient and uniform cooling to the over-shroud surfaces while the distribution of coolant on the shroud underside was significantly affected by the rotor secondary flow.

scholarly journals A Theoretical Study on the Spontaneous Radiation of Inertia–Gravity Waves Using the Renormalization Group Method. Part I: Derivation of the Renormalization Group Equations

2015 ◽  
Vol 72 (3) ◽  
pp. 957-983 ◽  
Author(s):  
Yuki Yasuda ◽  
Kaoru Sato ◽  
Norihiko Sugimoto
Keyword(s):  
Renormalization Group ◽  
Time Scales ◽  
Gravity Waves ◽  
Radiation Reaction ◽  
Vortical Flow ◽  
Group Method ◽  
Linear Potential ◽  
Slow Time ◽  
Balanced Flow ◽  
Inertia Gravity Waves

Abstract By using the renormalization group (RG) method, the interaction between balanced flows and Doppler-shifted inertia–gravity waves (GWs) is formulated for the hydrostatic Boussinesq equations on the f plane. The derived time-evolution equations [RG equations (RGEs)] describe the spontaneous GW radiation from the components slaved to the vortical flow through the quasi resonance, together with the GW radiation reaction on the large-scale flow. The quasi resonance occurs when the space–time scales of GWs are partially comparable to those of slaved components. This theory treats a coexistence system with slow time scales composed of GWs significantly Doppler-shifted by the vortical flow and the balanced flow that interact with each other. The theory includes five dependent variables having slow time scales: one slow variable (linear potential vorticity), two Doppler-shifted fast ones (GW components), and two diagnostic fast ones. Each fast component consists of horizontal divergence and ageostrophic vorticity. The spontaneously radiated GWs are regarded as superpositions of the GW components obtained as low-frequency eigenmodes of the fast variables in a given vortical flow. Slowly varying nonlinear terms of the fast variables are included as the diagnostic components, which are the sum of the slaved components and the GW radiation reactions. A comparison of the balanced adjustment equation (BAE) by Plougonven and Zhang with the linearized RGE shows that the RGE is formally reduced to the BAE by ignoring the GW radiation reaction, although the interpretation on the GW radiation mechanism is significantly different; GWs are radiated through the quasi resonance with a balanced flow because of the time-scale matching.

scholarly journals Renormalization group method for Farley-Buneman fluctuations: basic results

1996 ◽  
Vol 3 (1) ◽  
pp. 41-46
Author(s):  
A. M. Hamza
Keyword(s):  
Renormalization Group ◽  
Large Scale ◽  
Closed Form Solution ◽  
Power Spectra ◽  
Random Force ◽  
Form Solution ◽  
Density Fluctuations ◽  
Group Method ◽  
Ionospheric Physics ◽  
Weakly Ionized

Abstract. Sudan and Keskinen in [1979] derived a set of equations governing the nonlinear evolution of density fluctuations in a low-pressure weakly ionized plasma driven unstable by the E x B or gradient-drift instability. This problem is of fundamental importance in ionospheric physics. The nonlinear nature of the equations makes it very hard to write a closed form solution. In this paper we propose to use "Dynamical Renormalization Group" methods to study the long-- wavelength, long-time behaviour of density correlations generated in this ionospheric plasma stirred by a Gaussian random force characterized by a correlation function (fk fk) k. The effect of the small scales on the large scale dynamics in the limit k -> 0 and infinite "Reynolds" number, can be expressed in the form of renormalized coefficients; in our case renormalized diffusion. If one assumes the power spectra to be given by the kolmogorov argument of cascading of energy, then one can not only derive a subgrid model based on the results of RNG, and this has been done by Hamza and Sudan [1995], but one can also extract the skewness of the spectra as we do in this paper.

scholarly journals THE DENSITY MATRIX RENORMALIZATION GROUP AND THE NUCLEAR SHELL MODEL

2008 ◽  
Vol 17 (supp01) ◽  
pp. 122-132
Author(s):  
S. PITTEL ◽  
B. THAKUR ◽  
N. SANDULESCU
Keyword(s):  
Renormalization Group ◽  
Density Matrix ◽  
Shell Model ◽  
Large Scale ◽  
Group Method ◽  
Density Matrix Renormalization Group ◽  
Model Calculations ◽  
Density Matrix Renormalization ◽  
High Level ◽  
Level Of Agreement

We summarize recent efforts to develop an angular-momentum-conserving variant of the Density Matrix Renormalization Group method into a practical truncation strategy for large-scale shell model calculations of atomic nuclei. Following a brief description of the key elements of the method, we report the results of test calculations for 48 Cr and 56 Ni . In both cases we consider nucleons limited to the 2p-1f shell and interacting via the KB3 interaction. Both calculations produce a high level of agreement with the exact shell-model results. Furthermore, and most importantly, the fraction of the complete space required to achieve this high level of agreement goes down rapidly as the size of the full space grows.

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