scholarly journals Examining instabilities due to driven scalars in AdS

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Brad Cownden
Keyword(s):  
Turbulent Energy ◽  
Time Dependent ◽  
Linear Solution ◽  
Driven Systems ◽  
Flow Equations ◽  
Energy Cascades ◽  
Analytic Expressions ◽  
Bulk Scalar Field ◽  
Dependent Sources ◽  
Secular Terms

Abstract We extend the study of the non-linear perturbative theory of weakly turbulent energy cascades in AdSd+1 to include solutions of driven systems, i.e. those with time-dependent sources on the AdS boundary. This necessitates the activation of non-normalizable modes in the linear solution for the massive bulk scalar field, which couple to the metric and normalizable scalar modes. We determine analytic expressions for secular terms in the renormalization flow equations mass values $$ {m}_{BF}^2<{m}^2\le 0 $$ m BF 2 < m 2 ≤ 0 , and for various driving functions. Finally, we numerically evaluate these sources for d = 4 and discuss what role these driven solutions play in the perturbative stability of AdS.

scholarly journals Role of the forcing dimensionality in thin-layer turbulent energy cascades

2020 ◽  
Vol 5 (6) ◽  
Author(s):  
Basile Poujol ◽  
Adrian van Kan ◽  
Alexandros Alexakis
Keyword(s):  
Thin Layer ◽  
Turbulent Energy ◽  
Energy Cascades

scholarly journals Generalization of DT Equations for Time Dependent Sources

Sensors ◽  
2010 ◽  
Vol 10 (12) ◽  
pp. 10828-10836 ◽  
Author(s):  
Lorenzo Neri ◽  
Salvatore Tudisco ◽  
Francesco Musumeci ◽  
Agata Scordino ◽  
Giorgio Fallica ◽  
...  
Keyword(s):  
Time Dependent ◽  
Dependent Sources

Mass Flow and Thrust Performance of Nozzles With Mixed and Unmixed Nonuniform Flow

1995 ◽  
Vol 117 (4) ◽  
pp. 617-622 ◽  
Author(s):  
Reiner Decher
Keyword(s):  
Mass Flow ◽  
Total Pressure ◽  
Nonuniform Flow ◽  
Flow Properties ◽  
One Dimensional ◽  
Flow Equations ◽  
Design Variables ◽  
Analytic Expressions ◽  
The One ◽  
Thrust Performance

The calculated thrust and mass flow rate of a nozzle depend on the uniformity of the entering flow. The one-dimensional flow equations are extended to arrive at analytic expressions for the predicted performance of a nozzle processing two streams whose properties are determined ahead of the throat. The analysis approach forms the basis for the understanding of flows which have more complex distributions of total pressure and temperature. The uncertainty associated with mixing is examined by the consideration of the two limiting cases: compound flow with no mixing and completely mixed flow. Nozzle discharge and velocity coefficients accounting for non-uniformity are derived. The methodology can be extended to experimentally measured variations of flow properties so that proper geometric design variables may be obtained.

scholarly journals NONLINEAR SECOND SOUND WAVES IN SUPERFLUID HELIUM: INSTABILITIES, TURBULENCE AND ROGUE WAVES

2012 ◽  
Vol 22 (10) ◽  
pp. 1250242
Author(s):  
ANDREY N. GANSHIN ◽  
VICTOR B. EFIMOV ◽  
GERMAN V. KOLMAKOV ◽  
LEONID P. MEZHOV-DEGLIN ◽  
PETER V. E. McCLINTOCK
Keyword(s):  
Sound Wave ◽  
Superfluid Helium ◽  
Turbulent Energy ◽  
Rogue Waves ◽  
Nonlinear Dependence ◽  
Driving Frequency ◽  
Second Sound ◽  
Sound Waves ◽  
Energy Cascades ◽  
Good Agreement

Recent work on nonlinear second sound wave propagation and acoustic turbulence in superfluid 4 He is reviewed. Observations of direct and inverse turbulent energy cascades are described. The direct cascade arises due to the strong nonlinear dependence of the second sound wave velocity on its amplitude. The flux of energy injected at the driving frequency is transformed via successively higher harmonics until it is eventually attenuated by viscous dissipation at the short-wavelength edge of the spectrum. The onset of the inverse cascade occurs above a critical driving energy density, and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomena is outlined and shown to be in good agreement with the experiments.

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