scholarly journals Stratified Kelvin-Helmholtz turbulence of compressible shear flows

2018 ◽  
Author(s):  
Romit Maulik ◽  
Omer San
Keyword(s):  
Power Density ◽  
Spatial Resolution ◽  
Shear Flows ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Structure Functions ◽  
Compressible Turbulence ◽  
Power Density Spectrum ◽  
Two Dimensional ◽  
Density Spectrum

Abstract. We study the scaling laws and structure functions of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin-Helmholtz instability. An implicit large eddy simulation approach is adapted to solve our conservation laws for both two-dimensional (with a spatial resolution of 16,3842) and three-dimensional (with a spatial resolution of 5123) configurations utilizing different compressibility characteristics such as shocks. For three-dimensional turbulence, we find that both kinetic energy and density-weighted energy spectra follow the classical Kolmogorov k−5/3 inertial scaling. This phenomenon is observed due to the fact that the power density spectrum of three-dimensional turbulence yields the same k−5/3 scaling. However, we demonstrate that there is a significant difference between these two spectra in two-dimensional turbulence since the power density spectrum flattens to k−1/4. This flattening may be assumed to be a reason for the k−7/3 scaling observed in the two-dimensional density-weight kinetic every spectra for high compressibility as compared to the k−3 scaling traditionally assumed with incompressible flows. Further inquiries are made to validate the statistical behavior of the various configurations studied through the use of second and third order velocity structure functions where it is noticed that scaling behavior differs between the two- and three-dimensional cases wherein only the latter is seen to follow trends from K41 theory.

scholarly journals Stratified Kelvin–Helmholtz turbulence of compressible shear flows

2018 ◽  
Vol 25 (2) ◽  
pp. 457-476 ◽  
Author(s):  
Omer San ◽  
Romit Maulik
Keyword(s):  
Power Density ◽  
Spatial Resolution ◽  
Shear Flows ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Compressible Turbulence ◽  
Power Density Spectrum ◽  
Two Dimensional ◽  
Density Spectrum ◽  
Significant Difference

Abstract. We study scaling laws of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin–Helmholtz instability. An implicit large eddy simulation approach is adapted to solve our conservation laws for both two-dimensional (with a spatial resolution of 16 3842) and three-dimensional (with a spatial resolution of 5123) configurations utilizing different compressibility characteristics such as shocks. For three-dimensional turbulence, we find that both the kinetic energy and density-weighted energy spectra follow the classical Kolmogorov k-5/3 inertial scaling. This phenomenon is observed due to the fact that the power density spectrum of three-dimensional turbulence yields the same k-5/3 scaling. However, we demonstrate that there is a significant difference between these two spectra in two-dimensional turbulence since the power density spectrum yields a k-5/3 scaling. This difference may be assumed to be a reason for the k-7/3 scaling observed in the two-dimensional density-weight kinetic every spectra for high compressibility as compared to the k−3 scaling traditionally assumed with incompressible flows. Further inquiries are made to validate the statistical behavior of the various configurations studied through the use of the Helmholtz decomposition of both the kinetic velocity and density-weighted velocity fields. We observe that the scaling results are invariant with respect to the compressibility parameter when the density-weighted definition is used. Our two-dimensional results also confirm that a large inertial range of the solenoidal component with the k−3 scaling can be obtained when we simulate with a lower compressibility parameter; however, the compressive spectrum converges to k−2 for a larger compressibility parameter.

scholarly journals Stability of Two-Dimensional Viscous Incompressible Flows under Three-Dimensional Perturbations and Inviscid Symmetry Breaking

2013 ◽  
Vol 45 (3) ◽  
pp. 1871-1885 ◽  
Author(s):  
C. Bardos ◽  
M. C. Lopes Filho ◽  
Dongjuan Niu ◽  
H. J. Nussenzveig Lopes ◽  
E. S. Titi
Keyword(s):  
Symmetry Breaking ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Viscous Incompressible Flows

Three-dimensional vortex formation from an oscillating, non-uniform cylinder

1992 ◽  
Vol 238 ◽  
pp. 31-54 ◽  
Author(s):  
F. Nuzzi ◽  
C. Magness ◽  
D. Rockwell
Keyword(s):  
Flow Structure ◽  
Phase Plane ◽  
Shear Flows ◽  
Vortex Formation ◽  
Excitation Frequency ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Near Wake ◽  
Shedding Frequency

A cylinder having mild variations in diameter along its span is subjected to controlled excitation at frequencies above and below the inherent shedding frequency from the corresponding two-dimensional cylinder. The response of the near wake is characterized in terms of timeline visualization and velocity traces, spectra, and phase plane representations. It is possible to generate several types of vortex formation, depending upon the excitation frequency. Globally locked-in, three-dimensional vortex formation can occur along the entire span of the flow. Regions of locally locked-in and period-doubled vortex formation can exist along different portions of the span provided the excitation frequency is properly tuned. Unlike the classical subharmonic instability in free shear flows, the occurrence of period-doubled vortex formation does not involve vortex coalescence; instead, the flow structure alternates between two different states.

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