1 / 28

Relaminarisation of turbulent stratified flow

Relaminarisation of turbulent stratified flow. Bas van de Wiel Moene, Steeneveld, Holtslag. Overview. Motivation A simple Couette flow analogy Pressure driven flow: comparison with DNS Conclusion and perspectives. (1) Motivation. Why does the wind drop in the evening?.

hayes-meyers
Download Presentation

Relaminarisation of turbulent stratified flow

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Relaminarisation of turbulent stratified flow Bas van de Wiel Moene, Steeneveld, Holtslag

  2. Overview • Motivation • A simple Couette flow analogy • Pressure driven flow: comparison with DNS • Conclusion and perspectives

  3. (1) Motivation Why does the wind drop in the evening?

  4. (Nieuwstadt, 1984) t=3 t=2 t=1 t=0 z pot. T Classical picture of continuous turbulent quasi-steady SBL: Quasi-steady: Shape profiles cst. Linear heat flux profile

  5. Continuous turbulent, quasi-steady nocturnal boundary layer only observed for strong pressure gradient conditions (high geostrophic winds) Central question: what happens for low pressure gradients?

  6. Observational example(Cabauw, KNMI, Netherlands): • Clear sky conditions • Little wind near surface Collapse of turbulence→ decoupling of the surface from the atmosphere

  7. z Quasi-steady Temperature profiles T

  8. Rationale present work “Yet not every solution of the equations of motion, even if it is exact, can actually occur in nature. The flows that occur in nature must not only obey the equations of fluid dynamics but also be stable.” Landau and Lifschitz (1959) • We hypothesize that: • The continuous turbulent SBL is hydrodynamically stable for high pressure gradient and are therefore observed in nature. • The continuous turbulent SBL is hydrodynamically unstable for low pressure gradient and are therefore not observed in nature. Instead a SBL with collapsed turbulence is observed. In fact we aim to find the transition T-L!

  9. (2) A simple Coutte flow model Van de Wiel et al. (2006) Flows, Turbulence and Combustion, submitted • Some characteristics: • First order turbulence closure based on Ri • No radiative divergence • Rough flow using Z0=0.1 [m] • BC’s: • Top: Wind speed and temperature fixed • Bottom: No slip and fixed surface heat flux

  10. First order closure: Two major elements controlling dominant eddie size: stratification and presence solid boundary Turbulence closure • Non-trivial in a sense that collapse of system as whole occurs way before Rc! • Support locality of TKE in strongly stratified flow e.g.: • Nieuwstadt ’84, Lenshow, ’88, Duynkerke ’91(Observations) • Mason and Derbyshire ’90, Galmarini ’98, Basu ’05 (LES) • Coleman et al. 1992 (DNS); also recall presentation by Clercx

  11. Results

  12. Continuous turbulent case

  13. Continuous turbulent case

  14. Collapse case

  15. Collapse case

  16. Positive feedback mechanism: Increasing gradient: (following Van de Wiel et al. 2002, J. Atmos. Sc.).

  17. Equilibrium solutions: bifurcation analysis

  18. Linear stability analysis (i.e. on logarithmic profiles e.g. not linear!) Ansatz: (1-D!) BC’s

  19. Criterion for instability Previous example: =0.52 Agreement between theory and numerical results! Relaminarised cases Continuous turbulent cases 0.55

  20. Thus: • Collapse of SBL turbulence explained naturally from a linear stability analysis on the governing equations • (assuming local closure) • The crucial question: • how close is our model in comparison with reality (here say reality~DNS)

  21. (3) Comparison with DNS results from Nieuwstadt (2005) Pressure force Cooling Smooth flow; Re*= 360 BC’s Top: stress free, fixed T Bottom: no slip, prescribed heat extraction

  22. (3) Comparison with DNS results from Nieuwstadt (2005) Remarkable in view of origin model We used a priori: (smooth flow)

  23. (3) Comparison with DNS results from Nieuwstadt (2005) A posteriori

  24. DNS shows collapse at h/L~1.23 [-] Note: TKE normalised with u*^2

  25. Our model shows collapse at h/L~1.45 [-] A priori threshold h/L~1.55

  26. Predicting relaminarisation:Generalisation of the results Note: Continuous turbulent cases Relaminarised cases

  27. Summary/conclusions: • Relaminarization of turbulent stratified shear flows is predicted from linear stability analysis on parameterized equations • In this way relaminarization critically depends on two dimensionless parameters: Re* (or Z0/h) and h/L • The results seem to be confirmed by recent DNS results (at least in a qualitative sense)

  28. z Quasi-steady Wind speed profiles U

More Related