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The effect of a strong density step on blocked stratified flow over topography

Published online by Cambridge University Press:  24 February 2020

Arjun Jagannathan Open the ORCID record for Arjun Jagannathan [Opens in a new window] ,
Kraig B. Winters  and
Laurence Armi
Arjun Jagannathan*
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA
Kraig B. Winters
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA
Laurence Armi
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA
*
†Email address for correspondence: ajagannathan@atmos.ucla.edu
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Abstract

The dynamical connection between topographic control and wave excitation aloft is investigated theoretically and numerically in the idealized setting of two-dimensional stratified flow over an isolated ridge. We consider a constant far upstream inflow with uniform stratification except for a sharp density step located above the height of the ridge crest. Below this step, the stratification is sufficiently strong that the low level flow is blocked upstream and a hydraulically controlled flow spills over the crest. Above the density step, the flow supports upward radiating waves. In the inviscid limit, a bifurcating isopycnal separates the hydraulically controlled overflow from the wave field aloft. We show that, depending on the height of the density step, the sharp interface can either remain approximately flat, above the controlled downslope flow, or plunge in the lee of the obstacle as part of the controlled overflow itself. Whether the interface plunges or not is a direct consequence of hydraulic control at the crest. The flow above the crest responds to the top of the sharp density step as if it were a virtual topography. We find that a plunging interface can excite a wave field aloft that is approximately six times as energetic, with 15 % higher pressure drag, than that in a comparable flow in which the interface remains approximately flat.

JFM classification

Geophysical and Geological Flows: Hydraulic control Geophysical and Geological Flows: Topographic effects Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A23
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Armi, L. & Mayr, G. J. 2015 Virtual and real topography for flows across mountain ranges. J. Appl. Meteorol. Climatol. 54 (4), 723–731.CrossRefGoogle Scholar
Baines, P. G. 1987 Upstream blocking and airflow over mountains. Annu. Rev. Fluid Mech. 19 (1), 75–95.CrossRefGoogle Scholar
Baines, P. G. 1998 Topographic Effects in Stratified Flows. Cambridge University Press.Google Scholar
Baines, P. G. & Hoinka, K. P. 1985 Stratified flow over two-dimensional topography in fluid of infinite depth: a laboratory simulation. J. Atmos. Sci. 42 (15), 1614–1630.2.0.CO;2>CrossRefGoogle Scholar
Bell, T. H. 1974 Effects of shear on the properties of internal gravity wave modes. Dtsch. Hydrogr. Z. 27 (2), 57–62.CrossRefGoogle Scholar
Brighton, P. W. M. 1978 Strongly stratified flow past three-dimensional obstacles. Q. J. R. Meteorol. Soc. 104 (440), 289–307.CrossRefGoogle Scholar
Eliassen, A. & Palm, E. 1961 On the transfer of energy in stationary mountain waves. Geophys. Publ. 22, 1–23.Google Scholar
Epifanio, C. C. & Durran, D. R. 2001 Three-dimensional effects in high-drag-state flows over long ridges. J. Atmos. Sci. 58 (9), 1051–1065.2.0.CO;2>CrossRefGoogle Scholar
Gill, A. E. 1982 Atmosphere-Ocean Dynamics. Academic press.Google Scholar
Hunt, J. C. R., Feng, Y., Linden, P. F., Greenslande, M. D. & Mobbs, S. D. 1997 Low-Froude-number stable flows past mountains. Il Nuovo Cimento C 20 (3), 261–272.Google Scholar
Jagannathan, A., Winters, K. B. & Armi, L. 2017 Stability of stratified downslope flows with an overlying stagnant isolating layer. J. Fluid Mech. 810, 392–411.CrossRefGoogle Scholar
Jagannathan, A., Winters, K. B. & Armi, L. 2019 Stratified flows over and around long dynamically tall mountain ridges. J. Atmos. Sci. 76 (5), 1265–1287.CrossRefGoogle Scholar
Jiang, Q. 2014 Applicability of reduced-gravity shallow-water theory to atmospheric flow over topography. J. Atmos. Sci. 71 (4), 1460–1479.CrossRefGoogle Scholar
Klymak, J., Legg, S. & Pinkel, R. 2010 High-mode stationary waves in stratified flow over large obstacles. J. Fluid Mech. 644, 321–336.CrossRefGoogle Scholar
Legg, S. & Klymak, J. 2008 Internal hydraulic jumps and overturning generated by tidal flow over a tall steep ridge. J. Phys. Oceanogr. 38 (9), 1949–1964.CrossRefGoogle Scholar
Lilly, D. K. 1978 A severe downslope windstorm and aircraft turbulence event induced by a mountain wave. J. Atmos. Sci. 35 (1), 59–77.2.0.CO;2>CrossRefGoogle Scholar
Long, R. R. 1955 Some aspects of the flow of stratified fluids. III. Continuous density gradients. Tellus 7, 341.CrossRefGoogle Scholar
Miles, J. W. & Huppert, H. E. 1969 Lee waves in a stratified flow. Part 4. Perturbation approximations. J. Fluid Mech. 35 (3), 497–525.CrossRefGoogle Scholar
Nash, J. D., Alford, M. H. & Kunze, E. 2005 Estimating internal wave energy fluxes in the ocean. J. Atmos. Ocean. Technol. 22 (10), 1551–1570.CrossRefGoogle Scholar
Pal, A., Sarkar, S., Posa, A. & Balaras, E. 2017 Direct numerical simulation of stratified flow past a sphere at a subcritical Reynolds number of 3700 and moderate Froude number. J. Fluid Mech. 826, 5–31.CrossRefGoogle Scholar
Peltier, W. R. & Scinocca, J. F. 1990 The origin of severe downslope windstorm pulsations. J. Atmos. Sci. 47 (24), 2853–2870.2.0.CO;2>CrossRefGoogle Scholar
Pierrehumbert, R. T. & Wyman, B. 1985 Upstream effects of mesoscale mountains. J. Atmos. Sci. 42 (10), 977–1003.2.0.CO;2>CrossRefGoogle Scholar
Pratt, L. J., Johns, W., Murray, S. P. & Katsumata, K. 1999 Hydraulic interpretation of direct velocity measurements in the Bab al Mandab. J. Phys. Oceanogr. 29 (11), 2769–2784.2.0.CO;2>CrossRefGoogle Scholar
Pratt, L. J. & Whitehead, J. A. 2007 Rotating Hydraulics: Nonlinear Topographic Effects in the Ocean and Atmosphere, vol. 36. Springer Science & Business Media.CrossRefGoogle Scholar
Queney, P. 1948 The problem of air flow over mountains: a summary of theoretical studies. Bull. Am. Meteorol. Soc. 29, 16–26.CrossRefGoogle Scholar
Sheppard, P. A. 1956 Airflow over mountains. Q. J. R. Meteorol. Soc. 82 (354), 528–529.CrossRefGoogle Scholar
Smith, R. B. 1985 On severe downslope winds. J. Atmos. Sci. 42 (23), 2597–2603.2.0.CO;2>CrossRefGoogle Scholar
Smith, R. B. 1991 Kelvin–Helmholtz instability in severe downslope wind flow. J. Atmos. Sci. 48 (10), 1319–1324.2.0.CO;2>CrossRefGoogle Scholar
Smolarkiewicz, P. K. & Rotunno, R. 1989 Low Froude number flow past three-dimensional obstacles. Part I: baroclinically generated lee vortices. J. Atmos. Sci. 46 (8), 1154–1164.2.0.CO;2>CrossRefGoogle Scholar
Tessler, Z. D., Gordon, A. L., Pratt, L. J. & Sprintall, J. 2010 Transport and dynamics of the Panay Sill overflow in the Philippine seas. J. Phys. Oceanogr. 40 (12), 2679–2695.CrossRefGoogle Scholar
Vosper, S. B. 2004 Inversion effects on mountain lee waves. Q. J. R. Meteorol. Soc. 130 (600), 1723–1748.CrossRefGoogle Scholar
Winters, K. B. 2016 The turbulent transition of a supercritical downslope flow: sensitivity to downstream conditions. J. Fluid Mech. 792, 997–1012.CrossRefGoogle Scholar
Winters, K. B. & Armi, L. 2012 Hydraulic control of continuously stratified flow over an obstacle. J. Fluid Mech. 700, 502–513.CrossRefGoogle Scholar
Winters, K. B. & Armi, L. 2014 Topographic control of stratified flows: upstream jets, blocking and isolating layers. J. Fluid Mech. 753, 80–103.CrossRefGoogle Scholar
Winters, K. B. & De la Fuente, A. 2012 Modelling rotating stratified flows at laboratory-scale using spectrally-based DNS. Ocean Model. 49, 47–59.CrossRefGoogle Scholar