Short-wave vortex instability in stratified flow

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.euromechflu.2015.08.005. © 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper we investigate a new instability of the Lamb–Chaplygin dipole in a stratified fluid. Through numerical linear stability analysis, a secondary peak in the growth rate emerges at vertical scales about an order of magnitude smaller than the buoyancy scale Lb=U/NLb=U/N where U is the characteristic velocity and N is the Brunt–Väisälä frequency. This new instability exhibits a growth rate that is similar to, and even exceeds, that of the zigzag instability, which has the characteristic length of the buoyancy scale. This instability is investigated for a wide range of Reynolds numbers, Re=2000–20000, and horizontal Froude numbers, Fh=0.05–0.2, where Fh=U/NR, Re=UR/ν, R is the radius of the dipole, and ν is the kinematic viscosity. A range of vertical scales is explored from above the buoyancy scale to the viscous damping scale. Additionally, evidence is presented that the length scale and growth rate of this new instability are partially determined by the buoyancy Reynolds number, Reb=Fh^2Re.Natural Sciences and Engineering Research Council || RGPIN/386456-201

Spectral energy balance in dry convective boundary layers

Three-dimensional large-eddy simulations (LES) of the convective boundary layer over a domain of approximately 6 km are performed with the UCLA LES model. Simulations are forced with a constant surface heat flux and prescribed subsidence, and are run to equilibrium. Sub-grid scale fluxes are parameterised with the Smagorinsky–Lilly scheme. A range of grid spacings from 40 down to 5 m are employed. Kinetic energy spectra and the various terms in the kinetic energy spectral budget – heat flux, nonlinear transfer, pressure, and dissipation – are computed using two-dimensional discrete Fourier transforms at every vertical level. Despite the fact that isotropic grid spacings of down to 5 m (grid sizes of 11522×400) were used, an inertial range with a −5/3 spectrum is not obtained. Rather, shallower energy spectral slopes that are closer to −4/3 are found. The shallower spectra are shown to possibly result from the injection of kinetic energy over a wide range of scales via a very broad heat flux spectrum. Only with the highest resolution (Δx = 5 m) does the total heat flux begin to converge and the possibility of local isotropy emerge at small scales. Dependence on surface heat flux and domain size is considered. Preliminary sub-grid scale sensitivity results are obtained through comparison with the turbulent kinetic energy sub-grid scale model.Natural Sciences and Engineering Research Council || RGPIN/386456-201

Topographically generated internal waves and boundary layer instabilities

Copyright (2015) AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Soontiens, N., Stastna, M. & Waite, M.L. Topographically generated internal waves and boundary layer instabilities. Phys. Fluids 27, 086602 (2015), and may be found at http://dx.doi.org/10.1063/1.4929344.Flow over topography has been shown to generate finite amplitude internal waves upstream, over the topography and downstream. Such waves can interact with the viscous bottom boundary layer to produce vigorous instabilities. However, the strength and size of such instabilities depends on whether viscosity significantly modifies the wave generation process, which is usually treated using inviscid theory in the literature. In this work, we contrast cases in which boundary layer separation profoundly alters the wave generation process and cases for which the generated internal waves largely match inviscid theory. All results are generated using a numerical model that simulates stratified flow over topography. Several issues with using a wave-based Reynolds number to describe boundary layer properties are discussed by comparing simulations with modifications to the domain depth, background velocity, and viscosity. For hill-like topography, three-dimensional aspects of the instabilities are also discussed. Decreasing the Reynolds number by a factor of four (by increasing the viscosity), while leaving the primary two-dimensional instabilities largely unchanged, drastically affects their three-dimensionalization. Several cases at the laboratory scale with a depth of 1 m are examined in both two and three dimensions and a subset of the cases is scaled up to a field scale 10-m deep fluid while maintaining similar values for the background current and viscosity. At this scale, increasing the viscosity by an order of magnitude does not significantly change the wave properties but does alter the wave’s interaction with the bottom boundary layer through the bottom shear stress. Finally, two subcritical cases for which disturbances are able to propagate upstream showcase a set of instabilities forming on the upstream slope of the elevated topography. The time scale over which these instabilities develop is related to but distinct from the advective time scale of the waves. At a non-dimensional time when instabilities have formed in the field scale case, no instabilities have yet formed in the lab scale case.Natural Sciences and Engineering Research Council || RGPIN/386456-201

Realizing surface driven flows in the primitive equations

© Copyright 2015 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act September 2010 Page 2 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108, as revised by P.L. 94-553) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a web site or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. Additional details are provided in the AMS Copyright Policy, available on the AMS Web site located at (https://www.ametsoc.org/) or from the AMS at 617-227-2425 or [email protected] surface quasigeostrophic (SQG) model describes flows with surface buoyancy perturbations with no interior quasigeostrophic potential vorticity at small Rossby number Ro and O(1) Burger number, where quasigeostrophic dynamics are expected to hold. Numerical simulations of SQG dynamics have shown that vortices are frequently generated at small scales, which may have O(1) Rossby numbers and therefore may be beyond the limits of SQG. This paper examines the dynamics of an initially geostrophically balanced elliptical surface buoyancy perturbation in both the SQG model and the nonhydrostatic Boussinesq primitive equations (PE). In the case of very small Rossby number, it is confirmed that both models agree, as expected. For larger Ro, non-SQG effects emerge and as a result the solution of the PE deviates significantly from that of SQG. In particular, an increase in the Rossby number has the following effects: (i) the buoyancy filaments at the surface are stabilized in that they generate fewer secondary vortices; (ii) the core of the vortex experiences inertial instability, which results in a uniform buoyancy profile in its interior; (iii) the divergent part of the energy spectrum increases in magnitude; (iv) the PE model has significantly more gravity waves that are radiated from the vortex; (v) the magnitude of the vertical velocity increases; and (vi) in the mature stages of evolution, there are gravitational instabilities that develop because of the complicated dynamics inside the vortex. It is demonstrated that significant non-SQG effects are evident when the large-scale Rossby number of the initial flow is about 0.05 and the local Rossby number is O(1).Natural Sciences and Engineering Research Council || RGPIN/386456-201

Random forcing of geostrophic motion in rotating stratified turbulence

The following article appeared in (Waite, M. L. (2017). Random forcing of geostrophic motion in rotating stratified turbulence. Physics of Fluids, 29(12), 126602. https://doi.org/10.1063/1.5004986) and may be found at (https://doi.org/10.1063/1.5004986). This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.Random forcing of geostrophic motion is a common approach in idealized simulations of rotating stratified turbulence. Such forcing represents the injection of energy into large-scale balanced motion, and the resulting breakdown of quasi-geostrophic turbulence into inertia–gravity waves and stratified turbulence can shed light on the turbulent cascade processes of the atmospheric mesoscale. White noise forcing is commonly employed, which excites all frequencies equally, including frequencies much higher than the natural frequencies of large-scale vortices. In this paper, the effects of these high frequencies in the forcing are investigated. Geostrophic motion is randomly forced with red noise over a range of decorrelation time scales τ, from a few time steps to twice the large-scale vortex time scale. It is found that short τ (i.e., nearly white noise) results in about 46% more gravity wave energy than longer τ, despite the fact that waves are not directly forced. We argue that this effect is due to wave–vortex interactions, through which the high frequencies in the forcing are able to excite waves at their natural frequencies. It is concluded that white noise forcing should be avoided, even if it is only applied to the geostrophic motion, when a careful investigation of spontaneous wave generation is neededFinancial support from the Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN-386456-2015) is gratefully acknowledged

Dependence of model energy spectra on vertical resolution

© Copyright 2016 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act September 2010 Page 2 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108, as revised by P.L. 94-553) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a web site or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. Additional details are provided in the AMS Copyright Policy, available on the AMS Web site located at (https://www.ametsoc.org/) or from the AMS at 617-227-2425 or [email protected] high-resolution atmospheric models can reproduce the qualitative shape of the atmospheric kinetic energy spectrum, which has a power-law slope of −3 at large horizontal scales that shallows to approximately −5/3 in the mesoscale. This paper investigates the possible dependence of model energy spectra on the vertical grid resolution. Idealized simulations forced by relaxation to a baroclinically unstable jet are performed for a wide range of vertical grid spacings Δz. Energy spectra are converged for Δz 200 m but are very sensitive to resolution with 500 m ≤ Δz ≤ 2 km. The nature of this sensitivity depends on the vertical mixing scheme. With no vertical mixing or with weak, stability-dependent mixing, the mesoscale spectra are artificially amplified by low resolution: they are shallower and extend to larger scales than in the converged simulations. By contrast, vertical hyperviscosity with fixed grid-scale damping rate has the opposite effect: underresolved spectra are spuriously steepened. High-resolution spectra are converged except for the stability-dependent mixing case, which are damped by excessive mixing due to enhanced shear over a wide range of horizontal scales. It is shown that converged spectra require resolution of all vertical scales associated with the resolved horizontal structures: these include quasigeostrophic scales for large-scale motions with small Rossby number and the buoyancy scale for small-scale motions at large Rossby number. It is speculated that some model energy spectra may be contaminated by low vertical resolution, and it is recommended that vertical-resolution sensitivity tests always be performed.Natural Sciences and Engineering Research Council || RGPIN/386456-201

An Anisotropic Subgrid-Scale Parameterization for Large-Eddy Simulations of Stratified Turbulence

© Copyright 2020 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact [email protected]. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code §?107) or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC § 108) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. All AMS journals and monograph publications are registered with the Copyright Clearance Center (https://www.copyright.com). Additional details are provided in the AMS Copyright Policy statement, available on the AMS website (https://www.ametsoc.org/PUBSCopyrightPolicy).Subgrid-scale (SGS) parameterizations in atmosphere and ocean models are often defined independently in the horizontal and vertical directions because the grid spacing is not the same in these directions (anisotropic grids). In this paper, we introduce a new anisotropic SGS model in large-eddy simulations (LES) of stratified turbulence based on hor izontal filtering of the equations of motion. Unlike the common horizontal SGS parameterizations in atmosphere and ocean models, the vertical derivatives of the horizontal SGS fluxes are included in our anisotropic SGS scheme, and therefore the horizontal and vertical SGS dissipation mechanisms are not disconnected in the newly developed model. Our model is tested with two vertical grid spacings and various horizontal resolutions, where the horizontal grid spacing is comparatively larger than that in the vertical. Our anisotropic LES model can successfully reproduce the results of direct numerical simulations, while the computational cost is significantly reduced in the LES. We suggest the new anisotropic SGS model as an alternative to current SGS parameterizations in atmosphere and ocean models, in which the schemes for horizontal and vertical scales are often decoupled. The new SGS scheme may improve the dissipative performance of atmosphere and ocean models without adding any backscatter or other energizing terms at small horizontal scales.Funder 1, financial support provided by National Science Foundation through Awards 1536360 and 1536314 || Funder 2, M.L.W. gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada (Grant RGPIN-386456-2015)

Backscatter in stratified turbulence

The final publication is available at Elsevier via http://dx.doi.org/https://doi.org/10.1016/j.euromechflu.2016.06.012. © 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, kinetic and potential energy transfers around a spectral test fil ter scale in direct numerical simulations of decaying stratified turbulence are studied in both physical and spectral domains. It is shown that while the domain-averaged effective subgrid scale energy transfer in physical space is a net downscale cascade, it is actually a combination of large values of downscale and upscale transfer, i.e. forward- and backscatter, in which the forward scatter is slightly dominant. Our results suggest that spectral backscatter in stratified turbulence depends on the buoyancy Reynolds number Reb and the filtering scale ∆test. When the test filter scale ∆test is around the dissipation scale Ld, transfer spectra show spectral backscatter from sub-filter to intermediate scales, as reported elsewhere. However, we find that this spectral backscatter is due to viscous effects at vertical scales around the test filter. It is also shown that there is a non-local energy transfer from scales larger than the buoyancy scale Lb to small scales.The effective turbulent Prandtl number spectra demonstrate that the assumption P rt ≈ 1 is reasonable for the local energy transfer.Funder 1, SciNet is funded by the Canada Foundation for Innovation under the auspices of Compute Canada || Funder 2, the Government of Ontario || Funder 3, Ontario Research Fund–Research Excellence || Funder 4 , the University of Toronto || Funder 5, Financial support from the Natural Sciences and Engineering Research Council of Canada (grant number RGPIN-386456-2015) is gratefully acknowledged