scholarly journals Normal Mode Spectra of Idealized Baroclinic Waves

2020 ◽  
Vol 77 (3) ◽  
pp. 813-833
Author(s):  
Matthew R. Ambacher ◽  
Michael L. Waite
Keyword(s):  
Energy Spectrum ◽  
Potential Energy ◽  
Gravity Waves ◽  
Normal Modes ◽  
Helmholtz Decomposition ◽  
Wave Spectra ◽  
Baroclinic Wave ◽  
Vertical Mode ◽  
Baroclinic Waves ◽  
Inertia Gravity Waves

Abstract Normal modes are used to investigate the contributions of geostrophic vortices and inertia–gravity waves to the energy spectrum of an idealized baroclinic wave simulation. The geostrophic and ageostrophic modal spectra (GE and AE, respectively) are compared to the rotational and divergent kinetic energy (RKE and DKE, respectively), which are often employed as proxies for vortex and wave energy. In our idealized f-plane framework, the horizontal modes are Fourier, and the vertical modes are found by solving an appropriate eigenvalue problem. For low vertical mode number n, both the GE and AE spectra are steep; however, for higher n, while both spectra are shallow, the AE is shallower than the GE and the spectra cross. The AE spectra are peaked at the Rossby deformation wavenumber knR, which increases with n. Analysis of the horizontal mode equations suggests that, for large wavenumbers k≫knR, the GE is approximated by the RKE, while the AE is approximated by the sum of the DKE and potential energy. These approximations are supported by the simulations. The vertically averaged RKE and DKE spectra are compared to the sum of the GE and AE spectra over all vertical modes; the spectral slopes of the GE and AE are close to those of the RKE and DKE, supporting the use of the Helmholtz decomposition to estimate vortices and waves in the midlatitudes. However, the AE is consistently larger than the DKE because of the contribution from the potential energy. Care must be taken when diagnosing the mesoscale transition from the intersection of the vortex and wave spectra; GE and AE will intersect at a different scale than RKE and DKE, despite their similar slopes.

scholarly journals Ageostrophic instability in rotating, stratified interior vertical shear flows

2014 ◽  
Vol 755 ◽  
pp. 397-428 ◽  
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Claire Ménesguen
Keyword(s):  
Energy Source ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Gravity Waves ◽  
Shear Flows ◽  
Vertical Shear ◽  
Mean Flow ◽  
Efficient Energy Transfer ◽  
The Mean ◽  
Inertia Gravity Waves

AbstractThe linear instability of several rotating, stably stratified, interior vertical shear flows $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric $\overline{U}(z)$ for intermediate Rossby number ($\mathit{Ro}$). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate $\mathit{Ro}$ values and horizontal wavenumbers ($k,l$) that are far from $l= 0$ or $k = 0$, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of $A-S= 0$ (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.

Wind-driven Oscillations in the Meridional Overturning Circulation near the equator

2021 ◽  
Author(s):  
Adam Blaker ◽  
Michael Bell ◽  
Joel Hirschi ◽  
Amy Bokota
Keyword(s):  
Gravity Waves ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Ocean Basin ◽  
Ocean Model ◽  
Equatorial Region ◽  
Meridional Overturning Circulation ◽  
Overturning Circulation ◽  
Meridional Overturning ◽  
Inertia Gravity Waves

<p>Numerical model studies have shown the meridional overturning circulation (MOC) to exhibit variability on near-inertial timescales, and also indicate a region of enhanced variability on the equator. We present an analysis of a set of integrations of a global configuration of a numerical ocean model, which show very large amplitude oscillations in the MOCs in the Atlantic, Indian and Pacific oceans confined to the equatorial region. The amplitude of these oscillations is proportional to the width of the ocean basin, typically about 100 (200) Sv in the Atlantic (Pacific). We show that these oscillations are driven by surface winds within 10°N/S of the equator, and their periods (typically 4-10 days) correspond to a small number of low mode equatorially trapped planetary waves. Furthermore, the oscillations can be well reproduced by idealised wind-driven simulations linearised about a state of rest. Zonally integrated linearised equations of motion are solved using vertical normal modes and equatorial meridional modes representing Yanai and inertia-gravity waves. Idealised simulations capture between 85% and 95% of the variance of matching time-series segments diagnosed from the NEMO integrations. Similar results are obtained for the corresponding modes in the Atlantic and Indian Oceans. Our results raise questions about the roles of inertia-gravity waves near the equator in the vertical transfer of heat and momentum and whether these transfers will be explicitly resolved by ocean models or need to be parametrised.</p>

scholarly journals Application of the Compressible, Nonhydrostatic, Balanced Omega Equation in Estimating Diabatic Forcing for Parameterization of Inertia–Gravity Waves: Case Study of Moist Baroclinic Waves Using WRF

2019 ◽  
Vol 77 (1) ◽  
pp. 113-129
Author(s):  
Mahnoosh Haghighatnasab ◽  
Mohammad Mirzaei ◽  
Ali R. Mohebalhojeh ◽  
Christoph Zülicke ◽  
Riwal Plougonven
Keyword(s):  
Gravity Waves ◽  
General Circulation ◽  
Diabatic Heating ◽  
Wrf Model ◽  
Vertical Motion ◽  
General Circulation Models ◽  
Baroclinic Waves ◽  
Diabatic Forcing ◽  
Omega Equation ◽  
Inertia Gravity Waves

Abstract The parameterization of inertia–gravity waves (IGWs) is of considerable importance in general circulation models. Among the challenging issues faced in studies concerned with parameterization of IGWs is the estimation of diabatic forcing in a way independent of the physics parameterization schemes, in particular, convection. The requirement is to estimate the diabatic heating associated with balanced motion. This can be done by comparing estimates of balanced vertical motion with and without diabatic effects. The omega equation provides the natural method of estimating balanced vertical motion without diabatic effects, and several methods for including diabatic effects are compared. To this end, the assumption of spatial-scale separation between IGWs and balanced flows is combined with a suitable form of the balanced omega equation. To test the methods constructed for estimating diabatic heating, an idealized numerical simulation of the moist baroclinic waves is performed using the Weather Research and Forecasting (WRF) Model in a channel on the f plane. In overall agreement with the diabatic heating of the WRF Model, in the omega-equation-based estimates, the maxima of heating appear in the warm sector of the baroclinic wave and in the exit region of the upper-level jet. The omega-equation-based method with spatial smoothing for estimating balanced vertical motion is thus presented as the proper way to evaluate diabatic forcing for parameterization of IGWs.

scholarly journals The Mesoscale Kinetic Energy Spectrum of a Baroclinic Life Cycle

2009 ◽  
Vol 66 (4) ◽  
pp. 883-901 ◽  
Author(s):  
Michael L. Waite ◽  
Chris Snyder
Keyword(s):  
Life Cycle ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Gravity Waves ◽  
Linear Instability ◽  
Mature Stage ◽  
Flux Divergence ◽  
Full Spectrum ◽  
Kinetic Energy Spectrum ◽  
Inertia Gravity Waves

Abstract The atmospheric mesoscale kinetic energy spectrum is investigated through numerical simulations of an idealized baroclinic wave life cycle, from linear instability to mature nonlinear evolution and with high horizontal and vertical resolution (Δx ≈ 10 km and Δz ≈ 60 m). The spontaneous excitation of inertia–gravity waves yields a shallowing of the mesoscale spectrum with respect to the large scales, in qualitative agreement with observations. However, this shallowing is restricted to the lower stratosphere and does not occur in the upper troposphere. At both levels, the mesoscale divergent kinetic energy spectrum—a proxy for the inertia–gravity wave energy spectrum—resembles a −5/3 power law in the mature stage. Divergent kinetic energy dominates the lower stratospheric mesoscale spectrum, accounting for its shallowing. Rotational kinetic energy, by contrast, dominates the upper tropospheric spectrum and no shallowing of the full spectrum is observed. By analyzing the tendency equation for the kinetic energy spectrum, it is shown that the lower stratospheric spectrum is not governed solely by a downscale energy cascade; rather, it is influenced by the vertical pressure flux divergence associated with vertically propagating inertia–gravity waves.

scholarly journals Diffusion of inertia-gravity waves by geostrophic turbulence

2019 ◽  
Vol 869 ◽  
Author(s):  
Hossein A. Kafiabad ◽  
Miles A. C. Savva ◽  
Jacques Vanneste
Keyword(s):  
Energy Spectrum ◽  
Gravity Waves ◽  
Wave Energy ◽  
Large Scale ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Constant Frequency ◽  
Geostrophic Turbulence ◽  
Wave Energy Spectrum ◽  
Inertia Gravity Waves

The scattering of inertia-gravity waves by large-scale geostrophic turbulence in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave energy on the constant-frequency cone in wavenumber space. We derive the corresponding diffusion equation and relate its diffusivity to the wave characteristics and the energy spectrum of the turbulent flow. We check the predictions of this equation against numerical simulations of the three-dimensional Boussinesq equations in initial-value and forced scenarios with horizontally isotropic wave and flow fields. In the forced case, wavenumber diffusion results in a $k^{-2}$ wave energy spectrum consistent with as-yet-unexplained features of observed atmospheric and oceanic spectra.

scholarly journals On the Quantification of Imbalance and Inertia–Gravity Waves Generated in Numerical Simulations of Moist Baroclinic Waves Using the WRF Model

2017 ◽  
Vol 74 (12) ◽  
pp. 4241-4263 ◽  
Author(s):  
Mohammad Mirzaei ◽  
Ali R. Mohebalhojeh ◽  
Christoph Zülicke ◽  
Riwal Plougonven
Keyword(s):  
Numerical Simulations ◽  
Gravity Waves ◽  
Wrf Model ◽  
Weather Research And Forecasting ◽  
Baroclinic Waves ◽  
Surface Front ◽  
The Difference ◽  
Upper Level ◽  
Upper Level Jet ◽  
Inertia Gravity Waves

Abstract Quantification of inertia–gravity waves (IGWs) generated by upper-level jet–surface front systems and their parameterization in global models of the atmosphere relies on suitable methods to estimate the strength of IGWs. A harmonic divergence analysis (HDA) that has been previously employed for quantification of IGWs combines wave properties from linear dynamics with a sophisticated statistical analysis to provide such estimates. A question of fundamental importance that arises is how the measures of IGW activity provided by the HDA are related to the measures coming from the wave–vortex decomposition (WVD) methods. The question is addressed by employing the nonlinear balance relations of the first-order δ–γ, the Bolin–Charney, and the first- to third-order Rossby number expansion to carry out WVD. The global kinetic energy of IGWs given by the HDA and WVD are compared in numerical simulations of moist baroclinic waves by the Weather Research and Forecasting (WRF) Model in a channel on the f plane. The estimates of the HDA are found to be 2–3 times smaller than those of the optimal WVD. This is in part due to the absence of a well-defined scale separation between the waves and vortical flows, the IGW estimates by the HDA capturing only the dominant wave packets and with limited scales. It is also shown that the difference between the HDA and WVD estimates is related to the width of the IGW spectrum.

Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime

2010 ◽  
Vol 649 ◽  
pp. 187-203 ◽  
Author(s):  
PAUL D. WILLIAMS ◽  
PETER L. READ ◽  
THOMAS W. N. HAINE
Keyword(s):  
Aspect Ratio ◽  
Gravity Waves ◽  
Laboratory Experiments ◽  
Rossby Number ◽  
Large Aspect Ratio ◽  
Baroclinic Waves ◽  
Interfacial Surface ◽  
Theory Application ◽  
Systematic Biases ◽  
Inertia Gravity Waves

We compare laboratory observations of equilibrated baroclinic waves in the rotating two-layer annulus, with numerical simulations from a quasi-geostrophic model. The laboratory experiments lie well outside the quasi-geostrophic regime: the Rossby number reaches unity; the depth-to-width aspect ratio is large; and the fluid contains ageostrophic inertia–gravity waves. Despite being formally inapplicable, the quasi-geostrophic model captures the laboratory flows reasonably well. The model displays several systematic biases, which are consequences of its treatment of boundary layers and neglect of interfacial surface tension and which may be explained without invoking the dynamical effects of the moderate Rossby number, large aspect ratio or inertia–gravity waves. We conclude that quasi-geostrophic theory appears to continue to apply well outside its formal bounds.

scholarly journals Scale-dependent analysis of in situ observations in the mesoscale to submesoscale range around New Caledonia

Ocean Science ◽  
2020 ◽  
Vol 16 (4) ◽  
pp. 907-925
Author(s):  
Guillaume Sérazin ◽  
Frédéric Marin ◽  
Lionel Gourdeau ◽  
Sophie Cravatte ◽  
Rosemary Morrow ◽  
...  
Keyword(s):  
Potential Energy ◽  
Gravity Waves ◽  
New Caledonia ◽  
Mesoscale Eddies ◽  
Structure Functions ◽  
Ocean Dynamics ◽  
Small Scale ◽  
Available Potential Energy ◽  
Rotational Motions ◽  
Inertia Gravity Waves

Abstract. Small-scale ocean dynamics around New Caledonia (22∘ S) in the southwest Pacific Ocean occur in regions with substantial mesoscale eddies, complex bathymetry, complex intertwined currents, islands and strong internal tides. Using second-order structure functions applied to observational acoustic Doppler current profiler (ADCP) and thermosalinograph (TSG) datasets, these small-scale dynamics are characterised in the range of scales of 3–100 km in order to determine the turbulent regime at work. A Helmholtz decomposition is used to analyse the contribution of rotational and divergent motions. A surface-intensified regime is shown to be at work south and east of New Caledonia, involving substantial rotational motions such as submesoscale structures generated by mixed layer instabilities and frontogenesis. This regime is, however, absent north of New Caledonia, where mesoscale eddies are weaker and surface available potential energy is smaller at small scales. North of New Caledonia and below 200 m, in the regions south and east of New Caledonia, the dynamical regime at work could be explained by stratified turbulence as divergent and rotational motions have similar contribution, but weakly nonlinear interaction between inertia–gravity waves is also possible as structure functions get close to the empirical spectrum model for inertia–gravity waves. Seasonal variations of the available potential energy reservoir, associated with a change in the vertical profile rather than in horizontal density variance, suggest that submesoscale motions would also seasonally vary around New Caledonia. Overall, a loss of geostrophic balance is likely to occur at scales smaller than 10 km, where the contribution of divergent motions become significant.

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