scholarly journals The influence of front strength on the development and equilibration of symmetric instability. Part 2. Nonlinear evolution

2021 ◽  
Vol 926 ◽  
Author(s):  
A.F. Wienkers ◽  
L.N. Thomas ◽  
J.R. Taylor
Keyword(s):  
Primary Source ◽  
Inertial Oscillations ◽  
Turbulent Dissipation ◽  
Weakly Nonlinear ◽  
Thermal Wind ◽  
Background Density ◽  
Inertial Instability ◽  
Slantwise Convection ◽  
Symmetric Instability ◽  
Energy Pathways

In Part 1 (Wienkers, Thomas & Taylor, J. Fluid Mech., vol. 926, 2021, A6), we described the theory for linear growth and weakly nonlinear saturation of symmetric instability (SI) in the Eady model representing a broad frontal zone. There, we found that both the fraction of the balanced thermal wind mixed down by SI and the primary source of energy are strongly dependent on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Strong fronts with steep isopycnals develop a flavour of SI we call ‘slantwise inertial instability’ by extracting kinetic energy from the background flow and rapidly mixing down the thermal wind profile. In contrast, weak fronts extract more potential energy from the background density profile, which results in ‘slantwise convection.’ Here, we extend the theory from Part 1 using nonlinear numerical simulations to focus on the adjustment of the front following saturation of SI. We find that the details of adjustment and amplitude of the induced inertial oscillations depend on the front strength. While weak fronts develop narrow frontlets and excite small-amplitude vertically sheared inertial oscillations, stronger fronts generate large inertial oscillations and produce bore-like gravity currents that propagate along the top and bottom boundaries. The turbulent dissipation rate in these strong fronts is large, highly intermittent and intensifies during periods of weak stratification. We describe each of these mechanisms and energy pathways as the front evolves towards the final adjusted state, and in particular focus on the effect of varying the dimensionless front strength.

scholarly journals The influence of front strength on the development and equilibration of symmetric instability. Part 1. Growth and saturation

2021 ◽  
Vol 926 ◽  
Author(s):  
A.F. Wienkers ◽  
L.N. Thomas ◽  
J.R. Taylor
Keyword(s):  
Stability Analysis ◽  
Shear Instability ◽  
Nonlinear Stability Analysis ◽  
Coriolis Parameter ◽  
Weakly Nonlinear ◽  
Thermal Wind ◽  
Inertial Instability ◽  
Slantwise Convection ◽  
The Stability ◽  
Symmetric Instability

Submesoscale fronts with large horizontal buoyancy gradients and $O(1)$ Rossby numbers are common in the upper ocean. These fronts are associated with large vertical transport and are hotspots for biological activity. Submesoscale fronts are susceptible to symmetric instability (SI) – a form of stratified inertial instability which can occur when the potential vorticity is of the opposite sign to the Coriolis parameter. Here, we use a weakly nonlinear stability analysis to study SI in an idealised frontal zone with a uniform horizontal buoyancy gradient in thermal wind balance. We find that the structure and energetics of SI strongly depend on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Vertically bounded non-hydrostatic SI modes can grow by extracting potential or kinetic energy from the balanced front and the relative importance of these energy reservoirs depends on the front strength and vertical stratification. We describe two limiting behaviours as ‘slantwise convection’ and ‘slantwise inertial instability’ where the largest energy source is the buoyancy flux and geostrophic shear production, respectively. The growing linear SI modes eventually break down through a secondary shear instability, and in the process transport considerable geostrophic momentum. The resulting breakdown of thermal wind balance generates vertically sheared inertial oscillations and we estimate the amplitude of these oscillations from the stability analysis. We finally discuss broader implications of these results in the context of current parameterisations of SI.

scholarly journals Symmetric Instability, Inertial Oscillations, and Turbulence at the Gulf Stream Front

2016 ◽  
Vol 46 (1) ◽  
pp. 197-217 ◽  
Author(s):  
Leif N. Thomas ◽  
John R. Taylor ◽  
Eric A. D’Asaro ◽  
Craig M. Lee ◽  
Jody M. Klymak ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Gulf Stream ◽  
Surface Boundary ◽  
Unstable Flow ◽  
Inertial Oscillations ◽  
Surface Boundary Layer ◽  
Eddy Simulation ◽  
Symmetric Instability ◽  
Shear Production

AbstractThe passage of a winter storm over the Gulf Stream observed with a Lagrangian float and hydrographic and velocity surveys provided a unique opportunity to study how the interaction of inertial oscillations, the front, and symmetric instability (SI) shapes the stratification, shear, and turbulence in the upper ocean under unsteady forcing. During the storm, the rapid rise and rotation of the winds excited inertial motions. Acting on the front, these sheared motions modulate the stratification in the surface boundary layer. At the same time, cooling and downfront winds generated a symmetrically unstable flow. The observed turbulent kinetic energy dissipation exceeded what could be attributed to atmospheric forcing, implying SI drew energy from the front. The peak excess dissipation, which occurred just prior to a minimum in stratification, surpassed that predicted for steady SI turbulence, suggesting the importance of unsteady dynamics. The measurements are interpreted using a large-eddy simulation (LES) and a stability analysis configured with parameters taken from the observations. The stability analysis illustrates how SI more efficiently extracts energy from a front via shear production during periods when inertial motions reduce stratification. Diagnostics of the energetics of SI from the LES highlight the temporal variability in shear production but also demonstrate that the time-averaged energy balance is consistent with a theoretical scaling that has previously been tested only for steady forcing. As the storm passed and the winds and cooling subsided, the boundary layer restratified and the thermal wind balance was reestablished in a manner reminiscent of geostrophic adjustment.

Symmetric Instability in the Outflow Layer of a Major Hurricane

2014 ◽  
Vol 71 (10) ◽  
pp. 3739-3746 ◽  
Author(s):  
John Molinari ◽  
David Vollaro
Keyword(s):  
Potential Temperature ◽  
Outer Edge ◽  
Unstable State ◽  
Upper Troposphere ◽  
Hurricane Ivan ◽  
Equivalent Potential ◽  
Inertial Instability ◽  
Major Hurricane ◽  
Cloudy Region ◽  
Symmetric Instability

Abstract A set of 327 dropsondes from the NOAA G-IV aircraft was used to create a composite analysis of the azimuthally averaged absolute angular momentum in the outflow layer of major Hurricane Ivan (2004). Inertial instability existed over a narrow layer in the upper troposphere between the 350- and 450-km radii. Isolines of potential and equivalent potential temperature showed that the conditions for both dry and moist symmetric instability were satisfied in the same region, but over a deeper layer from 9 to 12 km. The radial flow maximized at the outer edge of the unstable region. The symmetrically unstable state existed above a region of outward decrease of temperature between the cirrus overcast of the storm and clear air outside. It is hypothesized that the temperature gradient was created as a result of longwave heating within the cirrus overcast and longwave cooling outside the cloudy region. This produced isentropes that sloped upward with radius in the same region that absolute momentum surfaces were flat or sloping downward, thus creating symmetric instability. Although this instability typically follows rather than precedes intensification, limited numerical evidence suggests that the reestablishment of a symmetrically neutral state might influence the length of the intensification period.

The nonlinear evolution of zonally symmetric equatorial inertial instability

2003 ◽  
Vol 474 ◽  
pp. 245-273 ◽  
Author(s):  
STEPHEN D. GRIFFITHS
Keyword(s):  
Long Memory ◽  
Initial Conditions ◽  
Zonal Flow ◽  
Nonlinear Regime ◽  
Mean Flow ◽  
Coriolis Parameter ◽  
Weakly Nonlinear ◽  
Flow Change ◽  
Inertial Instability ◽  
The Mean

The inertial instability of equatorial shear flows is studied, with a view to understanding observed phenomena in the Earth's stratosphere and mesosphere. The basic state is a zonal flow of stratified fluid on an equatorial β-plane, with latitudinal shear. The simplest self-consistent model of the instability is used, so that the basic state and the disturbances are zonally symmetric, and a vertical diffusivity provides the scale selection. We study the interaction between the inertial instability, which takes the form of periodically varying disturbances in the vertical, and the mean flow, where ‘mean’ is a vertical mean.The weakly nonlinear regime is investigated analytically, for flows with an arbitrary dependence on latitude. An amplitude equation of the form dA/dt = A−k2A∫[mid ]A[mid ]2dt is derived for the disturbances, and the evolving stability properties of the mean flow are discussed. In the final steady state, the disturbances vanish, but there is a persistent mean flow change that stabilizes the flow. However, the magnitude of the mean flow change depends strongly on the initial conditions, so that the system has a long memory. The analysis is extended to include the effects of Rayleigh friction and Newtonian cooling, destroying the long-memory property.A more strongly nonlinear regime is investigated with the help of numerical simulations, extending the results up to the point where the instability leads to density contour overturning. The instability is shown to lead to a homogenization of fQ¯ around the initially unstable region, where f is the Coriolis parameter, and Q¯ is the vertical mean of the potential vorticity. As the instability evolves, the line of zero Q¯ moves polewards, rather than equatorwards as might be expected from a simple self-neutralization argument.

scholarly journals Decoupling of Balanced and Unbalanced Motions and Inertia–Gravity Wave Emission: Small versus Large Rossby Numbers

2008 ◽  
Vol 65 (11) ◽  
pp. 3528-3542 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Gravity Wave ◽  
Stratified Fluid ◽  
Geostrophic Adjustment ◽  
Inertial Instability ◽  
Wave Emission ◽  
Symmetric Instability

Abstract This paper provides a brief review of recent results on decoupling of fast [inertia–gravity wave (IGW)] and slow (vortex) motions at small Rossby numbers obtained in the framework of the geostrophic adjustment of localized perturbations. Special attention is paid to the IGW emission and its interpretation in the context of “spontaneous imbalance.” Several mechanisms that lead to spontaneous IGW emission and, thus, to violations of fast–slow splitting at large Rossby numbers are reviewed: Lighthill radiation, symmetric/inertial instability, and ageostrophic shear (Rossby–Kelvin) instability. New results on the saturation of symmetric instability and on the existence of Rossby–Kelvin instability in continuously stratified fluid are presented.

scholarly journals Assessment of Conditional Symmetric Instability from Global Reanalysis Data

2018 ◽  
Vol 75 (7) ◽  
pp. 2425-2443 ◽  
Author(s):  
Ting-Chen Chen ◽  
M. K. Yau ◽  
Daniel J. Kirshbaum
Keyword(s):  
Convective Available Potential Energy ◽  
Reanalysis Data ◽  
Statistical Investigation ◽  
Extratropical Cyclones ◽  
Rapid Intensification ◽  
Significant Drop ◽  
Surface Precipitation ◽  
Slantwise Convection ◽  
Symmetric Instability ◽  
Conditional Symmetric Instability

Abstract Slantwise convection, the process by which moist symmetric instability is released, has often been linked to banded clouds and precipitation, especially in frontal zones within extratropical cyclones. Studies also suggest that the latent heat release associated with slantwise convection can lead to a spinup of surface frontogenesis, which can enhance the rapid intensification of extratropical cyclones. However, most of these studies considered only local areas or short time durations. In this study, we provide a novel statistical investigation of the global climatology of the potential occurrence of slantwise convection, in terms of conditional symmetric instability, and its relationship with precipitating systems. Using the 6-hourly ERA-Interim, two different indices are calculated, namely, slantwise convective available potential energy (SCAPE) and vertically integrated extent of realizable symmetric instability (VRS), to assess the likelihood of occurrence of slantwise convection around the globe. The degree of association is quantified between these indices and the observed surface precipitation as well as the cyclone activity. The susceptibility of midlatitude cyclones to slantwise convection at different stages of their life cycle is also investigated. As compared to the nonexplosive cyclone cases, the time evolution of SCAPE and VRS within rapidly deepening cyclones exhibit higher values before, and a more significant drop after, the onset of rapid intensification, supporting the idea that the release of symmetric instability might contribute to the intensification of storms.

scholarly journals Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Theory

2010 ◽  
Vol 40 (5) ◽  
pp. 1055-1074 ◽  
Author(s):  
Maxim Nikurashin ◽  
Raffaele Ferrari
Keyword(s):  
Internal Waves ◽  
Bottom Topography ◽  
Drake Passage ◽  
Wave Radiation ◽  
Small Scale ◽  
Ocean Bottom ◽  
Inertial Oscillations ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Internal Wave Generation

Abstract Observations and inverse models suggest that small-scale turbulent mixing is enhanced in the Southern Ocean in regions above rough topography. The enhancement extends O(1) km above the topography, suggesting that mixing is supported by the breaking of gravity waves radiated from the ocean bottom. In this study, it is shown that the observed mixing rates can be sustained by internal waves generated by geostrophic motions flowing over bottom topography. Weakly nonlinear theory is used to describe the internal wave generation and the feedback of the waves on the zonally averaged flow. Vigorous inertial oscillations are driven at the ocean bottom by waves generated at steep topography. The wave radiation and dissipation at equilibrium is therefore the result of both geostrophic flow and inertial oscillations differing substantially from the classical lee-wave problem. The theoretical predictions are tested versus two-dimensional high-resolution numerical simulations with parameters representative of Drake Passage. This work suggests that mixing in Drake Passage can be supported by geostrophic motions impinging on rough topography rather than by barotropic tidal motions, as is commonly assumed.

Interaction between upper-ocean submesoscale currents and convective turbulence

2021 ◽  
Keyword(s):  
Potential Energy ◽  
Gravitational Instability ◽  
Baroclinic Instability ◽  
Upper Ocean ◽  
Surface Cooling ◽  
Convective Turbulence ◽  
Velocity Gradients ◽  
Submesoscale Currents ◽  
Symmetric Instability ◽  
Energy Pathways

Abstract The interaction between upper-ocean submesoscale fronts evolving with coherent features, such as vortex filaments and eddies, and finescale convective turbulence generated by surface cooling of varying magnitude is investigated. While convection is energized by gravitational instability, predominantly at the finescale (FS), which feeds off the potential energy that is input through cooling, the submesoscale (SMS) is energized at larger scales by the release of available potential energy stored in the front. Here, we decompose the flow into FS and SMS fields explicitly to investigate the energy pathways and the strong interaction between them. Overall, the SMS is energized due to surface cooling. The frontogenetic tendency at the submesoscale increases, which counters the enhanced horizontal diffusion by convection-induced turbulence. Downwelling/upwelling strengthens, and the peak SMS vertical buoyancy flux increases as surface cooling is increased. Furthermore, the production of FS energy by SMS velocity gradients is significant, up to half of the production by convection. Examination of potential vorticity reveals that surface cooling promotes higher levels of secondary symmetric instability, which coexists with the persistent baroclinic instability.

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