Optimal excitation of two dimensional Holmboe instabilities

Constantinou, Navid C.; Ioannou, Petros J.

doi:10.1063/1.3609283

Cited by 7 publications

(11 citation statements)

References 60 publications

(105 reference statements)

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“…As can be seen in figure 3, O(10-100) energy growth may be observed for intermediate target times, even for flows expected to be stable to normal-mode instability (Ri b > 1/4), as in Farrell & Ioannou (1993b) and Constantinou & Ioannou (2011). For flows predicted to be linearly stable by the Miles-Howard theorem, G(T) reaches a maximum value at an intermediate target time, T, before decreasing for higher T. The maximum value of the gain is highly sensitive to the bulk Richardson number, with G(T = 15) 47 when Ri b = 0.3 and G(T = 15) 13 when Ri b = 0.5.…”

Section: Resultsmentioning

confidence: 90%

“…First, we wish to explore the properties of linear optimal perturbations, their connection to the KH instability, and the modifying effect of stratification on their dynamics. Second, and more importantly, we wish to investigate whether there can be substantial linear transient growth for Ri g (z) > 1/4 everywhere, by analogy with the observations of Constantinou & Ioannou (2011). They observed transient growth in a flow restricted to two dimensions with a 'sharp' density interface for wavenumbers outside the range predicted to be unstable to the travelling wave instability originally discussed by Holmboe (1962).…”

Section: Introductionmentioning

confidence: 93%

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Transient growth in strongly stratified shear layers

2014

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We investigate numerically transient linear growth of three-dimensional perturbations in a stratified shear layer to determine which perturbations optimize the growth of the total kinetic and potential energy over a range of finite target time intervals. The stratified shear layer has an initial parallel hyperbolic tangent velocity distribution with Reynolds number Re = U 0 h/ν = 1000 and Prandtl number ν/κ = 1, where ν is the kinematic viscosity of the fluid and κ is the diffusivity of the density. The initial stable buoyancy distribution has constant buoyancy frequency N 0 , and we consider a range of flows with different bulk Richardson number Ri b = N 2 0 h 2 /U 2 0 , which also corresponds to the minimum gradient Richardson number Ri g (z) = N 2 0 /(dU/dz) 2 at the midpoint of the shear layer. For short target times, the optimal perturbations are inherently three-dimensional, while for sufficiently long target times and small Ri b the optimal perturbations are closely related to the normal-mode 'Kelvin-Helmholtz' (KH) instability, consistent with analogous calculations in an unstratified mixing layer recently reported by Arratia et al. (J. Fluid Mech., vol. 717, 2013, pp. 90-133). However, we demonstrate that non-trivial transient growth occurs even when the Richardson number is sufficiently high to stabilize all normal-mode instabilities, with the optimal perturbation exciting internal waves at some distance from the midpoint of the shear layer.

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Section: Resultsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 93%

Transient growth in strongly stratified shear layers

2014

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“…Constantinou & Ioannou 2011;Guha & Lawrence 2013). Further, our profiles were chosen so that, when M 1, |B| |U| pointwise everywhere, and a stability theorem forbids normal mode instabilities.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Interacting vorticity waves as an instability mechanism for magnetohydrodynamic shear instabilities

et al. 2015

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The interacting vorticity wave formalism for shear flow instabilities is extended here to the magnetohydrodynamic (MHD) setting, to provide a mechanistic description for stabilising and destabilising shear instabilities by the presence of a background magnetic field. The interpretation relies on local vorticity anomalies inducing a non-local velocity field, resulting in action at a distance. It is shown here that the waves supported by the system are able to propagate vorticity via the Lorentz force, and waves may interact. The existence of instability then rests upon whether the choice of basic state allows for phase locking and constructive interference of the vorticity waves via mutual interaction. To substantiate this claim, we solve the instability problem of two representative basic states, one where a background magnetic field stabilises an unstable flow and the other where the field destabilises a stable flow, and perform relevant analyses to show how this mechanism operates in MHD.

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“…The liquid mode may have some resemblance to the Holmboe () instability. The Holmboe instability appears in a number of atmospheric, oceanic, and astrophysical problems (Alexakis, ; Constantinoua & Ioannoub, ; Smyth, ; Smyth & Peltier, ). The Holmboe instability can develop in highly stratified shear layers when the density stratification is concentrated in a small region of the shear layer.…”

Section: The State Of the Air‐sea Interface Under Tropical Cyclonesmentioning

confidence: 99%

Is the State of the Air‐Sea Interface a Factor in Rapid Intensification and Rapid Decline of Tropical Cyclones?

et al. 2017

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Tropical storm intensity prediction remains a challenge in tropical meteorology. Some tropical storms undergo dramatic rapid intensification and rapid decline. Hurricane researchers have considered particular ambient environmental conditions including the ocean thermal and salinity structure and internal vortex dynamics (e.g., eyewall replacement cycle, hot towers) as factors creating favorable conditions for rapid intensification. At this point, however, it is not exactly known to what extent the state of the sea surface controls tropical cyclone dynamics. Theoretical considerations, laboratory experiments, and numerical simulations suggest that the air‐sea interface under tropical cyclones is subject to the Kelvin‐Helmholtz type instability. Ejection of large quantities of spray particles due to this instability can produce a two‐phase environment, which can attenuate gravity‐capillary waves and alter the air‐sea coupling. The unified parameterization of waveform and two‐phase drag based on the physics of the air‐sea interface shows the increase of the aerodynamic drag coefficient Cd with wind speed up to hurricane force ( U10≈35 m s−1). Remarkably, there is a local Cd minimum—“an aerodynamic drag well”—at around U10≈60 m s−1. The negative slope of the Cd dependence on wind‐speed between approximately 35 and 60 m s−1 favors rapid storm intensification. In contrast, the positive slope of Cd wind‐speed dependence above 60 m s−1 is favorable for a rapid storm decline of the most powerful storms. In fact, the storms that intensify to Category 5 usually rapidly weaken afterward.

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Optimal excitation of two dimensional Holmboe instabilities

Cited by 7 publications

References 60 publications

Transient growth in strongly stratified shear layers

Transient growth in strongly stratified shear layers

Interacting vorticity waves as an instability mechanism for magnetohydrodynamic shear instabilities

Is the State of the Air‐Sea Interface a Factor in Rapid Intensification and Rapid Decline of Tropical Cyclones?

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