Scale-dependent infrared radiative damping rates on Mars and their role in the deposition of gravity-wave momentum flux

Eckermann, Stephen D.; Ma, Jun; Zhu, Xun

doi:10.1016/j.icarus.2010.10.029

Cited by 35 publications

(49 citation statements)

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“…In reality, the radiative relaxation time scale is dependent upon vertical scale, and for typical scales for polar vortex variability (10-40 km), values of t rad ' 0.5-2 sols are more appropriate (Eckermann et al 2011). These values are similar to or less than typical barotropic instability time scales t inst and therefore consistent with our understanding that t r & t inst is a necessary condition in order for a persistent annular vortex to exist.…”

supporting

confidence: 77%

The Stability of Mars’s Annular Polar Vortex

Seviour

Waugh

Scott

2017

Journal of the Atmospheric Sciences

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The Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising, since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here the stability of a Mars-like annular vortex is investigated using numerical integrations of the rotating shallow-water equations. The mode of instability and its growth rate is shown to depend upon the latitude and width of the annulus. By introducing thermal relaxation toward an annular equilibrium profile with a time scale similar to that of the instability, a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere can be simulated. This time scale, typically 0.5-2 sols, is similar to radiative relaxation time scales for Mars's polar atmosphere. The persistence of an annular vortex is also shown to be robust to topographic forcing, as long as it is below a certain amplitude. It is therefore proposed that the persistence of this barotropically unstable annular vortex is permitted owing to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.

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supporting

confidence: 77%

The Stability of Mars’s Annular Polar Vortex

Seviour

Waugh

Scott

2017

Journal of the Atmospheric Sciences

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“…where n is the viscosity coefficient and e(v) is a frequency-dependent polarization factor near unity [the full expression is given in (18)-(19) of Eckermann et al (2011)]. This damping is applied by adding an imaginary component m i 5 (tc gz ) 21 to the vertical wavenumber in (22).…”

Section: Summary and Discussionmentioning

confidence: 99%

“…is the so-called normalized obstacle height (Eckermann et al 2010), equivalent to both the peak wave steepness amplitude at the surface and the inverse surface Froude number [see (6)]. Figure 4 compares a h (z) and a h z (z) profiles for a range of different b.…”

Section: Hydrostatic Waves In Uniform Flowmentioning

confidence: 99%

“…1 For three-dimensional OGWs, however, the vertical flux of horizontal momentum is conserved only when integrated over the entire horizontal domain (e.g., Vosper and Mobbs 1998), and local values can and do change because of horizontal geometrical spreading [i.e., J h 6 ¼ 1: e.g., Fig. 5 of Eckermann et al (2010)]. Since it is local rather than domainaveraged wave amplitudes that determine where OGWs break and how much momentum and energy they deposit locally, OGWD parameterizations should ideally be incorporating horizontal geometrical spreading effects on local wave amplitudes.…”

Section: Introductionmentioning

confidence: 99%

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Effects of Horizontal Geometrical Spreading on the Parameterization of Orographic Gravity Wave Drag. Part I: Numerical Transform Solutions

Eckermann

Broutman

2015

Journal of the Atmospheric Sciences

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Numerical transform solutions for hydrostatic gravity waves generated by both uniform and sheared flow over elliptical obstacles are used to quantify effects of horizontal geometrical spreading on amplitude evolution with height. Both vertical displacement and steepness amplitudes are considered because of their close connections to drag parameterizations in weather and climate models. Novel diagnostics quantify the location and value of the largest wavefield amplitudes most likely to break at each altitude. These horizontal locations do not stray far from the obstacle peak even at high altitudes. Resulting vertical profiles of wave amplitude are normalized to remove density and refraction effects, thereby quantifying the horizontal geometrical spreading contribution, currently absent from parameterizations. Horizontal geometrical spreading produces monotonic amplitude decreases with height through wave-action conservation as waves propagate into progressively larger horizontal areas. Accumulated amplitude reductions are appreciable for all but the most quasi-two-dimensional obstacles with long axes orthogonal to the flow, and even these are impacted appreciably if the obstacle is rotated by more than 208-308. Profiles are insensitive to the obstacle's functional form but vary strongly in response to changes in its horizontal aspect ratio. Responses to background winds are captured by a vertical coordinate transformation that remaps profiles to a universal form for a given obstacle. These results show that horizontal geometrical spreading has comparable or larger effects on wave amplitudes as the refraction of vertical wavenumbers and thus is important for accurate parameterizations of wave breaking and drag.

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“…On the other hand, if w9T9 varies slowly with altitude over H, then kwT/H can still be omitted because jkw9T9/Hj ( jw9T9/Hj . Radiative heat exchange of a temperature perturbation damps its amplitude (e.g., Fels 1984;Zhu 1993;Eckermann et al 2011), which in turn also damps the velocity amplitude of the wave component through the polarization relation. The last two terms in Eq.…”

Section: Total Potential Energy Versus Available Potential Energymentioning

confidence: 99%