Linearly forced fluid flow on a rotating sphere

Supekar, Rohit; Heinonen, Vili; Burns, Keaton J.; Dunkel, Jörn

doi:10.1017/jfm.2020.205

Cited by 7 publications

(7 citation statements)

References 57 publications

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“…In a second set of simulations, we use a linear, resonant forcing that excites only inertial waves through a parametric resonance. Linear and time-coherent forcing of turbulence has recently proved a useful tool to better control the energy injection process [12,26,27]. In the present case, the linear forcing is…”

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confidence: 97%

Evidence of the Zakharov-Kolmogorov spectrum in numerical simulations of inertial wave turbulence

Reun

Favier

Bars

2020

EPL

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Rotating turbulence is commonly known for being dominated by geostrophic vortices that are invariant along the rotation axis and undergo inverse cascade. Yet, it has recently been shown to sustain fully three-dimensional states with a downscale energy cascade. In this letter, we investigate the statistical properties of three-dimensional rotating turbulence by the means of direct numerical simulations in a triply periodic box where geostrophic vortices are specifically damped. The resulting turbulent flow is an inertial wave turbulence that verifies the Zakharov-Kolmogorov spectrum derived analytically by Galtier (Phys. Rev. E, 68, 2003), thus offering numerical proof of the relevance of wave turbulence theory for three-dimensional, anisotropic waves. Lastly, we show that the same forcing leads to either geostrophic or wave turbulence depending on the initial condition. Our results thus bring further evidence for bi-stability in rotating turbulent flows.

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confidence: 97%

Evidence of the Zakharov-Kolmogorov spectrum in numerical simulations of inertial wave turbulence

Reun

Favier

Bars

2020

EPL

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“…A recent numerical statistical study of flow in an entirely fluid sphere, using spherical harmonics, shows flow anomalies at high latitudes that evolve into bands as rotation velocity is increased (Supekar et al 2020). "Dipole" (anomalous) flow structures appear near the poles and may persist as velocity is increased.…”

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confidence: 99%

A strong link between variations in sea-ice extent and global atmospheric pressure?

Mouël

Lopes

Courtillot

2021

Preprint

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Abstract. Abstract. This paper reports spectral analyses, using Singular Spectral Analysis, of variations of the Arctic and Antarctic sea-ice extents (SI), and of the atmospheric surface pressure (AP) in both hemispheres (NH and SH). The ice-extents are dominated by a quasi-linear trend over the 42 yr period when data are available (1978–2020) and an annual component. Taken together, these two components represent more than 98 % of the signal variance. Both ice-extent series share the same 5 set of harmonics of the annual component (1/2, 1/3, 1/4 and 1/5 yr). The multi-decadal trends of sea-ice extent in the Arctic and Antarctic are of opposite sign. The series of harmonics of 1 year are consequences of the Earth’s revolution about the Sun. The components with period longer than a year form a set of even harmonics of the Schwabe cycle. The pressure series also exhibits the four harmonics of 1 year, that is not found in many series previously analysed in the same way. This could suggest a connection between variations in pressure and sea-ice extent. Geographical pressure structures (SSA trends) are stable on a 10 decadal to centennial time scale and exhibit a three-fold symmetry in the NH. In the SH that order-3 symmetry is altered by the Ross-Weddell “dipole” pressure anomaly. This anomaly is seen in maps of correlations of variations in sea-ice extent with atmospheric pressure, surface temperature and winds. It fits topographic forcing. There is phase opposition between the annual components of SI and AP in the SH, and the same decreasing phase lag from −30 to −60 days over 42 years for the four harmonic components of SHSI and SHAP. The (negative) sign of the trend of pressure and (positive) sign of the trend of temperature 15 beg for an explanation. The relative change in pressure over the past 50 years is two orders of magnitude smaller than that of warming. This relatively strong warming would be expected to have a larger effect on pressure. The ratio of relative changes of sea-ice extent vs pressure is 400 for the NH and 17 for the SH. The SSA components reported in this paper should help in understanding the mechanisms that govern changes in sea-ice extent: these changes reflect forcings related to the Earth’s revolution about the Sun on the shorter period side, and on the longer period side to the Sun and planets (Jupiter). Advanced 20 explanation of the physics underling these observations may need advances in solving the generalized Navier-Stokes equations, which is very difficult in the spherical case.

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“…Our algorithm makes it straightforward to couple surface dynamics with the interior dynamics once the user specifies separate evolution equations for the surface potentials of the compressible and rotational components of the velocity field on the boundary. Such active surface-driven flows could be important, for example, in studies of bulk flows driven by active stresses confined to a boundary 31,32,33,34 .…”

Section: Discussionmentioning

confidence: 99%

An optimal complexity spectral method for Navier--Stokes simulations in the ball

Boullé,

Słomka,

Townsend

2021

Preprint

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We develop a spectral method for solving the incompressible generalized Navier-Stokes equations in the ball with no-flux and prescribed slip boundary conditions.The algorithm achieves an optimal complexity per time step of ( log 2 ( )), where is the number of spatial degrees of freedom. The method relies on the poloidaltoroidal decomposition of solenoidal vector fields, the double Fourier sphere method, the Fourier and ultraspherical spectral method, and the spherical harmonics transform to decouple the Navier-Stokes equations and achieve the desired complexity and spectral accuracy.

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Linearly forced fluid flow on a rotating sphere

Cited by 7 publications

References 57 publications

Evidence of the Zakharov-Kolmogorov spectrum in numerical simulations of inertial wave turbulence

Evidence of the Zakharov-Kolmogorov spectrum in numerical simulations of inertial wave turbulence

A strong link between variations in sea-ice extent and global atmospheric pressure?

An optimal complexity spectral method for Navier--Stokes simulations in the ball

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