Inertial Waves in a Rotating Spherical Shell with Homogeneous Boundary Conditions

We find the analytical form of inertial waves in an incompressible, rotating fluid constrained by concentric inner and outer spherical surfaces with homogeneous boundary conditions on the normal components of velocity and vorticity. These fields are represented by Galerkin expansions whose basis consists of toroidal and poloidal vector functions, i.e., products and curls of products of spherical Bessel functions and vector spherical harmonics. These vector basis functions also satisfy the Helmholtz equation and this has the benefit of providing each basis function with a well-defined wavenumber. Eigenmodes and associated eigenfrequencies are determined for both the ideal and dissipative cases. These eigenmodes are formed from linear combinations of the Galerkin expansion basis functions. The system is truncated to numerically study inertial wave structure, varying the number of eigenmodes. The largest system considered in detail is a 25 eigenmode system and a graphical depiction is presented of the five lowest dissipation eigenmodes, all of which are non-oscillatory. These results may be useful in understanding data produced by numerical simulations of fluid and magnetofluid turbulence in a spherical shell that use a Galerkin, toroidal–poloidal basis as well as qualitative features of liquids confined by a spherical shell.

Flow structures in spanwise rotating plane Poiseuille flow based on thermal analogy

The analogy between rotating shear flow and thermal convection suggests the existence of plumes, inertial waves and plume currents in plane Poiseuille flow under spanwise rotation. The existence of these flow structures is examined with the results of three-dimensional and two-dimensional three-component direct numerical simulations. The dynamics of plumes near the unstable side is embodied in a truncated exponential distribution of turbulent fluctuations. For large rotation numbers, inertial waves are identified near the stable side, and these can be used to explain the abnormal flow statistics, such as the large root-mean-square of the streamwise velocity fluctuation and the nearly negligible Reynolds shear stress. For small or medium rotation numbers, plumes generated from the unstable side form large-scale plume currents and the patterns of the plume currents show different capabilities in scalar transport.

Wolkenverfolgung: Vom Experiment zur Realität

<p>Die Wolkenverfolgung ist die einzige Möglichkeit zur Beobachtung der zeitlichen Entwicklung von Wolken und zur Quantifizierung der Veränderung ihrer physikalischen Eigenschaften während ihrer Lebensdauer (Seelig et al., 2021). Der Schlüssel dazu sind zeitaufgelöste Messungen von Instrumenten an Bord geostationärer Satelliten. Experimente mit atmosphärenähnlicher Konfiguration treiben die Entwicklung von Messmethoden und Alghoritmen unter Laborbedingungen voran. Heutzutage ist es z.B. möglich zweidimensionale, zeitlich und räumlich hochaufgelöste Geschwindigkeitsfelder auf Basis der Verschiebung kleinster Partikel zu messen (Seelig and Harlander, 2015; Seelig et al., 2018). Die Methodik der Partikelgeschwindigkeitsmessung dient als Anfangsbedingung zum Verfolgen dieser Partikel und kann auf troposphärische Wolken angewendet werden. Diese Präsentation stellt die Analogie von Experiment zur Realität vor, beschreibt das Verfahren der Partikelgeschwindigkeitsmessung und die Anwendung auf Daten geostationärer Satelliten.</p> <p><strong>Literatur:</strong></p> <p>Seelig, T., Deneke, H., Quaas, J., and Tesche, M.: Life cycle of shallow marine cumulus clouds from geostationary satellite observations, J. Geophys. Res.: Atmos., 126(22), e2021JD035577, https://doi.org/10.1029/2021JD035577, 2021.</p> <p>Seelig, T., Harlander, U., and Gellert, M.: Experimental investigation of stratorotational instability using a thermally stratified system: instability, waves and associated momentum flux, Geophys. Astrophys. Fluid Dyn., 112, 239-264, https://doi.org/10.1080/03091929.2018.1488971, 2018.</p> <p>Seelig, T. and Harlander, U.: Can zonally symmetric inertial waves drive an oscillating zonal mean flow?, Geophys. Astrophys. Fluid Dyn., 109, 541-566, https://doi.org/10.1080/03091929.2015.1094064, 2015.</p>

Poleward Propagation of Typhoon-Induced Near-Inertial Waves in the Northern South China Sea

One of the main responses of the ocean to typhoons is the generation of near-inertial waves (NIWs), whose intrinsic frequency is close to the local inertial frequency. Based on the mooring observations, we carefully investigated the spatial–temporal variations in NIWs in the northern South China Sea (SCS) after Typhoon “Haima,” which passed through the northern SCS from October 20 to 21, 2016, with its track parallel to the mooring array on its northeast side. Moorings in different locations responded differently to this typhoon, with stronger NIWs found on the continental slope to the shelf break and relatively weak NIWs found on the shallow continental shelf. Strong NIWs appeared twice within a short period and showed different characteristics and frequencies. The first NIWs were generated locally with blue-shifted (super-inertial) frequencies. These initial NIWs were dominated by the first three baroclinic modes and rapidly weakened due to their propagation away and local dissipation. However, the second NIWs mainly consisted of higher baroclinic modes with red-shifted (sub-inertial) frequencies. The analysis of the mean background flow revealed that these red-shifted NIWs were excited at low latitudes, and subsequently advected by the poleward background flow to moorings whose latitudes were higher than their critical latitudes. Higher-mode (n > 3) NIWs were more easily carried away by mean background flow, and, at the same time, high-mode NIWs propagated downward to the subsurface layer, leading to the significant elevation of velocity shear therein. Given these findings, the mean background flow may provide an important route to redistributing the energy of the upper ocean imported from typhoons.

Observed Near-Inertial Waves in the Northern South China Sea

Characteristics of near-inertial waves (NIWs) induced by the tropical storm Noul in the South China Sea are analyzed based on in situ observations, remote sensing, and analysis data. Remote sensing sea level anomaly data suggests that the NIWs were influenced by a southwestward moving anticyclonic eddy. The NIWs had comparable spectral density with internal tides, with a horizontal velocity of 0.14–0.21 m/s. The near-inertial kinetic energy had a maximum value of 7.5 J/m3 and propagated downward with vertical group speed of 10 m/day. Downward propagation of near-inertial energy concentrated in smaller wavenumber bands overwhelmed upward propagation energy. The e-folding time of NIWs ranged from 4 to 11 days, and the larger e-folding time resulted from the mesoscale eddies with negative vorticity. Modified by background relative vorticity, the observed NIWs had both red-shifted and blue-shifted frequencies. The upward propagating NIWs had larger vertical phase speeds and wavelengths than downward propagating NIWs. There was energy transfer from the mesoscale field to NIWs with a maximum value of 8.5 × 10−9 m2 s−3 when total shear and relative vorticity of geostrophic currents were commensurate. Our results suggest that mesoscale eddies are a significant factor influencing the generation and propagation of NIWs in the South China Sea.

Modal Decomposition and Linear Modeling of Swirl Fluctuations in the Mixing Section of a Model Combustor Based On PIV Data

In order to determine the flame transfer function of a combustion system, different mechanisms have been identified that need to be modeled. This study focuses on the generation and propagation of one of these mechanisms, namely the swirl fluctuations downstream of a radial swirl combustor under isothermal conditions. Swirl fluctuations are generated experimentally by imposing acoustic perturbations. Time-resolved longitudinal and crosswise PIV measurements are conducted inside the mixing tube and combustion chamber to quantify the evolution of the swirl fluctuations. The measured flow response is decomposed using spectral proper orthogonal decomposition to unravel the contributions of different dynamical modes. In addition a resolvent analysis is conducted based on the linearized Navier-Stokes equations to reveal the intrinsically most amplified flow structures. Both, the data-driven and analytic approach, show that inertial waves are indeed present in the flow response and an inherent flow instability downstream of the swirler, which confirms recent theoretical works on inertial waves. However, the contribution of the identified inertial waves to the total swirl fluctuations turns out to be very small. This is suggested to be due to the very structured forcing at the swirler and the additional amplification of shear-driven modes. Overall, this work confirms the presence of inertial waves in highly turbulent swirl combustors and evaluates its relevance for industry-related configurations. It further outlines a methodology to analyze and predict their characteristics based on mean fields only, which is applicable for complex geometries of industrial relevance.