stationary waves
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Abstract An isentropic 1½-layer model based on modified shallow water equations is presented, including terms mimicking convection and precipitation. This model is an updated version of the isopycnal single-layer modified shallow water model presented in Kent et al. (2017). The clearer link between fluid temperature and model variables together with a double-layer structure make this revised, isentropic model a more suitable tool to achieve our future goal: to conduct idealized experiments for investigating satellite data assimilation. The numerical model implementation is verified against an analytical solution for stationary waves in a rotating fluid, based on Shrira’s methodology for the isopycnal case. Recovery of the equivalent isopycnal model is also verified, both analytically and numerically. With convection and precipitation added, we show how complex model dynamics can be achieved exploiting rotation and relaxation to a meridional jet in a periodic domain. This solution represents a useful reference simulation or “truth” in conducting future (satellite) data-assimilation experiments, with additional atmospheric conditions and data. A formal analytical derivation of the isentropic 1½-layer model from an isentropic 2-layer model without convection and precipitation is shown in a companion paper (Part II).


2021 ◽  
Vol 932 ◽  
Author(s):  
Philip Hall

A strongly nonlinear theory describing the effect of small amplitude boundary forcing in the form of waves on high Reynolds number shear flows is given. The interaction leads to an $O(1)$ change in the unperturbed flow and is relevant to a number of forcing mechanisms. The cases of the shear flow being bounded or unbounded are both considered and the results for the unbounded case apply to quite arbitrary flows. The instability criterion for unbounded flows is expressed in terms of the wall forcing and the friction Reynolds number. As particular examples we investigate wall transpiration or surface undulations as sources of the forcing and both propagating and stationary waves are considered. Results are given for propagating waves with crests perpendicular to the flow direction and for stationary waves with crests no longer perpendicular to the flow direction. In the first of those situations we find the instability induced by transpiration waves is independent of the propagation speed. For wavy walls downstream propagation completely stabilises the flow at a critical speed whereas upstream propagation greatly destabilises the flow. For stationary oblique waves we find that the instability is enhanced and a much wider range of unstable wavenumbers exists. For the bounded case with a wall of fixed wavelength we identify a critical wavelength where the most dangerous mode switches from the aligned to the oblique configuration. For the transpiration problem in the oblique configuration a strong resonance occurs when the vortex wavelength coincides with the spanwise wavelength of the forcing.


Author(s):  
Chenning Zhang ◽  
Oleksandr Evtushevsky ◽  
Gennadi Milinevsky

The 10-year climatology (2011–2020) of quasi-stationary planetary waves in the mid-latitude stratosphere and mesosphere (40–50N, up to 90 km) has been analyzed. Longitude–altitude sections of geopotential height and ozone have been obtained using the Aura MLS satellite data. It is found that stationary wave 1 propagates into the mesosphere from the North American High and Icelandic Low, which are adjacent surface pressure anomalies in the structure of stationary wave 2. Unexpectedly, the strongest pressure anomaly in the Aleutian Low region does not contribute to the stationary wave 1 formation in the mesosphere. The vertical phase transformations of stationary waves in geopotential height and ozone show inconsistencies that should be studied separately.


Author(s):  
Leo Dostal ◽  
Marten Hollm ◽  
Andrei V. Metrikine ◽  
Apostolos Tsouvalas ◽  
Karel N. van Dalen

AbstractThis paper aims at investigating the existence of localized stationary waves in the shallow subsurface whose constitutive behavior is governed by the hyperbolic model, implying non-polynomial nonlinearity and strain-dependent shear modulus. To this end, we derive a novel equation of motion for a nonlinear gradient elasticity model, where the higher-order gradient terms capture the effect of small-scale soil heterogeneity/micro-structure. We also present a novel finite-difference scheme to solve the nonlinear equation of motion in space and time. Simulations of the propagation of arbitrary initial pulses clearly reveal the influence of the nonlinearity: strain-dependent speed in general and, as a result, sharpening of the pulses. Stationary solutions of the equation of motion are obtained by introducing the moving reference frame together with the stationarity assumption. Periodic (with and without a descending trend) as well as localized stationary waves are found by analyzing the obtained ordinary differential equation in the phase portrait and integrating it along the different trajectories. The localized stationary wave is in fact a kink wave and is obtained by integration along a homoclinic orbit. In general, the closer the trajectory lies to a homoclinic orbit, the sharper the edges of the corresponding periodic stationary wave and the larger its period. Finally, we find that the kink wave is in fact not a true soliton as the original shapes of two colliding kink waves are not recovered after interaction. However, it may have high amplitude and reach the surface depending on the damping mechanisms (which have not been considered). Therefore, seismic site response analyses should not a priori exclude the presence of such localized stationary waves.


Author(s):  
Kaoru Sato ◽  
Takenari Kinoshita ◽  
Yuki Matsushita ◽  
Masashi Kohma

Abstract This study formulates three-dimensional (3-D) residual flow, treating both stationary and transient waves. The zonal and meridional momentum equations contain four terms: the geostrophic wind tendency, Coriolis force for the residual horizontal flow, product of the geostrophic wind and potential vorticity other than the constant planetary vorticity, and friction. The thermodynamic equation contains three terms: the potential temperature tendency, advection of the basic potential temperature by the residual vertical flow, and diabatic heating. The zonal mean of the 3-D residual flow equals the time mean of the residual flow of the transformed Eulerian mean equations. The new residual flow is the sum of that derived by Plumb for transient waves and the quadratic terms of the time-mean fields, which correspond approximately to the Stokes correction due to stationary waves. The 3-D residual flow and momentum equations are symmetric in the zonal and meridional directions, in contrast with those formulated by Kinoshita et al., which treat the time-mean zonal-mean zonal wind as the basic wind. The newly derived formulae are applied to the climatology of the 3-D structure of the deep branch of the Brewer–Dobson circulation. In the Northern Hemisphere in December–January–February, the residual flows are directed inward toward the polar vortex strongly over East Siberia, where the downward flow is maximized, and weakly over the Atlantic; meanwhile, they are directed outward from the vortex over North America and Europe. A longitudinal dependence of the poleward flow is also observed in the Southern Hemisphere in June–July–August.


2021 ◽  
Vol 359 (8) ◽  
pp. 959-968
Author(s):  
Youpei Zhang ◽  
Xianhua Tang ◽  
Vicenţiu Rădulescu
Keyword(s):  

2021 ◽  
Author(s):  
Yueyue Yu ◽  
Rongcai Ren ◽  
Xin Xia ◽  
Ruxue Liang ◽  
Jian Rao

Abstract The topographic dynamical effect from Eurasia (EA_Topo) and North America (NA_Topo) on the winter isentropic meridional mass circulation (IMMC) is investigated using the WACCM. The independent effect of EA_Topo and that of NA_Topo, with the former much stronger, are both to strengthen the IMMC that is composed of the lower equatorward cold air branch (CB) and the upper poleward warm air branch in the extratropical tropopshere (WB_TR) and stratosphere (WB_ST). Further investigation of the individual contributions from changes in stationary vs. transient and zonal-mean flow vs. waves reveals that, due to the topography-forced mass redistribution, changes in the low-level meridional pressure gradient force a zonal-mean counter-clockwise/ clockwise meridional cell in the southern/northern side of topography. This weakens/strengthens the IMMC south/north of 30°N from the troposphere to lower stratosphere, acting as a dominant contributor to the IMMC changes south of 50°N. Meanwhile, the EA/NA_Topo-forced amplification of stationary waves constructively interacts with those determined by land-sea contrast, making the dominant/minor contributions to the strengthening of CB and WB_TR north of 50°N. The related increase in the upward wave propagation further dominates the WB_ST strengthening in the subpolar region. Meanwhile, transient eddy activities are depressed by EA/NA_Topo along with the weakened background westerly, which partly-offset/dominate-over the contribution from stationary flow in midlatitudes and subpolar region. The coexistence of the other topography (NA/EA_Topo) yields destructive mutual interferrence, which can weaken/offset the independent-EA/NA_Topo-forced meridional mass transport mainly via changing the zonal-mean as well as the downstream wave pattern of mass and meridional wind.


2021 ◽  
pp. 1-43
Author(s):  
Bo Pang ◽  
Adam A. Scaife ◽  
Riyu Lu ◽  
Rongcai Ren

AbstractThis study investigates the stratosphere-troposphere coupling associated with the Scandinavian (SCA) pattern in boreal winter. The results indicate that the SCA impacts stratospheric circulation but that its positive and negative phases have different effects. The positive phase of the SCA (SCA+) pattern is restricted to the troposphere, but the negative phase (SCA−) extends to the upper stratosphere. The asymmetry between phases is also visible in the lead-lag evolution of the stratosphere and troposphere. Prominent stratospheric anomalies are found to be intensified following SCA+ events, but prior to SCA− events. Further analysis reveals that the responses are associated with upward propagation of planetary waves, especially wavenumber 1 which is asymmetric between SCA phases. The wave amplitudes in the stratosphere, originating from the troposphere, are enhanced after the SCA+ events and before the SCA− events. Furthermore, the anomalous planetary wave activity can be understood through its interference with climatological stationary waves. Constructive wave interference is accompanied by clear upward propagation in the SCA+ events, while destructive interference suppresses stratospheric waves in the SCA− events. Our results also reveal that the SCA+ events are more likely to be followed by sudden stratospheric warming (SSW) events, because of the deceleration of stratospheric westerlies following the SCA+ events.


2021 ◽  
Author(s):  
Chen Schwartz ◽  
Chaim I. Garfinkel ◽  
Priyanka Yadav ◽  
Wen Chen ◽  
Daniela Domeisen

2021 ◽  
Author(s):  
Chen Schwartz ◽  
Chaim I. Garfinkel ◽  
Priyanka Yadav ◽  
Wen Chen ◽  
Daniela Domeisen

Abstract. The simulated Northern Hemisphere stationary wave (SW) field is investigated in 11 subseasonal-to-seasonal (S2S) models. It is shown that while most models considered can well-simulate the stationary wavenumbers 1 and 2 during the first two weeks of integration, they diverge from observations following week 3. Those models with a poor resolution in the stratosphere struggle to simulate the waves, both in the troposphere and the stratosphere, even during the first two weeks, and biases extend from the troposphere all the way up to the stratosphere. Focusing on the tropospheric regions where SWs peak in amplitude reveals that the models generally do a better job in simulating the Northwest Pacific stationary trough, while certain models struggle to simulate the stationary ridges both in Western North America and the North Atlantic. In addition, a strong relationship is found between regional biases in the stationary height field and model errors in simulated upward propagation of planetary waves into the stratosphere. In the stratosphere, biases mostly are in wave-2 in those models with high stratospheric resolution, whereas in those models with low resolution in the stratosphere, a wave-1 bias is evident, which leads to a strong bias in the stratospheric mean zonal circulation due to the predominance of wave-1 there. Finally, biases in both amplitude and location of mean tropical convection and the subsequent subtropical downwelling, are identified as possible contributors to biases in the regional SW field in the troposphere.


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