Wave drag in oscillatory mean flows

2021 ◽  
Author(s):  
Callum Shakespeare ◽  
Brian Arbic ◽  
Andrew Hogg
Keyword(s):  
Large Scale ◽  
Numerical Models ◽  
Wave Drag ◽  
Global Ocean ◽  
Ocean Tide ◽  
Invariant Mean ◽  
Mean Flow ◽  
Lee Waves ◽  
Time Invariant ◽  
The Waves

<p>In both the atmosphere and ocean, large-scale (mean) flows over topography generate internal waves. A longstanding question in both fields is what forces – often known as ‘wave drag’ – are exerted on the mean flow in this process, as such forces must be parameterized in non-wave-resolving numerical models. For a time-invariant mean flow, it is well known that lee waves are generated which extract momentum from the solid earth and deposit it where they break and dissipate at height. Here, I address the equivalent problem for a time-periodic mean flow (e.g. the ocean tide) using theory and numerical simulations. In this situation, the waves influence the amplitude and phase of the periodic mean flow near the topography regardless of where they dissipate. Dissipation plays a role in terms of controlling the magnitude of wave reflections from an upper boundary (e.g. the ocean surface) which modifies the forces acting near the topography. Our results form a framework for parameterizing tidal internal wave drag in global ocean models.</p>

A closure for lee wave drag on the large-scale ocean circulation

2021 ◽  
Author(s):  
Carsten Eden ◽  
Dirk Olbers ◽  
Thomas Eriksen
Keyword(s):  
Large Scale ◽  
Surface Wind ◽  
Wave Drag ◽  
Ocean Model ◽  
Mean Flow ◽  
Model Simulations ◽  
Energy Transfers ◽  
Lee Waves ◽  
Lee Wave ◽  
The Mean

AbstractA new, energetically and dynamically consistent closure for the lee wave drag on the large scale circulation is developed and tested in idealized and realistic ocean model simulations. The closure is based on the radiative transfer equation for internal gravity waves, integrated over wavenumber space, and consists of two lee wave energy compartments for up-and downward propagating waves, which can be co-integrated in an ocean model. Mean parameters for vertical propagation, mean-ow interaction, and the vertical wave momentum flux are calculated assuming that the lee waves stay close to the spectral shape given by linear theory of their generation.Idealized model simulations demonstrate how lee waves are generated and interact with the mean flow and contribute to mixing, and document parameter sensitivities. A realistic eddy-permitting global model at 1/10° resolution coupled to the new closure yields a globally integrated energy flux of 0.27 TW into the lee wave field. The bottom lee wave stress on the mean flow can be locally as large as the surface wind stress and can reach into the surface layer. The interior energy transfers by the stress are directed from the mean flow to the waves, but this often reverses, for example in the Southern Ocean in case of shear reversal close to the bottom. The global integral of the interior energy transfers from mean ow to waves is 0.14 TW, while 0.04 TW is driving the mean ow, but this share depends on parameter choices for non-linear effects.

Forcing of oceanic mean flows by dissipating internal tides

2012 ◽  
Vol 708 ◽  
pp. 250-278 ◽  
Author(s):  
Nicolas Grisouard ◽  
Oliver Bühler
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Wave Drag ◽  
Perturbation Series ◽  
Internal Tides ◽  
Time Averaging ◽  
Mean Flow ◽  
Wave Source ◽  
Lee Waves ◽  
Lee Wave

AbstractWe present a theoretical and numerical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by the oscillatory flow of a barotropic tide over undulating topography and are also subject to dissipation. This extends the classic lee-wave drag problem of atmospheric wave–mean interaction theory to a more complicated oceanographic setting, because now the steady lee waves are replaced by oscillatory internal tides and, most importantly, because now the three-dimensional oceanic mean flow is defined by time averaging over the fast tidal cycles rather than by the zonal averaging familiar from atmospheric theory. Although the details of our computation are quite different, we recover the main action-at-a-distance result from the atmospheric setting, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, we derive an explicit expression for the effective mean force at leading order using a perturbation series in small wave amplitude within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and then compute the effective mean force numerically in a number of idealized examples with simple topographies.

New unconstrained global ocean tide solutions for satellite gravimetry including minor tides

2020 ◽  
Author(s):  
Roman Sulzbach ◽  
Henryk Dobslaw ◽  
Maik Thomas
Keyword(s):  
Numerical Models ◽  
Signal To Noise Ratio ◽  
Column Height ◽  
Global Ocean ◽  
Ocean Tide ◽  
Data Sets ◽  
Satellite Gravimetry ◽  
The North ◽  
The Individual ◽  
Ocean Tide Models

<p>The quality of global ocean tide models has increased drastically over the last decades due to the availability of dense open-ocean observations from satellite altimetry. In regions of poor altimetry coverage (e.g., polar seas and coastal areas) and for minor tides with a small signal-to-noise ratio, however, reliable estimates from unconstrained global numerical models are still (and will remain) critically important. We will present in this contribution recent results from the purely-hydrodynamic, barotropic tidal model TiME (Weis et al., 2008) that benefit from a newly introduced rotated grid avoiding the singularity at the North Pole; a revised scheme for dynamic feedbacks of self-attraction and loading; and revised bathymetry data-sets that also include water column height modifications in cavities underneath the Antarctic ice-shelves.</p><p>By focussing exemplarily on the M<sub>2</sub> tide, we will demonstrate the individual impact of all those changes on the simulated water height variations. It will be shown that the effects of ice-shelf cavities extend well beyond the Southern Ocean and affect even amphidromic systems in the Northern Hemisphere. We will also emphasize the ability of unconstrained numerical models as TiME to explicitly simulate minor tidal lines, thereby allowing to thoroughly test (and subsequently improve) admittance-based methods currently employed for the processing of satellite gravimetry data from the GRACE and GRACE-FO missions.</p>

scholarly journals The Dissipation of Trapped Lee Waves. Part II: The Relative Importance of the Boundary Layer and the Stratosphere

2016 ◽  
Vol 73 (3) ◽  
pp. 943-955 ◽  
Author(s):  
Matthew O. G. Hills ◽  
Dale R. Durran ◽  
Peter N. Blossey
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Surface Friction ◽  
Static Stability ◽  
Relative Strength ◽  
Relative Importance ◽  
Trapped Waves ◽  
Wind Speeds ◽  
Lee Waves ◽  
The Waves

Abstract Decaying trapped waves exert a drag on the large-scale flow. The two most studied mechanisms for such decay are boundary layer dissipation and leakage into the stratosphere. If the waves dissipate in the boundary layer, they exert a drag near the surface, whereas, if they leak into the stratosphere, the drag is exerted at the level where the waves dissipate aloft. Although each of these decay mechanisms has been studied in isolation, their relative importance has not been previously assessed. Here, numerical simulations are conducted showing that the relative strength of these two mechanisms depends on the details of the environment supporting the waves. During actual trapped-wave events, the environment often includes elevated inversions and strong winds aloft. Such conditions tend to favor leakage into the stratosphere, although boundary layer dissipation becomes nonnegligible in cases with shorter resonant wavelengths and higher tropopause heights. In contrast, idealized two-layer profiles with constant wind speeds and high static stability beneath a less stable upper troposphere support lee waves that are much more susceptible to boundary dissipation and relatively unaffected by the presence of a stratosphere. One reason that trapped waves in the two-layer case do not leak much energy upward is that the resonant wavelength is greatly reduced in the presence of surface friction. This reduction in wavelength is well predicted by the linear inviscid equations if the basic-state profile is modified a posteriori to include the shallow ground-based shear layer generated by surface friction.

Some Aspects of Great Lakes Physics of Importance to Biological and Chemical Processes

1974 ◽  
Vol 31 (5) ◽  
pp. 689-730 ◽  
Author(s):  
F. M. Boyce
Keyword(s):  
Great Lakes ◽  
Large Scale ◽  
Numerical Models ◽  
Thermal Structure ◽  
Mechanical Energy ◽  
Surface Wind ◽  
Heat Fluxes ◽  
Dynamical Structure ◽  
Mean Flow ◽  
Advection Diffusion Equation

This is a discussion of some aspects of the physical behavior of the Great Lakes written for scientists with backgrounds in disciplines other than physics. The basic physical characteristics of Great Lakes basins are summarized. These characteristics are determined by the facts that (i) the basins are closed, (ii) the basins are large enough so that the Coriolis force is an important component of their dynamics, (iii) the principal source of mechanical energy is the wind, and (iv) the basins are vertically stratified in summer. Discussion of large-scale horizontal motions includes both currents and diffusion. The advection–diffusion equation is used as a framework for a discussion which includes a summary of the basic problem confronting hydrodynamic modellers, the parameterization of turbulence phenomena in terms of mean flow variables. Vertical transfer processes are considered, notably the measurement of vertical fluxes of heat and momentum and the computation of eddy diffusion coefficients, the prediction of thermal structure in terms of net surface wind stresses and heat fluxes, and the interactions of waves, currents, and turbulence in the thermocline. The dynamical structure of the coastal zone is outlined, and the review concludes with recommendations for future work on the understanding of vertical turbulent transports, the climatology of Great Lakes coastal zones, and an operational approach to verifying and improving numerical models of lake circulation.

 Generation of planetary waves by gravity-wave drag in the middle atmosphere

2021 ◽  
Author(s):  
Hye-Yeong Chun ◽  
Byeong-Gwon Song ◽  
In-Sun Song
Keyword(s):  
Large Scale ◽  
Middle Atmosphere ◽  
Weather Forecasting ◽  
Wave Theory ◽  
Wave Drag ◽  
Planetary Waves ◽  
Mean Flow ◽  
Long Time ◽  
The Mean

<p>Large-scale atmospheric circulation has been represented mostly by interaction between the mean flow and planetary waves (PWs). Although the importance of gravity waves (GWs) has been recognized for long time, contribution of GWs to the large-scale circulation is receiving more attention recently, with conjunction to GW drag (GWD) parameterizations for climate and global weather forecasting models that extend to the middle atmosphere. As magnitude of GWD increases with height significantly, circulations in the middle atmosphere are determined largely by interactions among the mean flow, PWs and GWs. Classical wave theory in the middle atmosphere has been represented mostly by the Transformed Eulerian Mean (TEM) equation, which include PW and GW forcing separately to the mean flow. Recently, increasing number of studies revealed that forcing by combined PWs and GWs is the same, regardless of different PW and GW forcings, implying a compensation between PWs and GWs forcing. There are two ways for GWs to influence on PWs: (i) changing the mean flow that either influences on waveguide of PWs or induces baroclinic/brotropic instabilities to generate in situ PWs, and (ii) generating PWs as a source of potential vorticity (PV) equation when asymmetric components of GWD exist. The fist mechanism has been studies extensively recently associated with stratospheric sudden warmings (SSWs) that are involved large amplitude PWs and GWD. The second mechanism represents more directly the relationship between PWs and GWs, which is essential to understand the dynamics in the middle atmosphere completely (among the mean flow, PWs and GWs). In this talk, a recently reported result of the generation of PWs by GWs associated with the strongest vortex split-type SSW event occurred in January 2009 (Song et al. 2020, JAS) is presented focusing on the second mechanism.  </p>

scholarly journals Estimating Eddy Stresses by Fitting Dynamics to Observations Using a Residual-Mean Ocean Circulation Model and Its Adjoint

2005 ◽  
Vol 35 (10) ◽  
pp. 1891-1910 ◽  
Author(s):  
David Ferreira ◽  
John Marshall ◽  
Patrick Heimbach
Keyword(s):  
Ocean Circulation ◽  
Large Scale ◽  
Three Dimensional ◽  
Circulation Model ◽  
Eddy Diffusivity ◽  
Ocean Model ◽  
Global Ocean ◽  
Western Boundary ◽  
Mean Flow ◽  
Ocean Circulation Model

Abstract A global ocean circulation model is formulated in terms of the “residual mean” and used to study eddy–mean flow interaction. Adjoint techniques are used to compute the three-dimensional eddy stress field that minimizes the departure of the coarse-resolution model from climatological observations of temperature. The resulting 3D maps of eddy stress and residual-mean circulation yield a wealth of information about the role of eddies in large-scale ocean circulation. In eddy-rich regions such as the Southern Ocean, the Kuroshio, and the Gulf Stream, eddy stresses have an amplitude comparable to the wind stress, of order 0.2 N m−2, and carry momentum from the surface down to the bottom, where they are balanced by mountain form drag. From the optimized eddy stress, 3D maps of horizontal eddy diffusivity κ are inferred. The diffusivities have a well-defined large-scale structure whose prominent features are 1) large values of κ (up to 4000 m2 s−1) in the western boundary currents and on the equatorial flank of the Antarctic Circumpolar Current and 2) a surface intensification of κ, suggestive of a dependence on the stratification N 2. It is shown that implementation of an eddy parameterization scheme in which the eddy diffusivity has an N 2 dependence significantly improves the climatology of the ocean model state relative to that obtained using a spatially uniform diffusivity.

scholarly journals Spatiotemporal Variability of the Global Ocean Internal Processes Inferred from Satellite Observations

2019 ◽  
Vol 49 (8) ◽  
pp. 2147-2164 ◽  
Author(s):  
Yang Yang ◽  
X. San Liang
Keyword(s):  
Southern Ocean ◽  
Large Scale ◽  
Kuroshio Extension ◽  
Spatiotemporal Variability ◽  
Global Ocean ◽  
Western Boundary ◽  
Analysis Tool ◽  
Mean Flow ◽  
Annual Fluctuation ◽  
The Mean

AbstractUsing a new analysis tool, namely, multiscale window transform (MWT), and the MWT-based theory of canonical transfer, this study investigates the spatiotemporal variations of the nonlinear interactions among the mean flows, interannual variabilities, quasi-annual fluctuations, and eddies in the global ocean. It is found that the canonical kinetic energy (KE) transfers are highly inhomogeneous in space, maximized in the western boundary current (WBC), Southern Ocean, and equatorial regions. In contrast to the equatorial and WBC regions where the temporal KE cascades are mainly forward, the Southern Ocean is the very place where coherent large-scale patterns of inverse KE cascade take place. The canonical transfers are also found to be highly variable in time. Specifically, in the Kuroshio Extension, the transfer from the mean flow to the interannual variability is in pace with the external winds from the eastern North Pacific; in the subtropical gyre, the mean flow-to-eddy transfer is responsible for the variability of the eddy kinetic energies (EKE) at both interannual and seasonal scales; in the tropics, the downscale transfers to the eddies from the other three scales all contribute to the interannual modulation of the EKE, and these transfers tend to decrease (increase) during El Niño (La Niña) events. In the Southern Ocean, the high-frequency eddies are found to feed KE to the low-frequency variability through temporal inverse cascade processes, which have been strengthened due to the enhanced eddy activities in the recent decade. Also discussed here is the relation between the seasonal EKE variability and the eddy–quasi-annual fluctuation interaction.

Nonstationary Trapped Lee Waves Generated by the Passage of an Isolated Jet

2012 ◽  
Vol 69 (10) ◽  
pp. 3040-3059 ◽  
Author(s):  
Matthew O. G. Hills ◽  
Dale R. Durran
Keyword(s):  
Large Scale ◽  
Wave Train ◽  
Three Dimensional ◽  
Zonal Flow ◽  
Mean Flow ◽  
Trapped Waves ◽  
Spatial Gradients ◽  
Lee Waves ◽  
Key Factor ◽  
3D Flows

Abstract The behavior of nonstationary trapped lee waves in a nonsteady background flow is studied using idealized three-dimensional (3D) numerical simulations. Trapped waves are forced by the passage of an isolated, synoptic-scale barotropic jet over a mountain ridge of finite length. Trapped waves generated within this environment differ significantly in their behavior compared with waves in the more commonly studied two-dimensional (2D) steady flow. After the peak zonal flow has crossed the terrain, two disparate regions form within the mature wave train: 1) upwind of the jet maximum, trapped waves increase their wavelength and tend to untrap and decay, whereas 2) downwind of the jet maximum, wavelengths shorten and waves remain trapped. Waves start to untrap approximately 100 km downwind of the ridge top, and the region of untrapping expands downwind with time as the jet progresses, while waves downstream of the jet maximum persist. Wentzel–Kramers–Brillouin (WKB) ray tracing shows that spatial gradients in the mean flow are the key factor responsible for these behaviors. An example of real-world waves evolving similarly to the modeled waves is presented. As expected, trapped waves forced by steady 2D and horizontally uniform unsteady 3D flows decay downstream because of leakage of wave energy into the stratosphere. Surprisingly, the downstream decay of lee waves is inhibited by the presence of a stratosphere in the isolated-jet simulations. Also unexpected is that the initial trapped wavelength increases quasi-linearly throughout the event, despite the large-scale forcing at the ridge crest being symmetric in time about the midpoint of the isolated-jet simulation.

Vertical-Mode and Cloud Decomposition of Large-Scale Convectively Coupled Gravity Waves in a Two-Dimensional Cloud-Resolving Model

2007 ◽  
Vol 64 (4) ◽  
pp. 1210-1229 ◽  
Author(s):  
Stefan N. Tulich ◽  
David A. Randall ◽  
Brian E. Mapes
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Deep Convection ◽  
Radiative Cooling ◽  
Convective Heating ◽  
Two Dimensional ◽  
Mean Flow ◽  
Vertical Mode ◽  
Cloud Resolving Model ◽  
The Waves

Abstract This paper describes an analysis of large-scale [O(1000 km)] convectively coupled gravity waves simulated using a two-dimensional cloud-resolving model. The waves develop spontaneously under uniform radiative cooling and approximately zero-mean-flow conditions, with wavenumber 2 of the domain appearing most prominently and right-moving components dominating over left-moving components for random reasons. The analysis discretizes the model output in two ways. First, a vertical-mode transform projects profiles of winds, temperature, and heating onto the vertical modes of the model’s base-state atmosphere. Second, a cloud-partitioning algorithm sorts sufficiently cloudy grid columns into three categories: shallow convective, deep convective, and stratiform anvil. Results show that much of the tilted structures of the waves can be captured by just two main vertical spectral “bands,” each consisting of a pair of vertical modes. The “slow” modes have propagation speeds of 16 and 18 m s−1 (and roughly a full-wavelength vertical structure through the troposphere), while the “fast” modes have speeds of 35 and 45 m s−1 (and roughly a half-wavelength structure). Deep convection anomalies in the waves are more or less in phase with the low-level cold temperature anomalies of the slow modes and in quadrature with those of the fast modes. Owing to the characteristic life cycle of deep convective cloud systems, shallow convective heating peaks ∼2 h prior to maximum deep convective heating, while stratiform heating peaks ∼3 h after. The onset of deep convection in the waves is preceded by a gradual deepening of shallow convection lasting a period of many hours. Results of this study are in broad agreement with simple two-mode models of unstable large-scale wave growth, under the name “stratiform instability.” Differences here are that 1) the key dynamical modes have speeds in the range 16–18 m s−1, rather than 23–25 m s−1 (owing to a shallower depth of imposed radiative cooling), and 2) deep convective heating, as well as stratiform heating, is essential for the generation and maintenance of the slow modes.

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