The Energy Budget of an Altimeter-Derived Baroclinic Tide Model

2021 ◽  
Author(s):  
Edward Zaron ◽  
Ruth Musgrave
Keyword(s):  
Energy Flux ◽  
Phase Speed ◽  
Linear Wave ◽  
Flux Divergence ◽  
Sources And Sinks ◽  
Wave Dynamics ◽  
Continental Shelves ◽  
New Information ◽  
Baroclinic Tide ◽  
Baroclinic Modes

<p>Over the last few years a number of groups have created maps of the baroclinic tide from satellite altimeter measurements of sea-surface height (SSH). These maps can be used as predictive models for the baroclinic tides, e.g., for removing aliased tidal signals from altimetry, but they can also be used to diagnose aspects of the tidal dynamics. This presentation uses the High Resolution Emprical Tide (HRET) model to compute the phase speed, energy, energy flux, and energy flux divergence of the first few baroclinic modes for the M2, S2, K1, and O1 tides, and compares these with independent estimates from the literature.</p><p>The phase speed of the waves in HRET are compared with the theoretically-predicted phase speeds computed from stratification. For the mode-1 M2 waves which are determined most accurately, the theoretical and observed phase speeds agree very well; however, there is a small bias, namely, the theoretical phase speed exceeds the observed phase speed by 1 to 2%. This offset could reflect either a methodological estimation bias, issues with the data used to compute the theoretical phase speed, or a limitation of the theory for the vertical modes.</p><p>The phase speed results provide some confidence in the usefulness of linear wave dynamics for interpreting the HRET SSH. Using a simplified form of the momentum equations, the area-integrated kinetic plus potential energy of the mode-1 M2 tide is found to be 43 PJ, larger than in other baroclinic tide models, and with nearly isotropic directional distribution. For mode 1, the divergence of the energy flux diagnosed from HRET agrees well with previous estimates based on the barotropic tides. For the most accurately-determined mode-1 M2 tide, the results provide new information about sources and sinks of baroclinic energy along the continental shelves, and they are used to examine the accuracy of a commonly-used approximation of the baroclinic energy flux.</p>

Structure of the Baroclinic Tide Generated at Kaena Ridge, Hawaii

2006 ◽  
Vol 36 (6) ◽  
pp. 1123-1135 ◽  
Author(s):  
Jonathan D. Nash ◽  
Eric Kunze ◽  
Craig M. Lee ◽  
Thomas B. Sanford
Keyword(s):  
Kinetic Energy ◽  
Energy Flux ◽  
Internal Tide ◽  
Vertical Displacement ◽  
Kinetic Energy Density ◽  
Net Energy ◽  
Flux Divergence ◽  
Vertical Displacements ◽  
Baroclinic Tide ◽  
Velocity Pressure

Abstract Repeat transects of full-depth density and velocity are used to quantify generation and radiation of the semidiurnal internal tide from Kaena Ridge, Hawaii. A 20-km-long transect was sampled every 3 h using expendable current profilers and the absolute velocity profiler. Phase and amplitude of the baroclinic velocity, pressure, and vertical displacement were computed, as was the energy flux. Large barotropically induced isopycnal heaving and strong baroclinic energy-flux divergence are observed on the steep flanks of the ridge where upward and downward beams radiate off ridge. Directly above Kaena Ridge, strong kinetic energy density and weak net energy flux are argued to be a horizontally standing wave. The phasing of velocity and vertical displacements is consistent with this interpretation. Results compare favorably with the Merrifield and Holloway model.

scholarly journals Critical reflection and abyssal trapping of near-inertial waves on a β-plane

2011 ◽  
Vol 684 ◽  
pp. 111-136 ◽  
Author(s):  
Kraig B. Winters ◽  
Pascale Bouruet-Aubertot ◽  
Theo Gerkema
Keyword(s):  
Wave Propagation ◽  
Spatial Patterns ◽  
Energy Flux ◽  
Traditional Approach ◽  
Forced Flow ◽  
Linear Wave ◽  
Inertial Waves ◽  
Flux Divergence ◽  
Multiple Reflections ◽  
Coriolis Parameter

AbstractWe consider near-inertial waves continuously excited by a localized source and their subsequent radiation and evolution on a two-dimensional $\ensuremath{\beta} $-plane. Numerical simulations are used to quantify the wave propagation and the energy flux in a realistically stratified ocean basin. We focus on the dynamics near and poleward of the inertial latitude where the local value of the Coriolis parameter $f$ matches the forcing frequency $\sigma $, contrasting the behaviour of waves under the traditional approximation (TA), where only the component of the Earth’s rotation aligned with gravity is retained in the dynamics, with that obtained under the non-traditional approach (non-TA) in which the horizontal component of rotation is retained. Under the TA, assuming inviscid linear wave propagation in the WKB limit, all energy radiated from the source eventually propagates toward the equator, with the initially poleward propagation being internally reflected at the inertial latitude. Under the non-TA however, these waves propagate sub-inertially beyond their inertial latitude, exhibiting multiple reflections between internal turning points that lie poleward of the inertial latitude and the bottom. The numerical experiments complement and extend existing theory by relaxing the linearity and WKB approximations, and by illustrating the time development of the steadily forced flow and the spatial patterns of energy flux and flux divergence. The flux divergence of the flow at both the forcing frequency and its first harmonic reveal the spatial patterns of nonlinear energy transfer and highlight the importance of nonlinearity in the vicinity of near-critical bottom reflection at the inertial latitude of the forced waves.

Dissipating and reflecting internal waves

2021 ◽  
Author(s):  
Callum J. Shakespeare ◽  
Brian K. Arbic ◽  
Andrew McC. Hogg
Keyword(s):  
Numerical Simulations ◽  
Linear Theory ◽  
Internal Waves ◽  
Energy Flux ◽  
Internal Tide ◽  
Internal Tides ◽  
Linear Wave ◽  
Lee Waves ◽  
Lee Wave ◽  
Upper Boundary

AbstractInternal waves generated at the seafloor propagate through the interior of the ocean, driving mixing where they break and dissipate. However, existing theories only describe these waves in two limiting cases. In one limit, the presence of an upper boundary permits bottom-generated waves to reflect from the ocean surface back to the seafloor, and all the energy flux is at discrete wavenumbers corresponding to resonant modes. In the other limit, waves are strongly dissipated such that they do not interact with the upper boundary and the energy flux is continuous over wavenumber. Here, a novel linear theory is developed for internal tides and lee waves that spans the parameter space in between these two limits. The linear theory is compared with a set of numerical simulations of internal tide and lee wave generation at realistic abyssal hill topography. The linear theory is able to replicate the spatially-averaged kinetic energy and dissipation of even highly non-linear wave fields in the numerical simulations via an appropriate choice of the linear dissipation operator, which represents turbulent wave breaking processes.

scholarly journals Internal tide energy flux over a ridge measured by a co-located ocean glider and moored ADCP

2019 ◽  
Author(s):  
Rob Hall ◽  
Barbara Berx ◽  
Gillian Damerell
Keyword(s):  
Energy Flux ◽  
Large Scale ◽  
Low Frequency ◽  
Internal Tide ◽  
Small Scale ◽  
Potential Density ◽  
The North ◽  
Model Study ◽  
Continental Shelves ◽  
Alternative Approach

Abstract. Internal tide energy flux is an important diagnostic for the study of energy pathways in the ocean, from large-scale input by the surface tide, to small-scale dissipation by turbulent mixing. Accurate calculation of energy flux requires repeated full-depth measurements of both potential density (ρ) and horizontal current velocity (u) over at least a tidal cycle and over several weeks to resolve the internal spring-neap cycle. Typically, these observations are made using full-depth oceanographic moorings that are vulnerable to being fished-out by commercial trawlers when deployed on continental shelves and slopes. Here we test an alternative approach to minimise these risks, with u measured by a low-frequency ADCP moored near the seabed and ρ measured by an autonomous ocean glider holding station by the ADCP. The method is used to measure the M2 internal tide radiating from the Wyville Thompson Ridge in the North Atlantic. The observed energy flux (4.2 ± 0.2 kW m−1) compares favourably with historic observations and a previous numerical model study. Error in the energy flux calculation due to imperfect co-location of the glider and ADCP is estimated by sub-sampling potential density in an idealised internal tide field along pseudorandomly distributed glider paths. The error is considered acceptable (

A Methodology to Characterize Internal Solitons in the Ocean

2018 ◽  
Author(s):  
Henrique Coelho ◽  
Zhong Peng ◽  
Dave Sproson ◽  
Jill Bradon
Keyword(s):  
Internal Waves ◽  
Large Scale ◽  
Numerical Models ◽  
Phase Speed ◽  
Selection Procedure ◽  
Wave Theory ◽  
Tidal Energy ◽  
Internal Tides ◽  
Linear Wave ◽  
Soliton Generation

Internal waves in the ocean occur in stably stratified fluids when a water parcel is vertically displaced by some external forcing and is restored by buoyancy forces. A specific case of such internal waves is internal tides and their associated currents. These currents can be significant in areas where internal waves degenerate into nonlinear solitary waves, known as solitons. Solitons are potentially hazardous for offshore engineering constructions, such as oil/gas pipelines and floating platforms. The most efficient mechanism of soliton generation is the tidal energy conversion from barotropic to baroclinic component over large-scale oceanic bottom obstructions (shelf breaks, seamounts, canyons and ridges). In this paper, a methodology is provided to compute diagnostics and prognostics for soliton generation and propagation, including the associated currents. The methodology comprises a diagnostic tool which, through the use of a set of theoretical and empirical formulations, selects areas where solitons are likely to occur. These theoretical and empirical formulations include the computation of the integral body force (1), the linear wave theory to compute the phase speed and the empirical model proposed by (2). After the selection procedure, the tool provides initial and boundary conditions for non-hydrostatic numerical models. The numerical models run in 2D-V configuration (vertical slices) with horizontal and vertical resolutions ranging from 50 to 200 m and 5 to 10 m, respectively. Examples are provided for an open ocean location over the Mascarene Plateau in the Indian Ocean. Validation of diagnostics and prognostics are provided against ADCP and satellite data.

Mid- to Inner-Shelf Coupled ROMS–SWAN Model–Data Comparison of Currents and Temperature: Diurnal and Semidiurnal Variability

2016 ◽  
Vol 46 (3) ◽  
pp. 841-862 ◽  
Author(s):  
Nirnimesh Kumar ◽  
Falk Feddersen ◽  
Sutara Suanda ◽  
Yusuke Uchiyama ◽  
James McWilliams
Keyword(s):  
Heat Budget ◽  
Time Derivative ◽  
Phase Speed ◽  
Internal Tide ◽  
Internal Variability ◽  
Flux Divergence ◽  
Inner Shelf ◽  
Swan Model ◽  
San Pedro ◽  
San Pedro Bay

AbstractAccurately representing diurnal and semidiurnal internal variability is necessary to investigate inner-shelf to midshelf exchange processes. Here, a coupled Regional Ocean Model System (ROMS)–Simulating Waves Nearshore (SWAN) model is compared to observed diurnal and semidiurnal internal tidal variability on the mid and inner shelf (26–8 m water depth) near San Pedro Bay, California. Modeled mean stratification is about one-half of that observed. Modeled and observed baroclinic velocity rotary spectra are similar in the diurnal and semidiurnal band. Modeled and observed temperature spectra have similar diurnal and semidiurnal band structure, although the modeled is weaker. The observed and modeled diurnal and semidiurnal baroclinic velocity- and temperature-dominant vertical structures are similar and consistent with mode-one internal motions. Both observed and modeled diurnal baroclinic kinetic energy are strongly correlated to diurnal wind forcing and enhanced by subtidal vorticity-induced reduction in the inertial frequency. The mid- and inner-shelf modeled diurnal depth-integrated heat budget is a balance between advective heat flux divergence and temperature time derivative. Temperature–velocity phase indicates progressive semidiurnal internal tide on the midshelf and largely standing internal tide on the inner shelf in both observed and modeled. The ratio of observed to modeled inferred phase speed is consistent with the observed to modeled stratification. The San Pedro Bay modeled semidiurnal internal tide has significant spatial variability, variable incident wave angles, and multiple local generation sites. Overall, the coupled ROMS–SWAN model represents well the complex diurnal and semidiurnal internal variability from the mid to the inner shelf.

scholarly journals Boundary Layer Dynamics in a Simple Model for Convectively Coupled Gravity Waves

2009 ◽  
Vol 66 (9) ◽  
pp. 2780-2795 ◽  
Author(s):  
Michael L. Waite ◽  
Boualem Khouider
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Deep Convection ◽  
Potential Temperature ◽  
Phase Speed ◽  
Free Troposphere ◽  
Synoptic Scale ◽  
Basic States ◽  
Boundary Layer Dynamics ◽  
Baroclinic Modes

Abstract A simplified model of intermediate complexity for convectively coupled gravity waves that incorporates the bulk dynamics of the atmospheric boundary layer is developed and analyzed. The model comprises equations for velocity, potential temperature, and moist entropy in the boundary layer as well as equations for the free tropospheric barotropic (vertically uniform) velocity and first two baroclinic modes of vertical structure. It is based on the multicloud model of Khouider and Majda coupled to the bulk boundary layer–shallow cumulus model of Stevens. The original multicloud model has a purely thermodynamic boundary layer and no barotropic velocity mode. Here, boundary layer horizontal velocity divergence is matched with barotropic convergence in the free troposphere and yields environmental downdrafts. Both environmental and convective downdrafts act to transport dry midtropospheric air into the boundary layer. Basic states in radiative–convective equilibrium are found and are shown to be consistent with observations of boundary layer and free troposphere climatology. The linear stability of these basic states, in the case without rotation, is then analyzed for a variety of tropospheric regimes. The inclusion of boundary layer dynamics—specifically, environmental downdrafts and entrainment of free tropospheric air—enhances the instability of both the synoptic-scale moist gravity waves and nonpropagating congestus modes in the multicloud model. The congestus mode has a preferred synoptic-scale wavelength, which is absent when a purely thermodynamic boundary layer is employed. The weak destabilization of a fast mesoscale wave, with a phase speed of 26 m s−1 and coupling to deep convection, is also discussed.

scholarly journals On the Generation of Bottom-Trapped Internal Tides

2015 ◽  
Vol 45 (2) ◽  
pp. 526-545 ◽  
Author(s):  
Saeed Falahat ◽  
Jonas Nycander
Keyword(s):  
Energy Density ◽  
Energy Flux ◽  
General Circulation ◽  
Bottom Topography ◽  
Vertical Mixing ◽  
Internal Tides ◽  
The Arctic ◽  
Linear Wave ◽  
Tidal Constituent ◽  
Tidal Constituents

AbstractThe interaction of the barotropic tide with bottom topography when the tidal frequency ω is smaller than the Coriolis frequency f is examined. The resulting waves are called bottom-trapped internal tides. The energy density associated with these waves is computed using linear wave theory and vertical normal-mode decomposition in an ocean of finite depth. The global calculation of the modal energy density is performed for the semidiurnal M2 tidal constituent and the two major diurnal tidal constituents K1 and O1. An observationally based decay time scale of 3 days is then used to transform the energy density to energy flux in units of watts per square meter. The globally integrated energy fluxes are found to be 1.99 and 1.43 GW for the K1 and O1 tidal constituents, respectively. For the M2 tidal constituent, it is found to be 1.15 GW. The Pacific Ocean is found to be the most energetic basin for the bottom-trapped diurnal tides. Two regional estimates of the bottom-trapped energy flux are given for the Kuril Islands and the Arctic Ocean, in which the bottom-trapped waves play a role for the tidally induced vertical mixing. The results of this study can be incorporated into ocean general circulation models and coupled climate models to improve the parameterization of the vertical mixing induced by breaking of the internal tides.

scholarly journals Connecting the Energy and Momentum Flux Response to Climate Change Using the Eliassen–Palm Relation

2018 ◽  
Vol 31 (18) ◽  
pp. 7401-7416 ◽  
Author(s):  
Orli Lachmy ◽  
Tiffany Shaw
Keyword(s):  
Climate Change ◽  
Potential Energy ◽  
Energy Flux ◽  
Momentum Flux ◽  
Climate Models ◽  
Storm Track ◽  
Phase Speed ◽  
Eddy Potential Energy ◽  
Flux Response ◽  
Radiation Scheme

Coupled climate models project that extratropical storm tracks and eddy-driven jets generally shift poleward in response to increased CO2 concentration. Here the connection between the storm-track and jet responses to climate change is examined using the Eliassen–Palm (EP) relation. The EP relation states that the eddy potential energy flux is equal to the eddy momentum flux times the Doppler-shifted phase speed. The EP relation can be used to connect the storm-track and eddy-driven jet responses to climate change assuming 1) the storm-track and eddy potential energy flux responses are consistent and 2) the response of the Doppler-shifted phase speed is negligible. We examine the extent to which the EP relation connects the eddy-driven jet (eddy momentum flux convergence) response to climate change with the storm-track (eddy potential energy flux) response in two idealized aquaplanet model experiments. The two experiments, which differ in their radiation schemes, both show a poleward shift of the storm track in response to climate change. However, the eddy-driven jet shifts poleward using the sophisticated radiation scheme but equatorward using the gray radiation scheme. The EP relation gives a good approximation of the momentum flux response and the eddy-driven jet shift, given the eddy potential energy flux response, because the Doppler-shifted phase speed response is negligible. According to the EP relation, the opposite shift of the eddy-driven jet for the different radiation schemes is associated with dividing the eddy potential energy flux response by the climatological Doppler-shifted phase speed, which is dominated by the zonal-mean zonal wind.

scholarly journals Systematic Bias in Baroclinic Energy Estimates in Shelf Seas

2016 ◽  
Vol 46 (9) ◽  
pp. 2851-2862 ◽  
Author(s):  
Gordon R. Stephenson ◽  
J. A. Mattias Green ◽  
Mark E. Inall
Keyword(s):  
Phase Speed ◽  
Internal Tide ◽  
Energy Estimates ◽  
Systematic Bias ◽  
Energy Fluxes ◽  
Sources And Sinks ◽  
Barotropic Flow ◽  
Shelf Seas ◽  
Low Pass ◽  
Low Pass Filters

AbstractA simple model of an internal wave advected by an oscillating barotropic flow suggests flaws in standard approaches to estimating properties of the internal tide. When the M2 barotropic tidal current amplitude is of similar size to the phase speed of the M2 baroclinic tide, spectral and harmonic analysis techniques lead to erroneous estimates of the amplitude, phase, and energy in the M2 internal tide. In general, harmonic fits and bandpass or low-pass filters that attempt to isolate the lowest M2 harmonic significantly underestimate the strength of M2 baroclinic energy fluxes in shelf seas. Baroclinic energy flux estimates may show artificial spatial variability, giving the illusion of sources and sinks of energy where none are actually present. Analysis of previously published estimates of baroclinic energy fluxes in the Celtic Sea suggests this mechanism may lead to values being 25%–60% too low.

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