scholarly journals Generation of Internal Lee Waves by Lateral Circulation in a Coastal Plain Estuary

2019 ◽  
Vol 49 (7) ◽  
pp. 1687-1697
Author(s):  
Xiaohui Xie ◽  
Ming Li
Keyword(s):  
Internal Waves ◽  
Lateral Flow ◽  
Coastal Plain Estuary ◽  
Deep Channel ◽  
Mode 2 ◽  
Lee Waves ◽  
Lee Wave ◽  
Lateral Circulation ◽  
Internal Hydraulic Jump ◽  
Internal Bores

AbstractRecent mooring observations at a cross-channel section in Chesapeake Bay showed that internal solitary waves regularly appeared during certain phases of a tidal cycle and propagated from the deep channel to the shallow shoal. It was hypothesized that these waves resulted from the nonlinear steepening of internal lee waves generated by lateral currents over channel-shoal topography. In this study numerical modeling is conducted to investigate the interaction between lateral circulation and cross-channel topography and discern the generation mechanism of the internal lee waves. During ebb tides, lateral bottom Ekman forcing drives a counterclockwise (looking into estuary) lateral circulation, with strong currents advecting stratified water over the western flank of the deep channel and producing large isopycnal displacements. When the lateral flow becomes supercritical with respect to mode-2 internal waves, a mode-2 internal lee wave is generated on the flank of the deep channel and subsequently propagates onto the western shoal. When the bottom lateral flow becomes near-critical or supercritical with respect to mode-1 internal waves, the lee wave evolves into an internal hydraulic jump. On the shallow shoal, the lee waves or jumps evolve into internal bores of elevation.

scholarly journals Generation of Internal Solitary Waves by Lateral Circulation in a Stratified Estuary

2017 ◽  
Vol 47 (7) ◽  
pp. 1789-1797 ◽  
Author(s):  
Xiaohui Xie ◽  
Ming Li ◽  
Malcolm Scully ◽  
William C. Boicourt
Keyword(s):  
Solitary Waves ◽  
Tidal Flow ◽  
Tidal Currents ◽  
Internal Solitary Waves ◽  
Deep Channel ◽  
Mode 2 ◽  
Lee Wave ◽  
Salinity Data ◽  
Lateral Circulation ◽  
Stratified Estuary

AbstractInternal solitary waves are commonly observed in the coastal ocean where they are known to contribute to mass transport and turbulent mixing. While these waves are often generated by cross-isobath barotropic tidal currents, novel observations are presented suggesting that internal solitary waves result from along-isobath tidal flows over channel-shoal bathymetry. Mooring and ship-based velocity, temperature, and salinity data were collected over a cross-channel section in a stratified estuary. The data show that Ekman forcing on along-channel tidal currents drives lateral circulation, which interacts with the stratified water over the deep channel to generate a supercritical mode-2 internal lee wave. This lee wave propagates onto the shallow shoal and evolves into a group of internal solitary waves of elevation due to nonlinear steepening. These observations highlight the potential importance of three-dimensionality on the conversion of tidal flow to internal waves in the rotating ocean.

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.

Diapycnal diffusivity induced by the breaking of lee waves

2020 ◽  
Author(s):  
Thomas Eriksen ◽  
Carsten Eden ◽  
Dirk Olbers
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Wave Energy ◽  
Diapycnal Mixing ◽  
Overturning Circulation ◽  
Lee Waves ◽  
Lee Wave ◽  
Wave Energy Flux ◽  
Diapycnal Diffusivity

<p>A key component in setting the large scale ocean circulation is the process of diapycnal mixing, since this can drive the meridional overturning circulation. Diapycnal mixing in the interior ocean is predominantly associated with the breaking of internal waves. Traditionally, diapycnal mixing has been represented in ocean models by a diapycnal diffusivity either constant or exponentially decreasing with depth. This approach, however, does not take into account the actual physics behind the breaking of internal waves. The energetically consistent internal wave model IDEMIX (Internal wave Dissipation, Energetics and MIXing), on the other hand, computes diffusivities directly on the basis of internal wave energetics. One such type of internal waves are lee waves. These are generated and subsequently dissipated when geostrophic currents interact with bottom topography and are therefore believed to be a source of energy for deep ocean mixing. In this study IDEMIX is coupled to a 1/12<sup>th</sup> degree regional model of the Atlantic. The lee wave energy flux is calculated and used as a bottom flux at each time step effectively allowing lee waves to propagate, interact with mean flow and waves, and subsequently dissipate. This setup enables not only an estimate of the lee wave energy flux but also a direct investigation of the influence of lee waves on dissipation, stratification and horizontal and overturning circulation.</p>

scholarly journals Sensitivity of the Ocean State to Lee Wave–Driven Mixing

2014 ◽  
Vol 44 (3) ◽  
pp. 900-921 ◽  
Author(s):  
Angélique Melet ◽  
Robert Hallberg ◽  
Sonya Legg ◽  
Maxim Nikurashin
Keyword(s):  
Internal Waves ◽  
Wave Energy ◽  
Energy Input ◽  
Climate Models ◽  
Internal Tide ◽  
Meridional Overturning Circulation ◽  
Internal Tides ◽  
Tidal Mixing ◽  
Lee Waves ◽  
Lee Wave

Abstract Diapycnal mixing plays a key role in maintaining the ocean stratification and the meridional overturning circulation (MOC). In the ocean interior, it is mainly sustained by breaking internal waves. Two important classes of internal waves are internal tides and lee waves, generated by barotropic tides and geostrophic flows interacting with rough topography, respectively. Currently, regarding internal wave–driven mixing, most climate models only explicitly parameterize the local dissipation of internal tides. In this study, the authors explore the combined effects of internal tide– and lee wave–driven mixing on the ocean state. A series of sensitivity experiments using the Geophysical Fluid Dynamics Laboratory CM2G ocean–ice–atmosphere coupled model are performed, including a parameterization of lee wave–driven mixing using a recent estimate for the global map of energy conversion into lee waves, in addition to the tidal mixing parameterization. It is shown that, although the global energy input in the deep ocean into lee waves (0.2 TW; where 1 TW = 1012 W) is small compared to that into internal tides (1.4 TW), lee wave–driven mixing makes a significant impact on the ocean state, notably on the ocean thermal structure and stratification, as well as on the MOC. The vertically integrated circulation is also impacted in the Southern Ocean, which accounts for half of the lee wave energy flux. Finally, it is shown that the different spatial distribution of the internal tide and lee wave energy input impacts the sensitivity described in this study. These results suggest that lee wave–driven mixing should be parameterized in climate models, preferably using more physically based parameterizations that allow the internal lee wave–driven mixing to evolve in a changing ocean.

scholarly journals Presence of Longitudinal Roll Structures during Synoptic Forced Conditions in Complex Terrain

Atmosphere ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 737
Author(s):  
Cory M. Payne ◽  
Jeffrey E. Passner ◽  
Robert E. Dumais ◽  
Abdessattar Abdelkefi ◽  
Christopher M. Hocut
Keyword(s):  
Boundary Layer ◽  
Agricultural Research ◽  
Wrf Model ◽  
Flow Characteristics ◽  
Critical Threshold ◽  
Department Of Agriculture ◽  
Synoptic Conditions ◽  
Lee Waves ◽  
Lee Wave ◽  
Usda Agricultural Research

To investigate synoptic interactions with the San Andres Mountains in southern New Mexico, the Weather Research and Forecasting (WRF) model was used to simulate several days in the period 2018–2020. The study domain was centered on the U.S. Department of Agriculture (USDA) Agricultural Research Service’s Jornada Experimental Range (JER) and the emphasis was on synoptic conditions that favor strong to moderate winds aloft from the southwest, boundary layer shear, a lack of moisture (cloud coverage), and modest warming of the surface. The WRF simulations on these synoptic days revealed two distinct regimes: lee waves aloft and SW-to-NE oriented Longitudinal Roll Structures (LRS) that have typical length scales of the width of the mountain basin in the horizontal and the height of the boundary layer (BL) in the vertical. Analysis of the transitional periods indicate that the shift from the lee wave to LRS regime occurs when the surface heating and upwind flow characteristics reach a critical threshold. The existence of LRS is confirmed by satellite observations and the longitudinal streak patterns in the soil of the JER that indicate this is a climatologically present BL phenomenon.

scholarly journals Application of a model of internal hydraulic jumps

2017 ◽  
Vol 834 ◽  
pp. 125-148 ◽  
Author(s):  
S. A. Thorpe ◽  
J. Malarkey ◽  
G. Voet ◽  
M. H. Alford ◽  
J. B. Girton ◽  
...  
Keyword(s):  
Hydraulic Jump ◽  
Mixing Layer ◽  
Strong Support ◽  
Deep Ocean ◽  
Hydraulic Jumps ◽  
Model Predictions ◽  
Mode 2 ◽  
Mediterranean Outflow ◽  
Unknown Structure ◽  
Internal Hydraulic Jump

A model devised by Thorpe & Li (J. Fluid Mech., vol. 758, 2014, pp. 94–120) that predicts the conditions in which stationary turbulent hydraulic jumps can occur in the flow of a continuously stratified layer over a horizontal rigid bottom is applied to, and its results compared with, observations made at several locations in the ocean. The model identifies two positions in the Samoan Passage at which hydraulic jumps should occur and where changes in the structure of the flow are indeed observed. The model predicts the amplitude of changes and the observed mode 2 form of the transitions. The predicted dissipation of turbulent kinetic energy is also consistent with observations. One location provides a particularly well-defined example of a persistent hydraulic jump. It takes the form of a 390 m thick and 3.7 km long mixing layer with frequent density inversions separated from the seabed by some 200 m of relatively rapidly moving dense water, thus revealing the previously unknown structure of an internal hydraulic jump in the deep ocean. Predictions in the Red Sea Outflow in the Gulf of Aden are relatively uncertain. Available data, and the model predictions, do not provide strong support for the existence of hydraulic jumps. In the Mediterranean Outflow, however, both model and data indicate the presence of a hydraulic jump.

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.

On Long's hypothesis of no upstream influence in uniformly stratified or rotating flow

1972 ◽  
Vol 52 (2) ◽  
pp. 209-243 ◽  
Author(s):  
Michael E. McIntyre
Keyword(s):  
Molecular Diffusion ◽  
Time Development ◽  
Narrow Gap ◽  
Dimensional Problem ◽  
Weakly Nonlinear ◽  
Lee Waves ◽  
Lee Wave ◽  
Wave Trains ◽  
Set Up ◽  
Boussinesq Fluid

The weakly nonlinear, two-dimensional problem for the disturbance due to a slender obstacle in a uniformly stratified, Boussinesq fluid moving past the obstacle with constant basic horizontal velocityU, is considered up to second order in the amplitude ε of the disturbance. Analogous rotating problems are also treated. Particular attention is given to calculating explicitly the columnar-disturbance strengths upstream and downstream of the obstacle, both in the stratified and in the rotating problems, with a view to discussing the truth or otherwise of Long's hypothesis (LH).Whether or not columnar disturbances are found far upstream, violating LH, depends,interalia, on whether or not the flow is externally bounded by rigid horizontal planes (or by a tube or annulus, in the rotating problem), and on whether the problem is made determinate by means of an ‘inviscid transient’ formulation, or by means of a ‘viscous’ one.The inviscid, transient, bounded problem, for time-development of lee waves from a state of no initial disturbance, always exhibits columnar disturbances oforder ε2somewhere in the fluid. They are generated, not near the obstacle, but in the ‘tails’ or transient terminal zones of the lee-wave trains. The columnar-disturbance strengths are largely independent of how the flow is set up from an initially undisturbed state. I n all but one instance the effect is non-zero far up-stream. The exception is the singly-subcritical stratified (or narrow-gap rotating) case, in which the excitation has modal structure sin(2z), the fluid region being 0 [les ]z[les ] π in this case the only columnar disturbance that can penetrate up-stream has structure sinzand so is not excited.A completely different result holds for ‘viscous’ formulations for unseparated, bounded régimes (with steady lee waves spatially attenuated by effects of small molecular diffusion). The strengths of all columnar disturbances, upstream and downstream, vanish in the limit of small diffusivity.In the inviscid, transient, unbounded problem, the upstream influence is, likewise, evanescent, beingO(ε2t−2) as timet→ ∞.The basic expansion in powers of ε will be invalid for times ∝ ε−1or greater, because of resonant-interactive instability of the lee waves.

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