A mathematical model for the 3-D dynamics of lee wave across a meso-scale mountain corner

A mathematical model for studying the 3-D dynamical structure of lee wave across a meso-scale mountain corner has been proposed for a mean flow with realistic vertical variation of wind and temperature. The basic flow consists of both zonal wind component (U) and meridional component (V), which are assumed to be dependent of height. The Brunt-Vaisala frequency (N) is also assumed to be dependent of height. This model has been applied to the mountain corner, in the North East India, formed by broadly North-South oriented Assam Burma Hills (ABH) and broadly East-West oriented Khasi Jayantia hills (KJH). The model has been solved following the quasi-numerical approach. The perturbation vertical velocity is expressed as a double integral. Three cases have been studied and in all cases the relation between the possible transverse and divergent lee wave numbers (k, l) and also the updraft/downdraft regions associated with lee waves at different heights has been mapped and discussed.

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

A 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.

The impact of lee waves on the Southern Ocean circulation

Lee waves play an important role in transferring energy from the geostrophic eddy field to turbulent mixing in the Southern Ocean. As such, lee waves can impact the Southern Ocean circulation and modulate its response to changing climate through their regulation on the eddy field and turbulent mixing. The drag effect of lee waves on the eddy field and the mixing effect of lee waves on the tracer field have been studied separately to show their importance. However, it remains unclear how the drag and mixing effects act together to modify the Southern Ocean circulation. In this study, a lee wave parameterization that includes both lee wave drag and its associated lee-wave-driven mixing is developed and implemented in an eddy-resolving idealized model of the Southern Ocean to simulate and quantify the impacts of lee waves on the Southern Ocean circulation. The results show that lee waves enhance the baroclinic transport of the Antarctic Circumpolar Current (ACC) and strengthen the lower overturning circulation. The impact of lee waves on the large-scale circulation are explained by the control of lee wave drag on isopycnal slopes through their effect on eddies, and by the control of lee-wave-driven mixing on deep stratification and water mass transformation. The results also show that the drag and mixing effects are coupled such that they act to weaken one another. The implication is that the future parameterization of lee waves in global ocean and climate models should take both drag and mixing effects into consideration for a more accurate representation of their impact on the ocean circulation.

Stereophotogrammetry of clouds observed during T-REX

Stereophotogrammetric images collected during the Terrain-induced Rotor Experiment (T-REX), which took place in Owens Valley, California, in the spring of 2006, were used to track clouds and cloud fragments in space and time. We explore how photogrammetric data complements other instruments deployed during T-REX, and how it supports T-REX objectives to study the structure and dynamics of atmospheric lee waves and rotors. Algorithms for camera calibration, automatic feature matching, and 3D positioning of clouds were developed which enabled the study of cloud motion in highly turbulent mountain wave scenarios.The dynamic properties obtained with photogrammetric tools compare well with data collected by other T-REX instruments. In a mild mountain wave event, the whole life cycle of clouds moving through a lee wave crest was tracked in space and time showing upward and downward motion at the upstream and downstream side of the wave crest, respectively. During strong mountain wave events the steepening of the first lee wave as it developed into a hydraulic jump was tracked and quantified. Vertical cloud motion increased from ~2 m/s to 4 m/s and horizontal cloud motion decreased from 20 m/s to 16 m/s with the development of the hydraulic jump. Clouds at distinct vertical layers were tracked in other mountain wave events: moderate southerly flow was observed in the valley (~8 m/s), westerly motion of the same magnitude at the Sierra Nevada mountain crest level, and westerlies with speeds of over 20 m/s at even higher altitudes.

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

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.

Near-inertial dissipation due to stratified flow over abyssal topography

Linear theory for steady stratified flow over topography sets the range for topographic wavenumbers over which freely propagating internal waves are generated, and the radiation and breaking of these waves contribute to energy dissipation away from the ocean bottom. However, previous numerical work demonstrated that dissipation rates can be enhanced by flow over large scale topographies with wavenumbers outside of the lee wave radiative range. We conduct idealized 3D numerical simulations of steady stratified flow over 1D topography in a rotating domain and quantify vertical distribution of kinetic energy dissipation. We vary two parameters: the first determines whether the topographic obstacle is within the lee wave radiative range and the second, proportional to the topographic height, measures the degree of flow non-linearity. For certain combinations of topographic width and height, breaking occurs in pulses every inertial period, such that kinetic energy dissipation develops inertial periodicity. In these simulations, kinetic energy dissipation rates are also enhanced in the interior of the domain. In the radiative regime the inertial motions arise due to resonant wave-wave interactions. In the small wavenumber non-radiative regime, instabilities downstream of the obstacle can facilitate the generation and propagation of non-linearly forced inertial motions, especially as topographic height increase. In our simulations, dissipation rates for tall and wide non-radiative topography are comparable to those of radiative topography, even away from the bottom, which is relevant to the ocean where the topographic spectrum is such that wider abyssal hills also tend to be taller.

Dissipating and reflecting internal waves

Internal 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.

An Idealized Model Study of Eddy Energetics in the Western Boundary “Graveyard”

Recent studies show that the western boundary acts as a “graveyard” for westward-propagating ocean eddies. However, how the eddy energy incident on the western boundary is dissipated remains unclear. Here we investigate the energetics of eddy–western boundary interaction using an idealized MIT ocean circulation model with a spatially variable grid resolution. Four types of model experiments are conducted: 1) single eddy cases, 2) a sea of random eddies, 3) with a smooth topography, and 4) with a rough topography. We find significant dissipation of incident eddy energy at the western boundary, regardless of whether the model topography at the western boundary is smooth or rough. However, in the presence of rough topography, not only the eddy energy dissipation rate is enhanced, but more importantly, the leading process for removing eddy energy in the model switches from bottom frictional drag as in the case of smooth topography to viscous dissipation in the ocean interior above the rough topography. Further analysis shows that the enhanced eddy energy dissipation in the experiment with rough topography is associated with greater anticyclonic, ageostrophic instability (AAI), possibly as a result of lee wave generation and nonpropagating form drag effect.