Lakshmi Kantha
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Lakshmi Kantha has a total of 41 co-authors. Here are the top co-authors by number of shared publications:
- Abhiram Doddi
Smead Aerospace Engineering Sciences, University of Colorado, Boulder, CO, USA
3 shared publications - Hiroyuki Hashiguchi
Research Institute for Sustainable Humanosphere, Kyoto University, Uji, 6110011, Japan
3 shared publications - Dale A. Lawrence
Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, Colorado
2 shared publications - David C. Fritts
GATS Inc. Boulder CO USA
2 shared publications Hans Ulrich Lass
Baltic Sea Research Institute
2 shared publicationsHartmut Prandke
ISW Wassermesstechnik
2 shared publications
Latest Publications
- Open Access
- 1 October 2024
- Published by Wiley in Quarterly Journal of the Royal Meteorological Society
- Vol. 150 (765) , 5561-5582
A high‐resolution climatological study of explosive cyclones in the Mediterranean region: Frequency, intensity and synoptic drivers
In the complex context of climate change and in a heavily populated area like the Mediterranean region, understanding and studying explosive cyclones (ECs) is crucial because of their potential to cause extreme weather events, including strong winds, heavy rainfall, and significant disruptions to human activities and infrastructure, as happened in 2018 with the Vaia storm. The genesis and persistence of ECs, characterized by a rapid drop in central mean sea level pressure exceeding 12 hPa in 12 hours, are influenced by various physical processes and while water vapour convergence in the mid‐low troposphere is crucial, mid‐upper tropospheric cyclonic vorticity advection and upper tropospheric divergence also play significant roles. In this study, we used ERA5 hourly data of mean sea level pressure from 1979 to 2020 to analyse EC occurrences in the Mediterranean. The identification of EC events followed the 12‐hr deepening‐rate criterion introduced by Zhang et al. (2017), as shorter deepening rates definitions proved unreliable. A total of 80 ECs were identified and classified based on their spatial occurrence and magnitude, 34 of which were concentrated in the northwest of the basin, likely due to orographic deformation caused by the Alps on baroclinic waves originating from the Atlantic. The study also identified recurring synoptic patterns associated with the persistence of ECs over the sea, including the presence of potential vorticity (PV) streamers and mid‐tropospheric dry‐air intrusions. Empirical Orthogonal Function (EOF) analysis highlighted the Scandinavian pattern as the primary driver, with blocking conditions over western Russia and Scandinavia, and composite analyses revealed the intrusion of PV to various atmospheric levels, extending up to 500 hPa. In summary, this study offers valuable insights into the complex mechanisms governing EC formation in the Mediterranean Basin, shedding light on the synoptic patterns, atmospheric dynamics, and potential impacts on regional weather systems.
- 1 October 2024
- Published by Wiley in Quarterly Journal of the Royal Meteorological Society
- Vol. 150 (765) , 5561-5582
Open AccessA high‐resolution climatological study of explosive cyclones in the Mediterranean region: Frequency, intensity and synoptic drivers
In the complex context of climate change and in a heavily populated area like the Mediterranean region, understanding and studying explosive cyclones (ECs) is crucial because of their potential to cause extreme weather events, including strong winds, heavy rainfall, and significant disruptions to human activities and infrastructure, as happened in 2018 with the Vaia storm. The genesis and persistence of ECs, characterized by a rapid drop in central mean sea level pressure exceeding 12 hPa in 12 hours, are influenced by various physical processes and while water vapour convergence in the mid‐low troposphere is crucial, mid‐upper tropospheric cyclonic vorticity advection and upper tropospheric divergence also play significant roles. In this study, we used ERA5 hourly data of mean sea level pressure from 1979 to 2020 to analyse EC occurrences in the Mediterranean. The identification of EC events followed the 12‐hr deepening‐rate criterion introduced by Zhang et al. (2017), as shorter deepening rates definitions proved unreliable. A total of 80 ECs were identified and classified based on their spatial occurrence and magnitude, 34 of which were concentrated in the northwest of the basin, likely due to orographic deformation caused by the Alps on baroclinic waves originating from the Atlantic. The study also identified recurring synoptic patterns associated with the persistence of ECs over the sea, including the presence of potential vorticity (PV) streamers and mid‐tropospheric dry‐air intrusions. Empirical Orthogonal Function (EOF) analysis highlighted the Scandinavian pattern as the primary driver, with blocking conditions over western Russia and Scandinavia, and composite analyses revealed the intrusion of PV to various atmospheric levels, extending up to 500 hPa. In summary, this study offers valuable insights into the complex mechanisms governing EC formation in the Mediterranean Basin, shedding light on the synoptic patterns, atmospheric dynamics, and potential impacts on regional weather systems.
- 1 August 2024
- Published by American Meteorological Society in Journal of the Atmospheric Sciences
- Vol. 81 (8) , 1495-1510
Reinterpretation of the Thorpe Length Scale
In 1977, S. A. Thorpe proposed a method to estimate the dissipation rate ε of turbulence kinetic energy (TKE) in an overturning turbulent layer in a lake, by sorting the observed (unstable) density profile to render it stable and thus deriving a length scale LT named after him, from the resulting vertical displacements of water parcels. By further proposing that this purely empirical scale (with no a priori physical basis, unlike many other turbulence length scales) is proportional to the Ozmidov scale LO, definable only for stably (not unstably or neutrally) stratified flows, he was able to extract ε. The simplicity of the approach that requires nothing but conductivity–temperature–depth (CTD) casts in water bodies, including lakes and oceans, made it attractive, until microstructure profilers were developed and perfected in later decades to actually make in situ measurements of ε. Since equivalent microstructure devices are not available for the atmosphere, the Thorpe technique has been resurrected in recent years for application to the atmosphere, using potential temperature profiles obtained from high-vertical-resolution radiosondes. Its popularity and utility have increased lately, in spite of unresolved issues related to the validity of assuming LT is proportional to LO. In this study, we touch upon these issues and offer an alternative interpretation of the Thorpe length scale as indicative of the turbulence velocity scale σK, which allows the Thorpe sorting technique to be applied to all turbulent flows, including those generated by convection. Significance Statement: Routine monitoring of the turbulence structure in the global atmosphere is of societal importance and practical utility. Remote sensing by wind profiler radars provides routine information at only a few stations around the globe. Monitoring by sensors deployed on commercial aircraft provides data only along flight routes and mostly at flight altitudes. However, high-vertical-resolution radiosondes that are now being routinely deployed at over 900 stations around the globe provide a means for routine probing and monitoring of turbulence in the global atmosphere, by using the Thorpe sorting technique to extract the dissipation rate of turbulence kinetic energy. Reinterpretation of the technique in this study extends its application to all turbulent flows in the atmospheric column, including convective turbulence.
- 1 August 2024
- Published by American Meteorological Society in Journal of the Atmospheric Sciences
- Vol. 81 (8) , 1495-1510
Reinterpretation of the Thorpe Length Scale
In 1977, S. A. Thorpe proposed a method to estimate the dissipation rate ε of turbulence kinetic energy (TKE) in an overturning turbulent layer in a lake, by sorting the observed (unstable) density profile to render it stable and thus deriving a length scale LT named after him, from the resulting vertical displacements of water parcels. By further proposing that this purely empirical scale (with no a priori physical basis, unlike many other turbulence length scales) is proportional to the Ozmidov scale LO, definable only for stably (not unstably or neutrally) stratified flows, he was able to extract ε. The simplicity of the approach that requires nothing but conductivity–temperature–depth (CTD) casts in water bodies, including lakes and oceans, made it attractive, until microstructure profilers were developed and perfected in later decades to actually make in situ measurements of ε. Since equivalent microstructure devices are not available for the atmosphere, the Thorpe technique has been resurrected in recent years for application to the atmosphere, using potential temperature profiles obtained from high-vertical-resolution radiosondes. Its popularity and utility have increased lately, in spite of unresolved issues related to the validity of assuming LT is proportional to LO. In this study, we touch upon these issues and offer an alternative interpretation of the Thorpe length scale as indicative of the turbulence velocity scale σK, which allows the Thorpe sorting technique to be applied to all turbulent flows, including those generated by convection. Significance Statement: Routine monitoring of the turbulence structure in the global atmosphere is of societal importance and practical utility. Remote sensing by wind profiler radars provides routine information at only a few stations around the globe. Monitoring by sensors deployed on commercial aircraft provides data only along flight routes and mostly at flight altitudes. However, high-vertical-resolution radiosondes that are now being routinely deployed at over 900 stations around the globe provide a means for routine probing and monitoring of turbulence in the global atmosphere, by using the Thorpe sorting technique to extract the dissipation rate of turbulence kinetic energy. Reinterpretation of the technique in this study extends its application to all turbulent flows in the atmospheric column, including convective turbulence.
- Open Access
- 7 July 2022
- Published by Copernicus GmbH in Atmospheric Measurement Techniques
- Vol. 15 (13) , 4023-4045
Instabilities, Dynamics, and Energetics accompanying Atmospheric Layering (IDEAL): high-resolution in situ observations and modeling in and above the nocturnal boundary layer
The Instabilities, Dynamics, and Energetics accompanying Atmospheric Layering (IDEAL) program was conceived to improve understanding of the dynamics of thin strongly stratified “sheet” and deeper weakly stratified “layer” (S&L) structures in the lower troposphere under strongly stable conditions. The field portion of the IDEAL program was conducted from 24 October to 15 November 2017 at Dugway Proving Ground, Utah, to target nighttime lower troposphere S&L conditions. It employed a synergistic combination of observations by multiple simultaneous DataHawk-2 (DH2) small unmanned aircraft systems (sUASs) and concurrent ground-based profiling by the NCAR Earth Observing Laboratory Integrated Sounding System (ISS) comprising a wind profiler radar and hourly high-resolution radiosonde soundings. DH2 measurement intervals as well as vertical (∼ 2–4 km) and horizontal (∼ 5–10 km) flight trajectories were chosen based on local high-resolution weather forecasting and guided by near-real-time ISS measurements. These flights combined simultaneous vertical and slant-path profiling, and/or horizontal racetrack sampling, spanning several hours before sunrise. High-spatial- and temporal-resolution data were downlinked in real time to enable near-real-time changes in DH2 flight paths based on observed flow features. The IDEAL field program performed 70 DH2 flights on 16 d, coordinated with 93 high-resolution radiosonde soundings. In this paper, raw and derived measurements from this campaign are outlined, and preliminary analyses are briefly described. This data set, along with “quick look” figures, is available for access by other researchers, as described herein.
- 7 July 2022
- Published by Copernicus GmbH in Atmospheric Measurement Techniques
- Vol. 15 (13) , 4023-4045
Open AccessInstabilities, Dynamics, and Energetics accompanying Atmospheric Layering (IDEAL): high-resolution in situ observations and modeling in and above the nocturnal boundary layer
The Instabilities, Dynamics, and Energetics accompanying Atmospheric Layering (IDEAL) program was conceived to improve understanding of the dynamics of thin strongly stratified “sheet” and deeper weakly stratified “layer” (S&L) structures in the lower troposphere under strongly stable conditions. The field portion of the IDEAL program was conducted from 24 October to 15 November 2017 at Dugway Proving Ground, Utah, to target nighttime lower troposphere S&L conditions. It employed a synergistic combination of observations by multiple simultaneous DataHawk-2 (DH2) small unmanned aircraft systems (sUASs) and concurrent ground-based profiling by the NCAR Earth Observing Laboratory Integrated Sounding System (ISS) comprising a wind profiler radar and hourly high-resolution radiosonde soundings. DH2 measurement intervals as well as vertical (∼ 2–4 km) and horizontal (∼ 5–10 km) flight trajectories were chosen based on local high-resolution weather forecasting and guided by near-real-time ISS measurements. These flights combined simultaneous vertical and slant-path profiling, and/or horizontal racetrack sampling, spanning several hours before sunrise. High-spatial- and temporal-resolution data were downlinked in real time to enable near-real-time changes in DH2 flight paths based on observed flow features. The IDEAL field program performed 70 DH2 flights on 16 d, coordinated with 93 high-resolution radiosonde soundings. In this paper, raw and derived measurements from this campaign are outlined, and preliminary analyses are briefly described. This data set, along with “quick look” figures, is available for access by other researchers, as described herein.
- 1 January 2022
- Published by Optica Publishing Group
- p. PTu3D.4
Turbulence Kinetic Energy dissipation rate estimated from clear air radar data: comparisons of models in light of DataHawk UAV measurements
TKE dissipation rate can be estimated from VHF/UHF Doppler radars. The currently used model for stably stratified conditions seems to be challenged by comparisons with UAV measurements. An alternative model derived for weakly stable conditions (Basu and Holtslag, EFM, 21, 1273, 2021) provides better agreements for shear-generated turbulent layers.
- 1 January 2022
- Published by Optica Publishing Group
- p. PTu3D.4
Turbulence Kinetic Energy dissipation rate estimated from clear air radar data: comparisons of models in light of DataHawk UAV measurements
TKE dissipation rate can be estimated from VHF/UHF Doppler radars. The currently used model for stably stratified conditions seems to be challenged by comparisons with UAV measurements. An alternative model derived for weakly stable conditions (Basu and Holtslag, EFM, 21, 1273, 2021) provides better agreements for shear-generated turbulent layers.
- 1 July 2020
- Published by American Meteorological Society in Journal of the Atmospheric Sciences
- Vol. 77 (7) , 2311-2326
On the Relationship between the TKE Dissipation Rate and the Temperature Structure Function Parameter in the Convective Boundary Layer
Under stably stratified conditions, the dissipation rate ε of turbulence kinetic energy (TKE) is related to the structure function parameter for temperature , through the buoyancy frequency and the so-called mixing efficiency. A similar relationship does not exist for convective turbulence. In this paper, we propose an analytical expression relating ε and in the convective boundary layer (CBL), by taking into account the effects of nonlocal heat transport under convective conditions using the Deardorff countergradient model. Measurements using unmanned aerial vehicles (UAVs) equipped with high-frequency response sensors to measure velocity and temperature fluctuations obtained during the two field campaigns conducted at Shigaraki MU observatory in June 2016 and 2017 are used to test this relationship between ε and in the CBL. The selection of CBL cases for analysis was aided by auxiliary measurements from additional sensors (mainly radars), and these are described. Comparison with earlier results in the literature suggests that the proposed relationship works, if the countergradient term γ D in the Deardorff model, which is proportional to the ratio of the variances of potential temperature θ and vertical velocity w, is evaluated from in situ (airplane and UAV) observational data, but fails if evaluated from large-eddy simulation (LES) results. This appears to be caused by the tendency of the variance of θ in the upper part of the CBL and at the bottom of the entrainment zone to be underestimated by LES relative to in situ measurements from UAVs and aircraft. We discuss this anomaly and explore reasons for it.
- 1 July 2020
- Published by American Meteorological Society in Journal of the Atmospheric Sciences
- Vol. 77 (7) , 2311-2326
On the Relationship between the TKE Dissipation Rate and the Temperature Structure Function Parameter in the Convective Boundary Layer
Under stably stratified conditions, the dissipation rate ε of turbulence kinetic energy (TKE) is related to the structure function parameter for temperature , through the buoyancy frequency and the so-called mixing efficiency. A similar relationship does not exist for convective turbulence. In this paper, we propose an analytical expression relating ε and in the convective boundary layer (CBL), by taking into account the effects of nonlocal heat transport under convective conditions using the Deardorff countergradient model. Measurements using unmanned aerial vehicles (UAVs) equipped with high-frequency response sensors to measure velocity and temperature fluctuations obtained during the two field campaigns conducted at Shigaraki MU observatory in June 2016 and 2017 are used to test this relationship between ε and in the CBL. The selection of CBL cases for analysis was aided by auxiliary measurements from additional sensors (mainly radars), and these are described. Comparison with earlier results in the literature suggests that the proposed relationship works, if the countergradient term γ D in the Deardorff model, which is proportional to the ratio of the variances of potential temperature θ and vertical velocity w, is evaluated from in situ (airplane and UAV) observational data, but fails if evaluated from large-eddy simulation (LES) results. This appears to be caused by the tendency of the variance of θ in the upper part of the CBL and at the bottom of the entrainment zone to be underestimated by LES relative to in situ measurements from UAVs and aircraft. We discuss this anomaly and explore reasons for it.
- Open Access
- 27 August 2019
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Atmospheres
- Vol. 124 (16) , 9372-9390
Numerical Simulations of High‐Frequency Gravity Wave Propagation Through Fine Structures in the Mesosphere
- 27 August 2019
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Atmospheres
- Vol. 124 (16) , 9372-9390
Open AccessNumerical Simulations of High‐Frequency Gravity Wave Propagation Through Fine Structures in the Mesosphere
- Open Access
- 23 March 2019
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Atmospheres
- Vol. 124 (6) , 3223-3245
Midlevel Cloud‐Base Turbulence: Radar Observations and Models
Midlevel Cloud‐base Turbulence (MCT) caused by ice/snow precipitation from midlevel clouds falling into dry air below the cloud base and sublimating is investigated. MCT phenomena in the lower troposphere as revealed by the Middle and Upper atmosphere (MU) radar in Shigaraki, Japan, during the Shigaraki unmanned aerial vehicle and radar Experiment campaigns in the spring‐summer of 2015 and 2016 are described. The MU radar was operated in a high‐resolution (~20‐m) range imaging mode and hence revealed the structure of these MCTs in great detail. These MCT layers grew to hundreds of meters in thickness, often reaching nearly 2,000 m in depth, lasting often for as much as 24 hr. A simple analytical model and a second‐moment closure‐based turbulent mixing model are used to estimate the levels of turbulence kinetic energy and its dissipation rate in the MCT layer and compare them to those measured by the MU radar. The study shows that MCT can give rise to moderate levels of turbulence of potential interest to aviation, confirming conclusions reached by earlier pioneering studies. However, to our knowledge, this important process has not received the attention it deserves by the atmospheric community so far, and therefore, it is the principal goal of this paper to not only present some observations and preliminary modeling results, but also redraw the attention of atmospheric scientists to this important process.
- 23 March 2019
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Atmospheres
- Vol. 124 (6) , 3223-3245
Open AccessMidlevel Cloud‐Base Turbulence: Radar Observations and Models
Midlevel Cloud‐base Turbulence (MCT) caused by ice/snow precipitation from midlevel clouds falling into dry air below the cloud base and sublimating is investigated. MCT phenomena in the lower troposphere as revealed by the Middle and Upper atmosphere (MU) radar in Shigaraki, Japan, during the Shigaraki unmanned aerial vehicle and radar Experiment campaigns in the spring‐summer of 2015 and 2016 are described. The MU radar was operated in a high‐resolution (~20‐m) range imaging mode and hence revealed the structure of these MCTs in great detail. These MCT layers grew to hundreds of meters in thickness, often reaching nearly 2,000 m in depth, lasting often for as much as 24 hr. A simple analytical model and a second‐moment closure‐based turbulent mixing model are used to estimate the levels of turbulence kinetic energy and its dissipation rate in the MCT layer and compare them to those measured by the MU radar. The study shows that MCT can give rise to moderate levels of turbulence of potential interest to aviation, confirming conclusions reached by earlier pioneering studies. However, to our knowledge, this important process has not received the attention it deserves by the atmospheric community so far, and therefore, it is the principal goal of this paper to not only present some observations and preliminary modeling results, but also redraw the attention of atmospheric scientists to this important process.
- Open Access
- 1 November 2018
- Published by American Meteorological Society in Journal of Physical Oceanography
- Vol. 48 (11) , 2649-2665
Mixing Coefficient in Stably Stratified Flows
Turbulent mixing in the interior of the oceans is not as well understood as mixing in the oceanic boundary layers. Mixing in the generally stably stratified interior is primarily, although not exclusively, due to intermittent shear instabilities. Part of the energy extracted by the Reynolds stresses acting on the mean shear is expended in increasing the potential energy of the fluid column through a buoyancy flux, while most of it is dissipated. The mixing coefficient χm, the ratio of the buoyancy flux to the dissipation rate of turbulence kinetic energy ε, is an important parameter, since knowledge of χm enables turbulent diffusivities to be inferred. Theory indicates that χm must be a function of the gradient Richardson number. Yet, oceanic studies suggest that a value of around 0.2 for χm gives turbulent diffusivities that are in good agreement with those inferred from tracer studies. Studies by scientists working with atmospheric radars tend to reinforce these findings but are seldom referenced in oceanographic literature. The goal of this paper is to bring together oceanographic, atmospheric, and laboratory observations related to χm and to report on the values deduced from in situ data collected in the lower troposphere by unmanned aerial vehicles, equipped with turbulence sensors and flown in the vicinity of the Middle and Upper Atmosphere (MU) radar in Japan. These observations are consistent with past studies in the oceans, in that a value of around 0.16 for χm yields good agreement between ε derived from turbulent temperature fluctuations using this value and ε obtained directly from turbulence velocity fluctuations.
- 1 November 2018
- Published by American Meteorological Society in Journal of Physical Oceanography
- Vol. 48 (11) , 2649-2665
Open AccessMixing Coefficient in Stably Stratified Flows
Turbulent mixing in the interior of the oceans is not as well understood as mixing in the oceanic boundary layers. Mixing in the generally stably stratified interior is primarily, although not exclusively, due to intermittent shear instabilities. Part of the energy extracted by the Reynolds stresses acting on the mean shear is expended in increasing the potential energy of the fluid column through a buoyancy flux, while most of it is dissipated. The mixing coefficient χm, the ratio of the buoyancy flux to the dissipation rate of turbulence kinetic energy ε, is an important parameter, since knowledge of χm enables turbulent diffusivities to be inferred. Theory indicates that χm must be a function of the gradient Richardson number. Yet, oceanic studies suggest that a value of around 0.2 for χm gives turbulent diffusivities that are in good agreement with those inferred from tracer studies. Studies by scientists working with atmospheric radars tend to reinforce these findings but are seldom referenced in oceanographic literature. The goal of this paper is to bring together oceanographic, atmospheric, and laboratory observations related to χm and to report on the values deduced from in situ data collected in the lower troposphere by unmanned aerial vehicles, equipped with turbulence sensors and flown in the vicinity of the Middle and Upper Atmosphere (MU) radar in Japan. These observations are consistent with past studies in the oceans, in that a value of around 0.16 for χm yields good agreement between ε derived from turbulent temperature fluctuations using this value and ε obtained directly from turbulence velocity fluctuations.
- Open Access
- 8 June 2016
- Published by Wiley in Advances in Astronomy
- Vol. 2016, 1-8
A Time-DependentandCosmological Model Consistent with Cosmological ConstraintsThe prevailing constantcosmological model agrees with observational evidence including the observed red shift, Big Bang Nucleosynthesis (BBN), and the current rate of acceleration. It assumes that matter contributes 27% to the current density of the universe, with the rest (73%) coming from dark energy represented by the Einstein cosmological parameterin the governing Friedmann-Robertson-Walker equations, derived from Einstein’s equations of general relativity. However, the principal problem is the extremely small value of the cosmological parameter (~10−52 m2). Moreover, the dark energy density represented byis presumed to have remained unchanged as the universe expanded by 26 orders of magnitude. Attempts to overcome this deficiency often invoke a variablemodel. Cosmic constraints from action principles require that either bothandremain time-invariant or both vary in time. Here, we propose a variablecosmological model consistent with the latest red shift data, the current acceleration rate, and BBN, provided the split between matter and dark energy is 18% and 82%.decreases (, whereis the normalized cosmic time) andincreases () with cosmic time. The model results depend only on the chosen value ofat present and in the far future and not directly on.- 8 June 2016
- Published by Wiley in Advances in Astronomy
- Vol. 2016, 1-8
Open AccessA Time-DependentandCosmological Model Consistent with Cosmological ConstraintsThe prevailing constantcosmological model agrees with observational evidence including the observed red shift, Big Bang Nucleosynthesis (BBN), and the current rate of acceleration. It assumes that matter contributes 27% to the current density of the universe, with the rest (73%) coming from dark energy represented by the Einstein cosmological parameterin the governing Friedmann-Robertson-Walker equations, derived from Einstein’s equations of general relativity. However, the principal problem is the extremely small value of the cosmological parameter (~10−52 m2). Moreover, the dark energy density represented byis presumed to have remained unchanged as the universe expanded by 26 orders of magnitude. Attempts to overcome this deficiency often invoke a variablemodel. Cosmic constraints from action principles require that either bothandremain time-invariant or both vary in time. Here, we propose a variablecosmological model consistent with the latest red shift data, the current acceleration rate, and BBN, provided the split between matter and dark energy is 18% and 82%.decreases (, whereis the normalized cosmic time) andincreases () with cosmic time. The model results depend only on the chosen value ofat present and in the far future and not directly on. - Open Access
- 19 February 2014
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Oceans
- Vol. 119 (2) , 1510-1515
Comment on “Wave‐turbulence interaction and its induced mixing in the upper ocean” by Huang and Qiao
- 19 February 2014
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Oceans
- Vol. 119 (2) , 1510-1515
Open AccessComment on “Wave‐turbulence interaction and its induced mixing in the upper ocean” by Huang and Qiao