arXiv subjects

Sutanu Sarkar

Publications and source records attributed to Sutanu Sarkar.

16 recordsLinked to original sources

arXiv2026

Stratified wakes of a prolate spheroid at moderate angle of attack

Ocean submersibles and aerial vehicles often encounter a density-stratified environment whose effect on flow features is of interest. A 6:1 prolate spheroid of diameter $D$ with velocity $U$ and at a moderate angle of attack (AOA) of $10^\circ$ is taken as a canonical example of a submersible. Buoyancy effects are examined in a parametric LES study of the spheroid wake at $Re = UD/ν= 5000$ where stratification is changed to cover a wide range of values of body Froude number ($Fr = U/ND$). The Froude number measures buoyancy time scale (1/$N$ where $N$ is the buoyancy frequency) relative to flow time scale ($D/U$). The simulated cases range from a baseline case without stratification, i.e. $Fr = \infty$, to the substantial stratification level of $Fr = 1$. The very near wake, just two body diameters aft of the trailing edge, is found to be substantially altered at even the relatively weak stratification of $Fr = 6$. Specifically, the coherence of the streamwise vortex pair shed from the body is weakened, the downward trajectory of the wake center is suppressed, and the mean/turbulence structure changes in the near wake. Diagnosis of the vorticity transport equation reveals that the baroclinic torque becomes an important contributor to the balance of mean streamwise vorticity in the very near wake at $Fr = 6$. With increasing stratification, the wake topology changes significantly, e.g. the $Fr =1$ case exhibits a secondary wake above the primary wake.

physics.flu-dyn↗

arXiv2026

Scale interactions and energy transfer in the turbulent wake of a bluff body

Turbulent bluff-body wakes exemplify the coexistence of large-scale coherent structures and fine-scale turbulence -- two ends of a wide dynamical range of scales connected through the turbulent cascade. In this work, we study the multiscale dynamics in the high-Reynolds-number wake behind a circular disk. One-point and two-point statistics are first examined, including the budget and spectra of the turbulent kinetic energy (TKE). Streamwise advection is found to contribute the most to the TKE balance, while the dissipation rate does not follow the classical equilibrium scaling ($\varepsilon \nsim \mathcal{U}^3/\mathcal{L}$). The largest scales are represented by the three-dimensional coherent modes extracted using spectral proper orthogonal decomposition, whereas the TKE and Reynolds shear stress spectra exhibit inertial-range scalings. A filtering-based triple decomposition further separates the fluctuations into large- and small-scale components and partitions the kinetic energy, with respective spatial transports at each scale and an inter-scale transfer in between. The inter-scale fluxes indicate a statistical forward cascade and follow the classical $\mathcal{U}^3/\mathcal{L}$ scaling, while their radial profiles become self-similar. The disequilibrium between inter-scale flux and dissipation is shown to arise from non-negligible streamwise advection at the sub-filter scale. Finally, the observed anti-correlation between the dissipation coefficient and the local Taylor Reynolds number, $C_\varepsilon = \varepsilon \mathcal{L}/\mathcal{U}^3 \sim Re_λ^{-1}$, is shown to originate from a similar correlation in the coarse-grained, locally averaged statistics. The results suggest that the instantaneous cascade-dissipation disequilibrium is intrinsic to turbulence and becomes apparent when large-scale unsteadiness and length-scale growth prevent statistical equilibrium.

physics.flu-dyn↗

arXiv2026

Leveraging modal structure similarity for simulation of spatially evolving wakes

We present a new methodology to enable efficient simulation of high Reynolds number wakes. In this approach, a body-exclusive hybrid simulation at Re = 5 x 10^4 is initialized using inflow fields reconstructed from a lower Reynolds number (Re = 5 x 10^3) body-inclusive simulation. Spectral Proper Orthogonal Decomposition (SPOD) is employed to identify dominant coherent structures, and a low-rank reconstruction generates physically meaningful inflow conditions. The resulting simulations accurately recover key large-scale flow, including the vortex shedding mode, and match the spectral content of a fully body-inclusive Re = 5 x 10^4 reference simulation beyond an adjustment region. SPOD eigenspectra confirm agreement across both low and high frequencies. This strategy achieves over an order-of-magnitude reduction in computational cost by avoiding direct high-Re body-inclusive simulations, offering a scalable framework for simulating complex wakes using low Re as well as reduced-order inflow prescriptions.

physics.flu-dyn↗

arXiv2025

Tidally dominated flows past a three-dimensional topography: Wake vortices, turbulence, and mixing

Oceanic turbulence influences the transport and mixing of freshwater, heat, nutrients, and other biogeochemical tracers. It also has broader implications for oceanic and atmospheric circulations. Tides contribute substantially to the mechanically driven turbulent ocean mixing through the internal waves resulting from tide-topography interactions. Tidal currents also drive turbulent wakes and shear layers when the topography is 3D. The hypothesis that seamounts are the ``stirring rods'' of the ocean has motivated considerable recent interest in turbulent flow features near 3D topography. It also motivates the present LES of tidally dominated flows (tidal oscillations superposed on a weaker mean) past an idealized steep seamount. Complex interactions occur between the topography, the near wake, and previously shed vortices, especially during the tidal phases when the flow direction is reversed. The topographic wake is shown to be a hotspot for mixing, featuring large dissipation rates in the attached shear layers, hydraulic jet, recirculation region in the near wake, and peripheries of shed vortices. The majority of the observed dissipation is due to the vertical shear. Over a tidal cycle, the volume-integrated local dissipation within the wake is at least four times greater than the internal wave flux that may be dissipated elsewhere. Furthermore, normalized dissipation rates are maximized for the purely tidal setting. Within the tidal cycle, bulk mixing efficiency ($η$) varies substantially and is maximized at $η\approx 0.25$ around flow reversals.

physics.flu-dyn↗

arXiv2025

Turbulence in stratified rotating topographic wakes

Turbulence generation mechanisms in stratified, rotating flows past three-dimensional (3D) topography remain underexplored, particularly in submesoscale (SMS) regimes critical to geophysical applications. Using turbulence-resolving large-eddy simulations, we systematically dissect the interplay of stratification and rotation in governing the dynamics of wake turbulence. Our parametric study reveals that turbulent dissipation in the near wake is dominated by two distinct instabilities: (1) vertical shear-driven Kelvin-Helmholtz instability (KHI), amplified by oblique dislocation of Kármán vortices under strong stratification, and (2) centrifugal/inertial instability (CI), which peaks at intermediate rotation rates (Rossby number order unity, SMS regime) and relatively weaker stratification. Notably, strong rotation dampens vertical shear and weakens KHI-driven turbulence, while strong stratification imposes smaller vertical length scales that restrict CI-driven turbulence. By quantifying dissipation across a broad parameter space of stratification and rotation, predictive relationships between the environmental parameters and instability dominance is established. These findings highlight the regime dependence of instability mechanisms and may inform targeted observational campaigns and numerical models of oceanic and atmospheric wakes.

physics.flu-dyn↗

arXiv2024

Internal gravity waves in flow past a bluff body under different levels of stratification

The flow field of a bluff body, a circular disk, that moves horizontally in a stratified environment is studied using large eddy simulations (LES). Five levels of stratification (body Froude numbers of Fr = 0.5, 1, 1.5, 2 and 5) are simulated at Reynolds number of Re = 5000 and Prandtl number of Pr = 1. A higher Re = 50, 000 database at Fr = 2, 10 and Pr = 1 is also examined for comparison. The wavelength and amplitude of steady lee waves are compared with a linear-theory analysis. Excellent agreement is found over the entire range of Fr if an equivalent body that includes the separation region is employed for the linear theory. For asymptotically large distance, the velocity amplitude varies theoretically as Fr raised to negative 1 but a correction owing to dependence of the separation zone on Fr is needed. The wake waves propagate in a narrow band of angles with the vertical and have a wavelength that increases with increasing Fr. The envelope of wake waves, demarcated using buoyancy variance, exhibits self-similar behavior. The higher Re results are consistent with the buoyancy effects exhibited at the lower Re. The wake wave energy is larger at Re = 50000. Nevertheless, independent of Fr and Re, the ratio of the wake wave potential energy to the wake turbulent energy increases to approximately 0.6 to 0.7 in the nonequilibrium (NEQ) stage showing their energetic importance besides suggesting universality in this statistic. There is a crossover of energetic dominance of lee waves at Fr less than 2 to wake-wave dominance at Fr approximately equal to 5.

physics.flu-dyn↗

arXiv2024

Effect of rotation on wake vortices in stratified flow

Stratified wakes past an isolated conical seamount are simulated at a Froude number of $Fr = 0.15$ and Rossby numbers of $Ro = 0.15$, 0.75, and $\infty$. The wakes exhibit a K{\' a}rm{\' a}n vortex street, unlike their unstratified, non-rotating counterpart. Vortex structures are studied in terms of large-scale global modes, as well as spatially localised vortex evolution, with a focus on rotation effects. The global modes are extracted by spectral proper orthogonal decomposition (SPOD). For all three studied $Ro$ ranging from mesoscale, submesoscale, and non-rotating cases, the frequency of the SPOD modes at different heights remains coupled as a global constant. However, the shape of the SPOD modes changes from slanted `tongues' at zero rotation ($Ro=\infty$) to tall hill-height columns at strong rotation ($Ro=0.15$). A novel method for vortex centre tracking shows that, in all three cases, the vortices at different heights advect uniformly at about $ 0.9U_{\infty}$ beyond the near wake, consistent with the lack of variability of the global modes. Under system rotation, cyclonic vortices (CVs) and anticyclonic vortices (AVs) present considerable asymmetry, especially at $Ro = 0.75$. The vorticity distribution as well as the stability of AVs are tracked downstream using statistics conditioned to the identified vortex centres. At $Ro=0.75$, intense AVs with relative vorticity up to $ω_z/f_{\rm c}=-2.4$ are seen with small regions of instability but all AVs evolve towards a more stable state. Recent stability analysis that accounts for stratification and viscosity is found to improve on earlier criteria.

physics.flu-dyn↗

arXiv2023

Large-scale streaks in a turbulent bluff body wake

A turbulent circular disk wake database (Chongsiripinyo \& Sarkar, \textit{J. Fluid Mech.}, vol. 885, 2020) at Reynolds number $\textit{Re} = U_\infty D/ν= 5 \times 10^{4}$ is interrogated to identify the presence of large-scale streaks - coherent elongated regions of streamwise velocity. The unprecedented streamwise length - until $x/D \approx 120$ - of the simulation enables investigation of the near and far wake. The near wake is dominated by the vortex shedding (VS) mode residing at azimuthal wavenumber $m=1$ and Strouhal number $\textit{St} = 0.135$. After filtering out the VS structure, conclusive evidence of large-scale streaks with frequency $\textit{St} \rightarrow 0$, equivalently streamwise wavenumber $k_x \rightarrow 0$ in the wake, becomes apparent in visualizations and spectra. These streaky structures are found throughout the simulation domain beyond $x/D \approx 10$. Conditionally averaged streamwise vorticity fields reveal that the lift-up mechanism is active in the near as well as the far wake, and that ejections contribute more than sweep to events of intense $-u'_xu'_r$. Spectral proper orthogonal decomposition (SPOD) is employed to extract the energy and the spatiotemporal features of the large-scale streaks. The streak energy is concentrated in the $m=2$ azimuthal mode over the entire domain. Finally, bispectral mode decomposition (BMD) is conducted to reveal strong interaction between $m=1$ and $\textit{St} = \pm 0.135$ modes to give the $m=2, \textit{St} = 0$ streak mode. Our results indicate that the self-interaction of the VS mode generates the $m=2, \textit{St} = 0$ streamwise vortices, which leads to streak formation through the lift-up process. To the authors' knowledge, this is the first study that reports and characterizes large-scale low-frequency streaks and the associated lift-up mechanism in a turbulent wake.

physics.flu-dyn↗

arXiv2022

Modal analysis of bluff body wakes

Spectral proper orthogonal decomposition (SPOD) analyses are performed for unstratified and stratified wakes of a circular disk at Reynolds number, $U_\infty D/ν= 50,000$, where $U_\infty$ is the freestream velocity and $D$ is the diameter of the circular disk. At $Re= 50,000$, three diameter-based Froude numbers, $\Fro = U_\infty/ND = \infty$, $2$ and $10$ are analyzed. We find that in the unstratified configuration, two modes: (i) the vortex shedding (VS) mode ($m=1, \Str = 0.135$) and (ii) the double helix (DH) mode ($m=2, \Str \rightarrow 0$) are the most dominant features. At far-downstream distances, DH mode is dominant while at near and intermediate locations, VS mode dominates the energetics. Reconstruction of TKE and Reynolds shear stresses are also explored at near and far wake locations. In the stratified cases ($\Fro = 2$ and $10$), the vortex shedding mode (at $\Str \approx 0.13-0.14$) dominates the wake. At intermediate to late streamwise locations ($x/D$), we establish through pressure wave flux reconstruction that the VS mode is responsible for the internal gravity wave (IGW) generation. A comparison between the SPOD decomposition analyses between $Re =5000$ and $Re = 50,000$ is also performed at $\Fro =2$. Preliminary results show that the low-$Re$ wake is also dominated by the VS mode but exhibits more coherence, namely higher contribution of leading SPOD modes, than the high-$Re$ wake.

physics.flu-dyn↗

arXiv2022

Lagrangian surface signatures reveal upper-ocean vertical displacement conduits near oceanic density fronts

Vertical transport in the ocean plays a critical role in the exchange of freshwater, heat, nutrients, and other biogeochemical tracers. While there are situations where vertical fluxes are important, studying the vertical transport and displacement of material requires analysis over a finite interval of time. One such example is the subduction of fluid from the mixed layer into the pycnocline, which is known to occur near density fronts. Divergence has been used to estimate vertical velocities indicating that surface measurements, where observational data is most widely available, can be used to locate these vertical transport conduits. We evaluate the correlation between surface signatures derived from Eulerian (horizontal divergence, density gradient, and vertical velocity) and Lagrangian (dilation rate and finite time Lyapunov exponent) metrics and vertical displacement conduits. Two submesoscale resolving models of density fronts and a data-assimilative model of the western Mediterranean were analyzed. The Lagrangian surface signatures locate significantly more of the strongest displacement features and the difference in the expected displacements relative to Eulerian ones increases with the length of the time interval considered. Ensemble analysis of forecasts from the Mediterranean model demonstrates that the Lagrangian surface signatures can be used to identify regions of strongest downward vertical displacement even without knowledge of the true ocean state.

physics.geo-ph↗

arXiv2021

Analysis of coherence in turbulent stratified wakes using spectral proper orthogonal decomposition

We use spectral proper orthogonal decomposition (SPOD) to extract and analyze coherent structures in the turbulent wake of a disk at Reynolds number $Re = 5 \times 10^{4}$ and Froude numbers $Fr$ = $2, 10$. We find that the SPOD eigenspectra of both wakes exhibit a low-rank behavior and the relative contribution of low-rank modes to total fluctuation energy increases with $x/D$. The vortex shedding (VS) mechanism, which corresponds to $St \approx 0.11-0.13$ in both wakes, is active and dominant throughout the domain in both wakes. The continual downstream decay of the SPOD eigenspectrum peak at the VS mode, which is a prominent feature of the unstratified wake, is inhibited by buoyancy, particularly for $Fr = 2$. The energy at and near the VS frequency is found to appear in the outer region of the wake when the downstream distance exceeds $Nt = Nx/U = 6 - 8$. Visualizations show that unsteady internal gravity waves (IGWs) emerge at the same $Nt = 6 - 8$. A causal link between the VS mechanism and the unsteady IGW generation is also established using the SPOD-based reconstruction and analysis of the pressure-transport term. These IGWs are also picked up in SPOD analysis as a structural change in the shape of the leading SPOD eigenmode. The $Fr = 2$ wake shows layering in the wake core at {$Nt > 15$} which is captured by the leading SPOD eigenmodes of the VS frequency at downstream locations $x/D > 30$. The VS mode of the $Fr = 2$ wake is streamwise-coherent, consisting of V-shaped structures at $x/D \gtrsim 30$. Overall, we find that the coherence of wakes, initiated by the VS mode at the body, is prolonged by buoyancy to far downstream. Also, this coherence is spatially modified by buoyancy into horizontal layers and IGWs. Low-order truncations of SPOD modes are shown to efficiently reconstruct important second-order statistics.

physics.flu-dyn↗

arXiv2021

High drag states in tidally modulated stratified wakes

Large eddy simulations (LES) are employed to investigate the role of time-varying currents on the form drag and vortex dynamics of submerged 3D topography in a stratified rotating environment. The current is of the form $U_c+U_t \sin(2πf_t t)$, where $U_c$ is the mean, $U_t$ is the tidal component and $f_t$ is its frequency. A conical obstacle is considered in the regime of low Froude number. When tides are absent, eddies are shed at the natural shedding frequency $f_{s,c}$. The relative frequency $f^*=f_{s,c}/f_t$ is varied in a parametric study which reveals states of high time-averaged form drag coefficient. There is a two-fold amplification of the form drag coefficient relative to the no-tide ($U_t=0$) case when $f^*$ lies between 0.5 and 1. The spatial organization of the near-wake vortices in the high drag states is different from a Kármán vortex street. For instance, the vortex shedding from the obstacle is symmetric when $f^*=5/12$ and strongly asymmetric when $f^*=5/6$. The increase in form drag with increasing $f^*$ stems from bottom intensification of the pressure in the obstacle lee which is linked to changes in flow separation and near-wake vortices.

physics.flu-dyn↗

arXiv2021

Second Moment Closure Modeling and DNS of Stratified Shear Layers

Buoyant shear layers are encountered in many engineering and environmental applications and have been studied by researchers in the context of experiments and modeling for decades. Often, these flows have high Reynolds and Richardson numbers, and this leads to significant/intractable space-time resolution requirements for DNS or LES modeling. On the other hand, many of the important physical mechanisms in these systems, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based RANS modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number non-stratified and stratified shear layers for which DNS is possible. A range of sub-model complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These sub-models are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds averaged terms, and how well they impact the accuracy of the full RANS closure. For the non-stratified case, the SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux, and variance decay rates, are captured with less accuracy than corresponding flow parameters in the non-stratified case. These studies lead to several recommendations for model improvement.

physics.flu-dyn↗

arXiv2020

Lagrangian study of dispersion and transport by submesoscale currents at an upper-ocean front

The three-dimensional transport pathways, the time scales of vertical transport, and the dispersion characteristics of submesoscale currents at an upper-ocean front are investigated using material points (tracer particles) that advect with the local fluid velocity. Coherent submesoscale vortex filaments and eddies which dominate submesoscale (0.1 - 10 km) dynamics are found to play a crucial role which is quantified here. These coherent structures are generated and sustained through nonlinear evolution of baroclinic instability. The collective motion of particles helps identify common features of transport at the front. It is found that the particles in the central region organize into inclined lobes, each associated with an eddy, and the filaments associated with the heavy- and light-edges of the front transfer edge particles to the lobes. This flux of new particles into the lobe causes local particles to adjust, which leads to slumping of the front. The particle motion in the vertical shows multiple time scales -- a fast time scale with O(10) m vertical displacement within an hour and a slower near-inertial time scale, comparable to the intrinsic time scale of the growing instability. The fast time scale motions typically occur in the vortex filaments. The overall slumping process is slower than what one might anticipate from the large magnitude of vertical velocity in the filaments and requires a sustained correlation over time between the lateral and the vertical motion. By tracking clouds of particles, we show that their centers of mass downwell/upwell over 1-2 inertial time periods, after which an adjustment follows with a sub-inertial time scale. The dispersion characteristics of the submesoscale turbulent currents using single- and pair-particle statistics have been investigated. The shape change in clusters of four particles reveals deformation into thin, needle-like structures.

physics.ao-ph↗

arXiv2020

Spectral POD analysis of the turbulent wake of a disk at Re = 50, 000

The coherent structures in the turbulent wake of a disk at a moderately high Reynolds number ($\Rey$) of $50,000$ are examined using spectral proper orthogonal decomposition (SPOD) which considers all three velocity components in a numerical database. The SPOD eigenvalues at a given streamwise ($x$) location are functions of azimuthal wavenumber ($m$), frequency ($\Str$), and SPOD index ($n$). By $x/D =10$, two specific modes dominate the fluctuation energy: (i) the vortex shedding (VS) mode with $m=1, \Str =0.135, n=1$, and (ii) the double helix (DH) mode with $m=2, \Str \rightarrow 0, n=1$. The VS mode is more energetic than the DH mode in the near wake but, in the far wake, it is the DH mode which is dominant. The DH mode, when scaled with local turbulent velocity and length scales, shows self-similarity in eigenvalues and eigenmodes while the VS mode, which is a global mode, does not exhibit strict self-similarity. Modes $m = 0$, 3 and 4, although subdominant, also make a significant net contribution to the fluctuation energy, and their eigenspectra are evaluated. The reconstruction of TKE and Reynolds shear stress, $\langle u'_{x} u'_{r} \rangle$, is evaluated by varying $(m,\Str,n)$ combinations. Higher SPOD modes contribute significantly to the TKE, especially near the centerline. In contrast, reconstruction of $\langle u'_{x}u'_{r}\rangle $ requires far fewer modes: $|m| \leq 4 $, $|\Str| \leq 1$ and $n \leq 3$. Among azimuthal modes, $m=1$ and $2$ are the leading contributors to both TKE and $\langle u'_{x}u'_{r} \rangle $. While $m=1$ captures the slope of the shear-stress profile near the centerline, $m=2$ is important to capture $\langle u'_{x}u'_{r} \rangle $ at and near its peak. SPOD is also performed in the vicinity of the disk to describe the modal transition to the principal contributors in the wake.

physics.flu-dyn↗

arXiv2019

The submesoscale, the finescale and their interaction at a mixed layer front

The spindown of a geostrophically balanced density front in an upper-ocean mixed layer is simulated with a large eddy simulation (LES) model that resolves O(1000) m down to O(1) m scale. Our goal is to examine the interaction between the submesoscale and the turbulent finescale, and better characterize vertical transport, frontogenesis and dissipative processes. The flow passes through symmetric and baroclinic instabilities, spawns vortex filaments of O(100) m thickness as well as larger eddies, and develops turbulence that is spatially localized and organized. A O(100) m physical-space filter is applied to the simulated flow to separate the coherent submesoscale from the finescale in a decomposition that preserves their spatial organization unlike the typical practice of along-front averaging. Analysis of the submesoscale vertical velocity (as large as 5 mm/s) reveals that downwelling is limited to the thin vortex filaments while upwelling occurs over spatially extensive regions in the eddies, resulting in an overall buoyancy flux that is restratifying. The kinetic energy (KE) transport equations are evaluated separately at both the scales to understand energy pathways in this problem. The buoyancy flux associated with coherent motions acts as the primary source of submesoscale KE which is then transported across the front with a fraction transferred to the finescale. The transfer, limited to thin regions of O(100) m horizontal width, is accomplished by primarily horizontal strain in the upper 10 m and by vertical shear in the rest of the 50 m deep mixed layer. Frontogenetic mechanisms are diagnosed through analysis of the transport equation for squared buoyancy gradient. Horizontal strain is the primary frontogenetic term and is counteracted primarily by horizontal diffusion in the top 10 m and by the horizontal gradient of vertical velocity further below.

physics.ao-ph↗