---
title: Vertical Velocity Anomaly (VVA)
url: https://www.emergentmind.com/topics/vertical-velocity-anomaly-vva
type: topic
---

# Vertical Velocity Anomaly (VVA)

Vertical velocity anomaly (VVA) is a context-dependent term for a physically significant departure in vertical motion from an adopted reference state. In Galactic dynamics, the term has been used for a localized perturbation in the mean stellar vertical velocity $\langle V_z\rangle$ and was reported as a coherent dip of $\simeq 7\,\mathrm{km\,s^{-1}}$ in the Milky Way disk near $(\ell,b,D)\simeq(15.8^\circ,-0.5^\circ,3.9$–$4.0\,\mathrm{kpc})$ [2508.19643]. In other literatures, the same label is applied to heavy-tailed wall-normal fluctuations in turbulent wall flows, subsurface supergranular upflows in helioseismology, residuals between measured and quasigeostrophic predictions in laboratory vortices, departures from climatological oceanic vertical velocity, and statistically extreme drafts in the mesosphere and lower thermosphere [2606.21046] [1209.6147] [2512.17324] [2509.21477] [2512.09612]. The term therefore denotes a family of anomaly diagnostics rather than a single invariant observable.

## 1. Terminological scope and operational definitions

Across the cited literature, VVA is defined operationally rather than universally. The reference state may be a local spatial background, an axisymmetric Galactic model, a climatological mean, a model-predicted field, or Gaussian reference statistics. This variation is not incidental: it reflects different inferential goals, including detection of perturbers, diagnosis of intermittency, and quantification of model deficiency.

| Domain | Operational definition | Representative paper |
|---|---|---|
| Galactic disk | Localized region where mean stellar vertical velocity differs significantly from the surrounding disk | [2508.19643] |
| Solar-neighbourhood Milky Way mapping | $\delta V_z(R,\phi,z)\equiv\langle V_z\rangle(R,\phi,z)-\langle V_z\rangle_{\rm axisym}(R,z)$ | [2207.03492] |
| Wall turbulence | $FF_w\equiv \langle w'^4\rangle/\sigma_w^4$, with $FF_w>3$ measuring heavy tails or intermittency | [2606.21046] |
| Solar supergranulation | Deviation of $v_z$ from zero mean, typically upflow at the cell center and downflow near cell boundaries | [1209.6147] |
| Quasigeostrophic vortices | $\mathrm{VVA}(x,y,z)\equiv w_{\rm meas}(x,y,z)-w_{\rm pred}(x,y,z)$ | [2512.17324] |
| Ocean reconstruction | $\mathrm{VVA}(x,y,z,t)=w(x,y,z,t)-\overline{w}(z)$ | [2509.21477] |
| MLT rogue drafts | Extreme events with $|w|\ge 12.5\,\mathrm{m/s}$ and anomaly parameter $A\ge 5$ | [2512.09612] |

A common source of ambiguity is that the same acronym may refer either to a field variable itself, to a residual after subtraction of a reference model, or to a higher-order statistic of fluctuations. In the Galactic-disk discovery paper, VVA denotes a localized kinematic feature in stars [2508.19643]. In Banerjee et al., by contrast, VVA is identified with intermittency in the flatness factor of wall-normal velocity fluctuations [2606.21046].

## 2. Localized stellar VVA in the Milky Way disk

In the Galactic-disk usage of Udagawa et al., a vertical velocity anomaly is defined as a localized region in which the mean vertical velocity of stars differs significantly—by several $\mathrm{km\,s^{-1}}$—from that in the immediately surrounding disk [2508.19643]. The reported anomaly is a coherent dip in $\langle V_z\rangle$ of $\simeq 7\,\mathrm{km\,s^{-1}}$ over a region $\sim 200\,\mathrm{pc}\times 50\,\mathrm{pc}$ in the outer disk near $\ell\sim 16^\circ$, $b\sim -0.5^\circ$, and $D\sim 3.9$–$4.0\,\mathrm{kpc}$ [2508.19643]. Prior to this result, large-scale vertical kinematic disturbances in the Milky Way disk had chiefly been discussed in connection with massive perturbers such as the Sagittarius dwarf spheroidal galaxy, which produce global warps, corrugations, or breathing modes. The reported VVA differs by being highly localized both spatially and kinematically [2508.19643].

The measurement used Gaia DR2 positions, parallaxes, and proper motions. Radial velocities were available for a subset but were not used in the principal VVA measurement; the analysis relied on transverse motions [2508.19643]. Starting from Galactic latitude $b$, longitude $\ell$, parallax $\varpi$, and proper motion $\mu_b$, the vertical component was written as
$$
V_z = 4.74047\,\bigl(\mu_b\,[\mathrm{mas\,yr^{-1}}]\bigr)\,\bigl(d\,[\mathrm{kpc}]\bigr) + v_{\rm rad}\,[\mathrm{km\,s^{-1}}]\sin b,
$$
with $d=1/\varpi$ and $k=4.74047$ converting $\mathrm{mas\,yr^{-1}}$ at $1\,\mathrm{kpc}$ to $\mathrm{km\,s^{-1}}$ [2508.19643]. In this study, the $\mu_b d$ term dominated, and the $v_{\rm rad}\sin b$ contribution was omitted because radial-velocity coverage was incomplete.

To isolate noncircular motions, the systemic LSR transverse velocity $V_t(\ell,D_p)$ was subtracted from the longitudinal velocity $V_\ell$, with $D_p=(1/\varpi)\cos b$, $R_0=8.27\,\mathrm{kpc}$, $\Theta_0=248\,\mathrm{km\,s^{-1}}$, and $\Theta(R)=\Theta_0(R/R_0)^\alpha$ for $\alpha=0.05$ [2508.19643]. Stars in the region $+13^\circ\le \ell\le +20^\circ$, $-8^\circ\le b\le +5^\circ$, $3.5\le D\le 4.5\,\mathrm{kpc}$ were gridded into voxels of size $0.25^\circ\times 0.25^\circ\times 0.1\,\mathrm{kpc}$; within each voxel the median $V_b$ was computed, and voxels containing fewer than five stars were discarded [2508.19643]. A one-sample z-test comparing the candidate region to an adjacent background yielded $z\simeq 6$, corresponding to a $6\sigma$ detection [2508.19643].

The anomaly is centered at $(\ell,b,D)\simeq(15.8^\circ,-0.5^\circ,3.9$–$4.0\,\mathrm{kpc})$ and is therefore a small-scale perturbation embedded within the broader vertical-kinematic structure of the Galactic disk [2508.19643]. This localization is central to its interpretation: it is not a manifestation of the known large-scale warp or solar-neighbourhood bending signatures, but a compact disturbance co-located with specific gaseous features.

## 3. Association with gaseous disturbances and dark-subhalo interpretation

The stellar VVA reported in the Milky Way disk is spatially coincident with a suite of gaseous disturbances previously interpreted as signatures of a dark matter subhalo collision [2508.19643]. The anomaly lies at the root of an H I filament seen in the HI4PI survey: a narrow, vertical feature $\sim 4^\circ$ long in $b$ and spanning LSR velocities $40$–$120\,\mathrm{km\,s^{-1}}$, with a central void of diameter $\simeq 1^\circ$ [2508.19643]. A molecular shell, the CO $J=1$–$0$ feature “CO 16.134–0.553,” of radius $\simeq 7\,\mathrm{pc}$ and velocity width $\simeq 30\,\mathrm{km\,s^{-1}}$ forms the eastern edge of the H I void [2508.19643]. In the paper’s overlays, the stellar $V_b$ map shows near-perfect positional coincidence between the VVA, the H I void, the CO shell, and the H I filament [2508.19643].

The proposed dynamical origin is an ultra-compact dwarf (UCD)-sized dark matter subhalo plunging through the disk at $V_{\rm pl}\simeq 130\,\mathrm{km\,s^{-1}}$ [2508.19643]. Under the impulse approximation for a point-mass perturber of mass $M$ and impact parameter $b$, the velocity kick is
$$
|\Delta v|\approx \frac{2GM}{b\,V_{\rm pl}}.
$$
Two mass constraints were given. A tidal-stability criterion,
$$
\frac{G\,M_{\rm DMSH}}{r_{\rm DMSH}^2}\gtrsim \frac{G\,M_{\rm gal}(R)\,r_{\rm DMSH}}{R^3},
$$
implies $M_{\rm DMSH}\gtrsim 6\times 10^3\,M_\odot$ for $R=4.6\,\mathrm{kpc}$ and $r_{\rm DMSH}=25\,\mathrm{pc}$ [2508.19643]. A second estimate based on the Hoyle–Lyttleton radius,
$$
r_{\rm HL}=\frac{2GM_{\rm DMSH}}{V_{\rm pl}^2}\simeq r_{\rm DMSH},
$$
yields $M_{\rm DMSH}\sim 5\times 10^7\,M_\odot$ for $V_{\rm pl}=130\,\mathrm{km\,s^{-1}}$ and $r_{\rm DMSH}=25\,\mathrm{pc}$ [2508.19643]. The absence of a luminous source at the filament’s terminus was therefore interpreted as evidence for a dark or failed UCD [2508.19643].

Within the paper’s cosmological framing, a dark subhalo of $\sim 10^7$–$10^8\,M_\odot$ is fully consistent with $\Lambda$CDM expectations for the subhalo mass function around Milky-Way-mass halos, $dN/dM\propto M^{-\alpha}$ with $\alpha\sim 1.9$ [2508.19643]. The cited theoretical context includes high-resolution N-body simulations predicting $\sim 10^2$–$10^3$ subhalos in the mass range $10^7$–$10^8\,M_\odot$ within a Milky-Way-type virial radius [2508.19643]. In that sense, the reported VVA is presented as one of the very few direct dynamical detections at this low-mass scale.

## 4. Related astrophysical usages: Galactic mapping and helioseismology

A distinct Galactic usage appears in large-area stellar-disk mapping with Gaia DR3 and StarHorse distances, where the anomaly is defined as
$$
\delta V_z(R,\phi,z)\equiv \langle V_z\rangle(R,\phi,z)-\langle V_z\rangle_{\rm axisym}(R,z).
$$
In the absence of bulk vertical streaming, $\langle V_z\rangle_{\rm axisym}(R,z)=0$, so $\delta V_z$ is the measured $\langle V_z\rangle$ after subtraction of the Sun’s reflex motion, taken as $+7.25\,\mathrm{km\,s^{-1}}$, and any smooth warp-induced gradient [2207.03492]. The analysis used stars with radial-velocity errors $<5\,\mathrm{km\,s^{-1}}$, transformed them into Galactocentric $(R,\phi,z)$ with $R_0=8.2\,\mathrm{kpc}$ and $Z_0=15\,\mathrm{pc}$, and computed $\langle V_z\rangle$ in spatial bins with $\Delta X=\Delta Y=100\,\mathrm{pc}$ and variable $\Delta Z$, requiring $N_i\ge 100$ effective stars per cell [2207.03492]. Two coherent anomalies emerged across all four magnitude bins: a Local-Spiral-Arm breathing mode centered near $(X,Y)\approx(-0.3,0.8)\,\mathrm{kpc}$ with peak $\delta V_z\simeq 3.0\pm 0.3\,\mathrm{km\,s^{-1}}$, peak $\delta n/n\simeq 0.40\pm 0.05$, wavelength $\lambda\simeq 1.0\pm 0.1\,\mathrm{kpc}$, and a $\pi/2$ phase shift between density and vertical motion; and a large-scale radial-gradient mode at $|z|>300\,\mathrm{pc}$ with $\beta\simeq (0.5\pm 0.1)\,\mathrm{km\,s^{-1}\,kpc^{-1}}$ in $\delta V_z$ and $\gamma\simeq (0.10\pm 0.02)\,\mathrm{kpc^{-1}}$ in density asymmetry [2207.03492]. Relative to the localized VVA of Udagawa et al., these are extended perturbative modes rather than a compact impact signature.

In helioseismology, the term denotes anomalous vertical plasma flow beneath an average solar supergranule rather than a stellar-kinematic perturbation in the Milky Way [1209.6147]. Using HMI Dopplergrams, finite-frequency kernels under the Born approximation, and SOLA inversion, Švanda constructed an average over $5\,582$ independent supergranules [1209.6147]. The inversion targeted $v_z(r_0,z_0)$ through a weighted combination of travel-time measurements,
$$
v_z^{\rm inv}(r_0,z_0)=\sum_i w_i(r_0,z_0)\,\delta \tau_i,
$$
with trade-off parameters controlling localization, noise, and cross-talk [1209.6147]. A good-localisation solution with single-supergranule noise of $\sim 100\,\mathrm{m\,s^{-1}}$ was combined with statistical averaging, reducing the random-noise level by $\sqrt{5582}\simeq 76$ and yielding an uncertainty $<2\,\mathrm{m\,s^{-1}}$ in the final average [1209.6147]. The resulting VVA peaked at
$$
v_z(0,z=1.2\,\mathrm{Mm}) = 117\pm 2\,\mathrm{m\,s^{-1}},
$$
with root-mean-square vertical velocity $\simeq 21\,\mathrm{m\,s^{-1}}$ over a cell radius $R_{\rm cell}\simeq 15\,\mathrm{Mm}$, whereas averaged line-of-sight Dopplergrams gave a photospheric upflow of only $\simeq 12\pm 1\,\mathrm{m\,s^{-1}}$ [1209.6147]. The discrepancy was interpreted as evidence that supergranular upflows are concentrated in a narrow subsurface layer and are smeared out by inversions that favor low noise over localization [1209.6147].

## 5. Fluid-dynamical, oceanic, and atmospheric formulations

In high-Reynolds-number wall turbulence, Banerjee et al. quantify VVA by the flatness factor of wall-normal velocity fluctuations,
$$
FF_w\equiv \frac{\langle w'^4\rangle}{\sigma_w^4},
$$
with $FF_w>3$ indicating heavy tails and large-scale intermittency [2606.21046]. Starting from the wall-normal Navier–Stokes fluctuation equation, they argue that in the inertial sublayer the dominant balance is between the pure-inertial divergence of the fifth moment and the pressure–velocity interaction, while the mixed term $\langle w'^3\rangle\,\partial \sigma_w^2/\partial z$ is negligible [2606.21046]. Using an extended Rotta closure, a quasi-Gaussian approximation, and a macro-scale choice $l_0=\tau \sigma_w$, they derive
$$
FF_w = \frac{4}{1+\alpha_I}\left[\frac{1}{A_w^4}+\frac{A_u^2+A_v^2}{2A_w^2}\right],
$$
where $A_i^2\equiv \sigma_i^2/u_*^2$ and $\alpha_I\equiv 6B_L/C_R$ [2606.21046]. Empirically, thirteen laboratory experiments spanning $Re_\tau\approx 331$–$13\,683$ and five near-neutral atmospheric surface-layer sites collapsed to a nearly constant plateau $FF_w\approx 3.3$ for $100\lesssim z^+\lesssim Re_\tau$, with field and lab inversions clustering around $\alpha_I\approx 3$ [2606.21046]. In this literature, the anomaly is a fourth-order intermittency diagnostic rather than a mean-velocity perturbation.

In quasigeostrophic laboratory vortices, the anomaly is defined pointwise as the discrepancy between measured and predicted vertical velocity:
$$
\mathrm{VVA}(x,y,z)\equiv w_{\rm meas}(x,y,z)-w_{\rm pred}(x,y,z).
$$
The classical QG $\omega$-equation predicted peak values $w_{\rm pred}\simeq \pm 2\times 10^{-5}\,\mathrm{m\,s^{-1}}$ ($\approx \pm 20\,\mu\mathrm{m/s}$) for a Gaussian vortex with $r_m=2\,\mathrm{cm}$, $f=2\,\mathrm{s^{-1}}$, and $Ro=-0.3$, with multipolar lobes concentrated at the vortex periphery [2512.17324]. However, independent measurements from horizontal-divergence integration and particle residence times both gave $|w_{\rm meas}|\approx 100\,\mu\mathrm{m/s}$, about five times larger [2512.17324]. The extended $\omega$-equation,
$$
N^2 \nabla_h^2 w + f^2\frac{\partial^2 w}{\partial z^2}
=
2\frac{g}{\rho_0}\nabla_h\!\cdot\!(\nabla_h u_g\cdot \nabla_h \rho)
+\frac{g}{\rho_0}(\nu-\kappa)\nabla^2\nabla_h^2\rho,
$$
was then used to test whether viscous and scalar diffusion could account for part of the missing vertical motion [2512.17324].

A different oceanographic usage appears in the VISION reconstruction framework, where the anomaly is defined relative to a climatological mean:
$$
\mathrm{VVA}(x,y,z,t)=w(x,y,z,t)-\overline{w}(z).
$$
Here the target field is low-pass-filtered vertical velocity $\tilde w(t,z,x,y)$ from the KD48 benchmark, a $1/48^\circ$ regional Kuroshio Extension subset of LLC4320 MITgcm with hourly snapshots over $366$ days and surface variables SSH, buoyancy, and zonal and meridional surface velocities [2509.21477]. VISION uses a Dynamic Prompting paradigm with an availability mask, a Universal Observation Adapter, a State-conditioned Prompting module, and geometry- and scale-aware operators, and is trained with smooth-$L_1$ loss on a denoised target $w^*$ [2509.21477]. On the reported benchmark, VISION achieved RMSE values of $5.519$, $10.34$, and $13.35$ (all $\times 10^{-5}$) at depths $20$, $40$, and $60$, with corresponding PCC values $0.667$, $0.634$, and $0.549$ [2509.21477]. In this framework, VVA is the reconstructed instantaneous departure from a depth-dependent climatological mean.

In a steady linear $n$-layer atmospheric model on an $f$-plane, the relevant anomaly concept concerns the vertical structure of $\omega$ profiles. The model admits free modes satisfying
$$
A\,\boldsymbol v_m = k_m^2\,\boldsymbol v_m,
$$
whose vertical structures resemble the first and second baroclinic modes [2509.15166]. In the standard parameter regime, the first-baroclinic mode has a characteristic horizontal scale of $\sim 1500\,\mathrm{km}$ and the second-baroclinic mode a smaller scale of $\sim 250\,\mathrm{km}$ [2509.15166]. Strong-gradient surface-temperature forcing projects strongly onto the second mode and yields bottom-heavy $\omega$ profiles, whereas weak-gradient forcing projects strongly onto the first mode and yields top-heavy profiles [2509.15166]. In that usage, “vertical velocity anomalies” refer to top- and bottom-heavy variants of tropical atmospheric ascent rather than local residuals with respect to a background field.

## 6. Extreme drafts in the mesosphere and lower thermosphere, and recurrent conceptual issues

In the mesosphere and lower thermosphere (MLT), VVA is identified with “Rogue Vertical Drafts” (RVDs), defined by two simultaneous criteria: $|w|\ge 12.5\,\mathrm{m/s}$ and exceedance of five standard deviations of the local vertical-velocity distribution [2512.09612]. The anomaly parameter is
$$
A=\frac{|w|-\mu_w}{\sigma_w},
$$
so rogue events satisfy $A\ge 5$ [2512.09612]. In multi-year summer observations over Northern Norway, the vertical-velocity distribution was approximated by a Gaussian with $\mu_w\approx 0\,\mathrm{m/s}$ and $\sigma_w\approx 2.6\,\mathrm{m/s}$, giving a five-sigma threshold of about $13\,\mathrm{m/s}$ [2512.09612]. Assuming independent samples every $100\,\mathrm{s}$, the expected waiting time between extreme events is modified by the fact that RVDs typically span $\sim 1000\,\mathrm{s}$ of consecutive samples, yielding an average recurrence of about one event every $12$ days in summer over Northern Norway [2512.09612]. Volumetric radar imaging further indicates varicose updraft–downdraft pairs with vertical extent $2$–$5\,\mathrm{km}$, horizontal widths $1$–$3\,\mathrm{km}$, occasional elongation to $\sim 10\,\mathrm{km}$, and durations from a few minutes to tens of minutes [2512.09612].

The broader literature reveals several recurring issues. First, the anomaly baseline is field-specific: local background in the Galactic-disk impact candidate [2508.19643], axisymmetric symmetry assumptions in Gaia DR3 disk mapping [2207.03492], zero mean in supergranular inversions [1209.6147], model-predicted $w$ in quasigeostrophic vortices [2512.17324], climatology in data-driven ocean reconstruction [2509.21477], and Gaussian reference statistics in MLT extremes [2512.09612]. Second, multiple papers frame VVA through model–data mismatch. In wall turbulence, a down-gradient closure predicts $FF_w\approx 0$ when skewness is constant and therefore fails to reproduce the observed inertial-sublayer plateau, whereas the extended Rotta–QGA approach recovers $FF_w>3$ and the observed weak decline and outer-layer upturn [2606.21046]. In quasigeostrophic vortices, the classical $\omega$-equation underestimates measured vertical velocity by a factor of about five, motivating inclusion of dissipative terms [2512.17324]. In helioseismology, the tension is between a subsurface updraft of $117\pm 2\,\mathrm{m\,s^{-1}}$ and a photospheric signal of only $\simeq 12\pm 1\,\mathrm{m\,s^{-1}}$, attributed to localization–noise trade-offs in inversion kernels [1209.6147].

A plausible implication is that “vertical velocity anomaly” is best understood as a methodological category for statistically or dynamically exceptional vertical motion, with the exact quantity determined by the governing equations, measurement geometry, and null model of the field under study. In Galactic dynamics, the term currently has particular prominence because the localized Milky Way VVA has been interpreted as rare observational evidence for a low-mass dark matter subhalo or dark, ultra-compact dwarf-sized intruder, linking stellar kinematics, gas morphology, and $\Lambda$CDM substructure directly [2508.19643].

Source: https://www.emergentmind.com/topics/vertical-velocity-anomaly-vva